{"id": "dm-algebra__linear_1d_composed-hard-0", "pool": "math", "split": "train", "question": "Let z(l) = 7*l + 10. Let h be z(-1). Let t(a) = 8 - a. Let q be t(h). Let w = 2 + 3. Solve -5 = q*n + w for n.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-1"}}
{"id": "dm-algebra__linear_1d_composed-hard-1", "pool": "math", "split": "train", "question": "Let i(a) = -a**2 - 137*a - 1014. Let q be i(-8). Solve q*y - 43 = -25*y for y.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-2"}}
{"id": "dm-algebra__linear_1d_composed-hard-2", "pool": "math", "split": "train", "question": "Suppose -8*y = -27*y - 190. Let w = -10 - y. Solve -5*b + 10 = -w*b for b.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-3"}}
{"id": "dm-algebra__linear_1d_composed-hard-3", "pool": "math", "split": "train", "question": "Suppose k - 261 = -4*a, 890 = 4*k - a - 120. Suppose -43*g - 38 = -k. Solve 2*u - 15 = -g for u.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-4"}}
{"id": "dm-algebra__linear_1d_composed-hard-4", "pool": "math", "split": "train", "question": "Let t be 17/4 - 105/(-140). Let d(l) = -6*l**2 + 30*l + 4. Let x be d(t). Let o = -23 - -28. Solve o*u = -14 + x for u.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-5"}}
{"id": "dm-algebra__linear_1d_composed-hard-5", "pool": "math", "split": "train", "question": "Let d = 5866 - 5840. Solve 103 = d*c - 27 for c.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-6"}}
{"id": "dm-algebra__linear_1d_composed-hard-6", "pool": "math", "split": "train", "question": "Suppose -2*w - 3*y + 1083 = -5*w, -5*w - 1781 = 3*y. Let j = w - -358. Solve j = -3*c + 4*c for c.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-7"}}
{"id": "dm-algebra__linear_1d_composed-hard-7", "pool": "math", "split": "train", "question": "Suppose -13*a = -24*a + 1870. Let d = a - 135. Suppose -5*l = 2*c + 17, -3*l = -5*c - 0*c + d. Solve 9*t - 15 = c*t for t.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-8"}}
{"id": "dm-algebra__linear_1d_composed-hard-8", "pool": "math", "split": "train", "question": "Let g(i) = 27 + 59 - 65 + 10*i. Let r be g(5). Let u = 71 - r. Solve u = 2*s - 0*s - 6 for s.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-9"}}
{"id": "dm-algebra__linear_1d_composed-hard-9", "pool": "math", "split": "train", "question": "Let j be 6/10 - ((-176)/40 - -5). Suppose -24*h + 36*h - 24 = j. Solve 4*f = -6 + h for f.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-10"}}
{"id": "dm-algebra__linear_1d_composed-hard-10", "pool": "math", "split": "train", "question": "Suppose -2 = -2*z, -4*u - 2*z + 57 = u. Let q(x) = u*x - 125*x**2 - 12 + 7*x - 3*x + 124*x**2. Let n be q(14). Solve 0 = -b + n*b - 3 for b.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-11"}}
{"id": "dm-algebra__linear_1d_composed-hard-11", "pool": "math", "split": "train", "question": "Let k = -12969 - -13011. Solve 0 = -16*l + 30*l + k for l.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-12"}}
{"id": "dm-algebra__linear_1d_composed-hard-12", "pool": "math", "split": "train", "question": "Let v = -6249 - -6249. Solve v = -45*n + 63*n + 162 for n.", "unit": "dimensionless", "value": "-9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-13"}}
{"id": "dm-algebra__linear_1d_composed-hard-13", "pool": "math", "split": "train", "question": "Let v(a) = a**2 - 25*a + 185. Let y be v(20). Solve -y*b + 171 = -28*b for b.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-14"}}
{"id": "dm-algebra__linear_1d_composed-hard-14", "pool": "math", "split": "train", "question": "Let u(m) = 36 - m. Suppose -n = 3*d - 3, -4*d = -4*n + 76 - 16. Let w be u(n). Let z = 26 - w. Solve z*v - 12 = -v for v.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-15"}}
{"id": "dm-algebra__linear_1d_composed-hard-15", "pool": "math", "split": "train", "question": "Let g be (125/(-75))/(10/(-1104)). Solve -189*b = -g*b + 15 for b.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-16"}}
{"id": "dm-algebra__linear_1d_composed-hard-16", "pool": "math", "split": "train", "question": "Suppose 5*h + 60*h - 2015 = 0. Solve 7*d + h*d = 22*d for d.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-17"}}
{"id": "dm-algebra__linear_1d_composed-hard-17", "pool": "math", "split": "train", "question": "Suppose 17*x = 9*x + 80. Let r = -3 + 8. Let n = 91 - 86. Solve -n*s = -x + r for s.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-18"}}
{"id": "dm-algebra__linear_1d_composed-hard-18", "pool": "math", "split": "train", "question": "Let c be (-14807)/(-136) + (-8)/(-64). Solve 101*x - c*x - 32 = 0 for x.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-19"}}
{"id": "dm-algebra__linear_1d_composed-hard-19", "pool": "math", "split": "train", "question": "Let g = -183 + 185. Let h(a) = -a**3 + 13*a**2 + 12*a + 33. Let t be h(14). Solve g*s = -1 + t for s.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-20"}}
{"id": "dm-algebra__linear_1d_composed-hard-20", "pool": "math", "split": "train", "question": "Let s(u) = u + 5. Let t(g) = 6*g + 107. Let w be t(-18). Let d be s(w). Let k = 6 + 2. Solve 16 = d*a - k*a for a.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-21"}}
{"id": "dm-algebra__linear_1d_composed-hard-21", "pool": "math", "split": "train", "question": "Suppose 0 = -3*y - 0 + 6. Suppose 3*o - 60 = -y*a - o, -5*a + 220 = -4*o. Suppose -2*v - 6*v + a = 0. Solve -v*z = -z + 16 for z.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-22"}}
{"id": "dm-algebra__linear_1d_composed-hard-22", "pool": "math", "split": "train", "question": "Let t(j) be the third derivative of -1/3*j**3 + 0*j - 1/4*j**4 + 0 + 15*j**2. Let k be t(-2). Solve 0 = 5*n + k for n.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-23"}}
{"id": "dm-algebra__linear_1d_composed-hard-23", "pool": "math", "split": "train", "question": "Let g(p) = -p - 1. Let z be g(-6). Let m(q) = -q**2 - 6*q + 5. Let i be m(-6). Let j(u) = 3*u**2 + 103*u - 198. Let n be j(2). Solve -z*h + i = -n for h.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-24"}}
{"id": "dm-algebra__linear_1d_composed-hard-24", "pool": "math", "split": "train", "question": "Let m(c) = 3*c**3 + c - 1. Suppose 6 = 4*v - l - 0, -5*l = v + 9. Let x be m(v). Solve -x - 2 = p for p.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-25"}}
{"id": "dm-algebra__linear_1d_composed-hard-25", "pool": "math", "split": "train", "question": "Suppose 4*u + 5*v - 22 = 0, -u - 2*u - 4*v + 17 = 0. Let p = -1269 - -1270. Let z be 1/p - u*(-5)/15. Solve -i = -z*i - 2 for i.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-26"}}
{"id": "dm-algebra__linear_1d_composed-hard-26", "pool": "math", "split": "train", "question": "Let j = -5034 - -5050. Solve 0 = j*p + 96 for p.", "unit": "dimensionless", "value": "-6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-27"}}
{"id": "dm-algebra__linear_1d_composed-hard-27", "pool": "math", "split": "train", "question": "Let u(n) be the second derivative of 5*n**4/12 - n**3 - n**2 + 2*n - 4. Let t be u(2). Solve 0 = -2*w + 4 - t for w.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-28"}}
{"id": "dm-algebra__linear_1d_composed-hard-28", "pool": "math", "split": "train", "question": "Let l be 45/(-5) + (24 - (-99)/(-9)). Solve l*r - 11 = -43 for r.", "unit": "dimensionless", "value": "-8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-29"}}
{"id": "dm-algebra__linear_1d_composed-hard-29", "pool": "math", "split": "train", "question": "Let q = 488 - 401. Solve -23*k - q = 28 for k.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-30"}}
{"id": "dm-algebra__linear_1d_composed-hard-30", "pool": "math", "split": "train", "question": "Let s(i) = 2*i**3 + 12*i**2 - 6*i - 8. Let l(v) be the third derivative of -v**5/60 + 5*v**4/24 + 4*v**3/3 + v**2. Let f be l(7). Let g be s(f). Solve -3 = -5*q - g for q.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-31"}}
{"id": "dm-algebra__linear_1d_composed-hard-31", "pool": "math", "split": "train", "question": "Suppose 4*w + 10 = 5*w. Let p(g) = 13 - 4 - 4 - g**2 - 3 + w*g. Let n be p(10). Solve -10 = n*x - 0*x for x.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-32"}}
{"id": "dm-algebra__linear_1d_composed-hard-32", "pool": "math", "split": "train", "question": "Let y be (2 - (-36)/(-10))/(1/(-5)). Let f = 499 - 499. Suppose 5*v - 6 = 19. Solve f = -b + v*b - y for b.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-33"}}
{"id": "dm-algebra__linear_1d_composed-hard-33", "pool": "math", "split": "train", "question": "Suppose -48 = -5*o + 2*f - 4, 0 = 5*o - 5*f - 65. Solve 0 = o*x + 12*x + 36 for x.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-34"}}
{"id": "dm-algebra__linear_1d_composed-hard-34", "pool": "math", "split": "train", "question": "Let r(s) = s + 6. Let n be r(-4). Let u be 37 + -2 + (-9 - -4). Let c = u + -28. Solve n*t + c - 6 = 0 for t.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-35"}}
{"id": "dm-algebra__linear_1d_composed-hard-35", "pool": "math", "split": "train", "question": "Let y = 137 + -129. Let b be -4 + 51/12 + 14/y. Suppose b*v + 3*u = 10, -4*u - 19 = -v - 2*u. Solve v + 1 = 4*o for o.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-36"}}
{"id": "dm-algebra__linear_1d_composed-hard-36", "pool": "math", "split": "train", "question": "Suppose 7*x - 8 = 125. Suppose 2*l = -c + 1, x*c + 13 = 20*c - l. Solve 0*s = -3*s - c for s.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-37"}}
{"id": "dm-algebra__linear_1d_composed-hard-37", "pool": "math", "split": "train", "question": "Let y be -5*(0 - -1 - (-13)/(-65)). Let i be 8/(-14)*(-1 - (-10)/y). Suppose 0 = -j - 0*h - 2*h, -3 = -i*j - h. Solve j*q = -3*q + 10 for q.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-38"}}
{"id": "dm-algebra__linear_1d_composed-hard-38", "pool": "math", "split": "train", "question": "Suppose 3*s + 37 = 3*o + 2*o, 5*s = -o + 13. Let g = -105 - -106. Suppose 0 = 2*j - 2, -m + 2*j = -g. Solve -m*p - 15 = -o*p for p.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-39"}}
{"id": "dm-algebra__linear_1d_composed-hard-39", "pool": "math", "split": "train", "question": "Let z be 6/18 + 39/(-9) + 0. Let c(d) = -d**2 - 8*d - 9. Let o be c(z). Let r = 9 - o. Solve 2*l + r = -4 for l.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-40"}}
{"id": "dm-algebra__linear_1d_composed-hard-40", "pool": "math", "split": "train", "question": "Let g be (26 - 1)/(12/16 - 5/(-20)). Solve 34*z - g*z = -36 for z.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-41"}}
{"id": "dm-algebra__linear_1d_composed-hard-41", "pool": "math", "split": "train", "question": "Suppose -15*s + 636 = 66. Solve -s = 4*b - 42 for b.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-42"}}
{"id": "dm-algebra__linear_1d_composed-hard-42", "pool": "math", "split": "train", "question": "Suppose 239*r - 237*r - p - 144 = 0, -2*p = 3*r - 216. Solve -r*u - 129 = 15 for u.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-43"}}
{"id": "dm-algebra__linear_1d_composed-hard-43", "pool": "math", "split": "train", "question": "Let h(w) = w**2 - 16*w + 2. Let k(z) = -3*z**2 + 69*z - 8. Let y(f) = -4*h(f) - k(f). Let s = 4 - 8. Let x be y(s). Solve x*t = -t + 5 for t.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-44"}}
{"id": "dm-algebra__linear_1d_composed-hard-44", "pool": "math", "split": "train", "question": "Suppose 719*g - 713*g = 18. Suppose 0 = g*j - i + 23 - 105, -4*i = j - 10. Solve -27*r = -j*r - 5 for r.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-45"}}
{"id": "dm-algebra__linear_1d_composed-hard-45", "pool": "math", "split": "train", "question": "Let r(g) = g**3 + 4*g**2 + 8*g + 20. Let b be r(-3). Solve -b*n + 23 = 33 for n.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-46"}}
{"id": "dm-algebra__linear_1d_composed-hard-46", "pool": "math", "split": "train", "question": "Suppose -u + 4*x + x - 2 = 0, -4*x = 5*u + 10. Let f be (-48)/(-10) + (u/(-10) - 0). Suppose -4*q + 16 + 4 = r, r + f*q = 24. Solve r = -0*p - p for p.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-47"}}
{"id": "dm-algebra__linear_1d_composed-hard-47", "pool": "math", "split": "train", "question": "Let w(k) = 4*k**2 - 1. Let d(m) = m - 19. Let s(z) = 19 - 2*z. Let r(x) = -4*d(x) - 3*s(x). Let f be r(-9). Let i be w(f). Solve 0 + 6 = i*y for y.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-48"}}
{"id": "dm-algebra__linear_1d_composed-hard-48", "pool": "math", "split": "train", "question": "Let n = 235 - 238. Let d be (n/8)/(11/(-88)). Solve d*j - 2*j - 3 = 0 for j.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-49"}}
{"id": "dm-algebra__linear_1d_composed-hard-49", "pool": "math", "split": "train", "question": "Suppose 5*k - 4 - 6 = 0. Suppose 0 = -k*p - 2*p - 152. Let b = -31 - p. Solve -b*m - 12 = -3*m for m.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-50"}}
{"id": "dm-algebra__linear_1d_composed-hard-50", "pool": "math", "split": "train", "question": "Let v = -17138 - -17154. Solve -v*p = -218 + 314 for p.", "unit": "dimensionless", "value": "-6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-51"}}
{"id": "dm-algebra__linear_1d_composed-hard-51", "pool": "math", "split": "train", "question": "Suppose 0 = v + 2, 5*v + 106 = 3*a - 48. Suppose -4*u = -0*u - 12, 4*r - 4*u - a = 0. Solve -9*q + 4*q = r for q.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-52"}}
{"id": "dm-algebra__linear_1d_composed-hard-52", "pool": "math", "split": "train", "question": "Suppose 0 = 5*d - 4*d - 3*f - 31, -4*d - 5*f + 73 = 0. Solve d = -4*p + 30 for p.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-53"}}
{"id": "dm-algebra__linear_1d_composed-hard-53", "pool": "math", "split": "train", "question": "Let l be (-2)/5 - 9744/(-35). Let f = l + -277. Solve -3*w + f + 5 = 0 for w.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-54"}}
{"id": "dm-algebra__linear_1d_composed-hard-54", "pool": "math", "split": "train", "question": "Suppose 52 = -3*i + 85. Suppose -i*p + 5*p + 120 = 0. Solve -r - 3*r = p for r.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-55"}}
{"id": "dm-algebra__linear_1d_composed-hard-55", "pool": "math", "split": "train", "question": "Let o = -270 - -406. Let w = o + -128. Solve -w + 2 = 2*p for p.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-56"}}
{"id": "dm-algebra__linear_1d_composed-hard-56", "pool": "math", "split": "train", "question": "Let g(b) be the third derivative of -b**4/12 - 23*b**3/6 - 30*b**2. Let o be g(-16). Solve -d = -5 + o for d.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-57"}}
{"id": "dm-algebra__linear_1d_composed-hard-57", "pool": "math", "split": "train", "question": "Let h be 52/(-39)*(18/(-8))/3. Let d = -180 + 189. Solve d = -4*m + h for m.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-58"}}
{"id": "dm-algebra__linear_1d_composed-hard-58", "pool": "math", "split": "train", "question": "Suppose -5 = 5*h + y, -5*y + 3*y - 10 = -4*h. Suppose h = -3*z - 5*o + 78, -4*z - 27 = -3*o - 102. Solve -23*m - 6 = -z*m for m.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-59"}}
{"id": "dm-algebra__linear_1d_composed-hard-59", "pool": "math", "split": "train", "question": "Suppose 4 = 5*t - 16. Let m(f) be the first derivative of -f**2/2 + 32*f + 56. Let k be m(16). Solve 0 = t*i - 4 + k for i.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-60"}}
{"id": "dm-algebra__linear_1d_composed-hard-60", "pool": "math", "split": "train", "question": "Suppose 9*k - 1320 + 456 = 0. Let r be (6/k*8)/((-2)/(-44)). Let j be (-10)/(-4)*(-16)/(-10). Solve j*n + r - 3 = 0 for n.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-61"}}
{"id": "dm-algebra__linear_1d_composed-hard-61", "pool": "math", "split": "train", "question": "Let x be ((-8)/(-12) - 1)*(-30)/10 + 13. Solve -x*v - 63 = -7 for v.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-62"}}
{"id": "dm-algebra__linear_1d_composed-hard-62", "pool": "math", "split": "train", "question": "Let b(m) = -m**3 + 15*m**2 + 148*m - 12. Let h be b(-7). Solve -32*i + h*i = 0 for i.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-63"}}
{"id": "dm-algebra__linear_1d_composed-hard-63", "pool": "math", "split": "train", "question": "Suppose -707 + 2219 = 63*l. Solve l*y - 9 = -9 for y.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-64"}}
{"id": "dm-algebra__linear_1d_composed-hard-64", "pool": "math", "split": "train", "question": "Let z be -4*7/(-42)*-39. Let m(y) = -2*y**3 - 52*y**2 + 3. Let n be m(z). Solve 0*l = n*l for l.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-65"}}
{"id": "dm-algebra__linear_1d_composed-hard-65", "pool": "math", "split": "train", "question": "Suppose 46*t + 155 - 1228 = 951. Solve -t*g - 36 = 52 for g.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-66"}}
{"id": "dm-algebra__linear_1d_composed-hard-66", "pool": "math", "split": "train", "question": "Let m = -21550 - -21559. Solve 8*a = -m*a + 51 for a.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-67"}}
{"id": "dm-algebra__linear_1d_composed-hard-67", "pool": "math", "split": "train", "question": "Let d(p) = -p**2 - 14*p + 5. Let x be d(-14). Suppose 0 = -x*z + 2*r + 25, -z - 32 = -5*z + 4*r. Solve b = z*b for b.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-68"}}
{"id": "dm-algebra__linear_1d_composed-hard-68", "pool": "math", "split": "train", "question": "Let z(a) = 59*a + 6081. Let x be z(-103). Suppose -c = 2*o - 3*c - 72, -2*o - 5*c + 93 = 0. Solve -7*b + o = x for b.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-69"}}
{"id": "dm-algebra__linear_1d_composed-hard-69", "pool": "math", "split": "train", "question": "Let h be (12/(-9))/((-1)/(-582))*6/(-12). Solve -h*a = -377*a + 33 for a.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-70"}}
{"id": "dm-algebra__linear_1d_composed-hard-70", "pool": "math", "split": "train", "question": "Let b(w) = -w**2 + 3*w + 10. Let u be b(-3). Let f be (18/12)/((-4)/u). Let j be (1 - -1) + (0 - -3). Solve -7 = -f*v + j for v.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-71"}}
{"id": "dm-algebra__linear_1d_composed-hard-71", "pool": "math", "split": "train", "question": "Let f(z) = z**3 - 4*z**2 - 10*z - 7. Let l(v) = -v - 1. Let k(x) = 6*x + 4. Let q(c) = k(c) + 5*l(c). Let h(p) = -f(p) + q(p). Let u be h(6). Solve u*o = 2*o + 10 for o.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-72"}}
{"id": "dm-algebra__linear_1d_composed-hard-72", "pool": "math", "split": "train", "question": "Let v(h) = 66 - 672*h. Let c be v(0). Solve c*y - 69*y = 0 for y.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-73"}}
{"id": "dm-algebra__linear_1d_composed-hard-73", "pool": "math", "split": "train", "question": "Let x(t) = t**3 + 9*t**2 - 22*t - 13. Let o be x(3). Solve 3*m - o*m - 104 = 0 for m.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-74"}}
{"id": "dm-algebra__linear_1d_composed-hard-74", "pool": "math", "split": "train", "question": "Let t be (14/(-21))/((-6)/(-4437)). Let w = -489 - t. Solve -5*k + 36 = w*k for k.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-75"}}
{"id": "dm-algebra__linear_1d_composed-hard-75", "pool": "math", "split": "train", "question": "Let w(z) = 19*z**2 - 4*z - 2. Let j be w(-1). Suppose -u - 5*l = 12 - 35, -3*l + j = 3*u. Solve -u*t + 2 = -13 for t.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-76"}}
{"id": "dm-algebra__linear_1d_composed-hard-76", "pool": "math", "split": "train", "question": "Let l = -271 + -84. Let v = l - -356. Solve w + 4 = v for w.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-77"}}
{"id": "dm-algebra__linear_1d_composed-hard-77", "pool": "math", "split": "train", "question": "Let p(h) = -1336*h - 8016. Let m be p(-6). Let o = 123 + -72. Solve 5*d - o + 36 = m for d.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-78"}}
{"id": "dm-algebra__linear_1d_composed-hard-78", "pool": "math", "split": "train", "question": "Let v = -510 - -262. Let x = v - -263. Solve -10 = x*r - 17*r for r.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-79"}}
{"id": "dm-algebra__linear_1d_composed-hard-79", "pool": "math", "split": "train", "question": "Let x = -54 + 98. Let q be x/8 + 1/(-2). Suppose 11*y - 3*j = 6*y + 25, -3*j - 20 = -4*y. Solve -q*g + 0*g - y = 0 for g.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-80"}}
{"id": "dm-algebra__linear_1d_composed-hard-80", "pool": "math", "split": "train", "question": "Let w = 63 + -63. Suppose w = 4*l + 3*s - 15, -s + 20 = 3*l + 3*s. Solve 3*n - 7*n + 8 = l for n.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-81"}}
{"id": "dm-algebra__linear_1d_composed-hard-81", "pool": "math", "split": "train", "question": "Suppose 3*a = -x + 94, -592 = 5*a + x - 752. Solve -a*d + 65 + 34 = 0 for d.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-82"}}
{"id": "dm-algebra__linear_1d_composed-hard-82", "pool": "math", "split": "train", "question": "Let a = 6740 - 3996. Solve -a*r + 2736*r = 16 for r.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-83"}}
{"id": "dm-algebra__linear_1d_composed-hard-83", "pool": "math", "split": "train", "question": "Let p be 4/12 - -14*5/15. Let y be p*1*(-78)/(-39). Solve -y = 3*s + 2 for s.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-84"}}
{"id": "dm-algebra__linear_1d_composed-hard-84", "pool": "math", "split": "train", "question": "Suppose 0 = -0*c + c - 9. Suppose -5*p - 2*z - 2 = -3*p, 5*p = 5*z + 35. Suppose 2*v - 8 = p*o, -45*v = -42*v - 2*o - 12. Solve -v*u = -c*u for u.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-85"}}
{"id": "dm-algebra__linear_1d_composed-hard-85", "pool": "math", "split": "train", "question": "Suppose -67 - 674 = 19*x. Let z be 18/42 + x/(-7). Let q = 12 + -7. Solve q*u - 3*u + z = 0 for u.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-86"}}
{"id": "dm-algebra__linear_1d_composed-hard-86", "pool": "math", "split": "train", "question": "Suppose -13*m + 30 + 269 = 0. Suppose -m*u + 5*u = 7*u. Solve -n = -u*n for n.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-87"}}
{"id": "dm-algebra__linear_1d_composed-hard-87", "pool": "math", "split": "train", "question": "Suppose 0 = 35*m - 605 - 200. Solve 28*h + m = 163 for h.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-88"}}
{"id": "dm-algebra__linear_1d_composed-hard-88", "pool": "math", "split": "train", "question": "Let l(w) = -3*w**3 - 15*w**2 + 2*w - 5. Let i be l(-5). Let t be 20/i*3/(-1). Suppose 0 = 5*g + 3*z + 6, -4*g + t = -z + 2. Solve -4*j = -16 - g for j.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-89"}}
{"id": "dm-algebra__linear_1d_composed-hard-89", "pool": "math", "split": "train", "question": "Let h(s) = -s**3 + 5*s**2 + 20*s - 64. Let p be h(4). Solve 0 = -55*m + p - 252 for m.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-90"}}
{"id": "dm-algebra__linear_1d_composed-hard-90", "pool": "math", "split": "train", "question": "Suppose -29*g - 220 = -33*g - 2*d, 3*g - 166 = -2*d. Suppose 0 = -l + 3*h + 66, l + l - 126 = 4*h. Let b = l - g. Solve 0*v + b*v = -6 for v.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-91"}}
{"id": "dm-algebra__linear_1d_composed-hard-91", "pool": "math", "split": "train", "question": "Suppose 0 = -2*o + h + 4*h + 25, 2*h = -10. Suppose w + 286 = -2*m, -6*m + 270 = -8*m + 3*w. Let x = 145 + m. Solve o = -9*r + x*r - 5 for r.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-92"}}
{"id": "dm-algebra__linear_1d_composed-hard-92", "pool": "math", "split": "train", "question": "Suppose -334 = 5*u + 341. Let i be (5 - u/(-25)) + (-542)/(-5). Suppose 19*l - i = 7*l. Solve 0 = -5*d + l + 6 for d.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-93"}}
{"id": "dm-algebra__linear_1d_composed-hard-93", "pool": "math", "split": "train", "question": "Let t(f) = f**2 + 10*f + 11. Let w be t(-8). Let g(i) = 2*i**2 + 9*i - 2. Let p be g(w). Solve q + p*q = 0 for q.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-94"}}
{"id": "dm-algebra__linear_1d_composed-hard-94", "pool": "math", "split": "train", "question": "Let y be 206/618*(-3 + 12). Solve 60 = -y*a - 27*a for a.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-95"}}
{"id": "dm-algebra__linear_1d_composed-hard-95", "pool": "math", "split": "train", "question": "Let j(q) = -q**2 - 5*q - 4. Let m be j(-4). Let a be (5 - -1)*(-2)/(-6). Let s = -410350 + 410352. Solve -s*x - a*x = m for x.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-96"}}
{"id": "dm-algebra__linear_1d_composed-hard-96", "pool": "math", "split": "train", "question": "Suppose -14*m = -4*m - 520. Suppose m*r = 36*r + 64. Solve -r*d - 12 = -d for d.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-97"}}
{"id": "dm-algebra__linear_1d_composed-hard-97", "pool": "math", "split": "train", "question": "Let l = -375 - -257. Let k = -115 - l. Solve -k*p = -p + 4 for p.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-98"}}
{"id": "dm-algebra__linear_1d_composed-hard-98", "pool": "math", "split": "train", "question": "Suppose -27*f - 2*m + 68 = -22*f, 4 = -f + 4*m. Solve l - f = -10 for l.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-99"}}
{"id": "dm-algebra__linear_1d_composed-hard-99", "pool": "math", "split": "train", "question": "Let u = 2149 - 2146. Solve -31*j = -u - 28 for j.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-100"}}
{"id": "dm-algebra__linear_1d_composed-hard-100", "pool": "math", "split": "train", "question": "Let b(i) = 7*i**2 - 15*i + 49. Let u be b(7). Let p = u - 282. Solve 7*y - p = 12*y for y.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-101"}}
{"id": "dm-algebra__linear_1d_composed-hard-101", "pool": "math", "split": "train", "question": "Let i(o) = o**3 - 30*o**2 + 28*o + 29. Let p(a) = -6*a**3 + 151*a**2 - 139*a - 145. Let b(m) = -11*i(m) - 2*p(m). Let g be b(-29). Suppose 2*l = -3*l + 15. Solve g = -3*x + l for x.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-102"}}
{"id": "dm-algebra__linear_1d_composed-hard-102", "pool": "math", "split": "train", "question": "Suppose 5*g + 5*z = 15, 0*g - 4*g + 16 = 5*z. Let q be 4/6 - (g - 3/9). Suppose -3*j + j - 5*f = -16, -q*j + 3*f = 0. Solve j*w = 5*w + 6 for w.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-103"}}
{"id": "dm-algebra__linear_1d_composed-hard-103", "pool": "math", "split": "train", "question": "Let j(s) = 6*s + 25. Let x be j(-11). Let k = 46 + x. Suppose -2*a + 5 = -k. Solve -2 = -a*r + 18 for r.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-104"}}
{"id": "dm-algebra__linear_1d_composed-hard-104", "pool": "math", "split": "train", "question": "Suppose -4*h = -3*d - 1337, -4*h - 5*d + 1338 = -7*d. Let x = h + -289. Solve -o + 50 - x = 0 for o.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-105"}}
{"id": "dm-algebra__linear_1d_composed-hard-105", "pool": "math", "split": "train", "question": "Let k(b) = 6*b**2 + 192*b + 1188. Let x be k(-6). Solve -6*z - x = -252 for z.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-106"}}
{"id": "dm-algebra__linear_1d_composed-hard-106", "pool": "math", "split": "train", "question": "Let r(q) = 631 - 24*q. Let g be r(19). Solve -165*w = -g*w for w.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-107"}}
{"id": "dm-algebra__linear_1d_composed-hard-107", "pool": "math", "split": "train", "question": "Let q(g) be the first derivative of -2*g**3/3 + 9*g**2/2 + 7*g + 2. Let r be q(7). Let u = r + 29. Solve 0*m = m - u for m.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-108"}}
{"id": "dm-algebra__linear_1d_composed-hard-108", "pool": "math", "split": "train", "question": "Suppose 4*y + 8 = 0, 8*a - 6*a - 3*y = 66. Solve -30*w - 60 = a*w for w.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-109"}}
{"id": "dm-algebra__linear_1d_composed-hard-109", "pool": "math", "split": "train", "question": "Suppose 2312 + 1080 = -8*d. Let n = -424 - d. Solve -2*p - 8*p - 20 = n for p.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-110"}}
{"id": "dm-algebra__linear_1d_composed-hard-110", "pool": "math", "split": "train", "question": "Suppose -28 - 77 = -21*r. Suppose -r*w - x = 2*x - 38, -4*w + x = -44. Solve -5*p + w*p - 20 = 0 for p.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-111"}}
{"id": "dm-algebra__linear_1d_composed-hard-111", "pool": "math", "split": "train", "question": "Let q be 11 + (-17 - (-6 - 167)). Solve 8*a - q = -119 for a.", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-112"}}
{"id": "dm-algebra__linear_1d_composed-hard-112", "pool": "math", "split": "train", "question": "Suppose 5*h = -2*i + 1492, -5*h - 422 = -i - 1926. Solve 0 = 31*t + 548 - h for t.", "unit": "dimensionless", "value": "-8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-113"}}
{"id": "dm-algebra__linear_1d_composed-hard-113", "pool": "math", "split": "train", "question": "Suppose 0 = -n - 3*r - 12, 2*n - 5*r = 8 + 12. Suppose -4*y - 5*w + 0*w = -48, 5*y - 2*w - 27 = n. Solve -y*x = -17 + 3 for x.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-114"}}
{"id": "dm-algebra__linear_1d_composed-hard-114", "pool": "math", "split": "train", "question": "Let o(q) = -2*q + 260 + q - 259. Let x(n) = n**2 + 11*n. Let s(v) = 2*o(v) - x(v). Let i be s(-13). Solve 5*l - 9 = i*l for l.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-115"}}
{"id": "dm-algebra__linear_1d_composed-hard-115", "pool": "math", "split": "train", "question": "Let s(k) = -2*k - 2. Let b be s(-5). Let u(o) = o**3 - 8*o**2 - 3*o + 27. Let i be u(b). Suppose 0 = 4*w - 4*z - 12, 8*w + i*z - 5 = 4*w. Solve w*j = -1 - 1 for j.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-116"}}
{"id": "dm-algebra__linear_1d_composed-hard-116", "pool": "math", "split": "train", "question": "Suppose -51*g - 40*g = 45*g - 5712. Solve -250 = -8*n - g*n for n.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-117"}}
{"id": "dm-algebra__linear_1d_composed-hard-117", "pool": "math", "split": "train", "question": "Let m(k) = -k - 62*k**2 + 2*k**3 + 0*k + 7 + 0*k + 61*k**2. Let b be m(0). Solve 0*h + b*h - 21 = 0 for h.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-118"}}
{"id": "dm-algebra__linear_1d_composed-hard-118", "pool": "math", "split": "train", "question": "Let q be 4*(3 - -3 - 4). Let o = -23 - -27. Suppose 4*j = o*j + 4*j. Solve 0*r - 4*r - q = j for r.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-119"}}
{"id": "dm-algebra__linear_1d_composed-hard-119", "pool": "math", "split": "train", "question": "Suppose 115*k = 116*k - 5*f - 107, 0 = 2*k - f - 151. Solve 924 - 348 = k*a for a.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-120"}}
{"id": "dm-algebra__linear_1d_composed-hard-120", "pool": "math", "split": "train", "question": "Let y(j) = -j**3 + 3*j**2 + 17*j - 16. Let h be y(7). Let x = h + 93. Solve x*t = -4*t for t.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-121"}}
{"id": "dm-algebra__linear_1d_composed-hard-121", "pool": "math", "split": "train", "question": "Suppose 4*s - 36 = -20. Suppose 0 = -s*k - 5 + 145. Solve 2*a - 31 + k = 0 for a.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-122"}}
{"id": "dm-algebra__linear_1d_composed-hard-122", "pool": "math", "split": "train", "question": "Let x be 2/6*0 + 0. Let o = -32 + 42. Suppose 0 = 7*s - o*s + 36. Solve 2*p + 2*p + s = x for p.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-123"}}
{"id": "dm-algebra__linear_1d_composed-hard-123", "pool": "math", "split": "train", "question": "Let i(p) = 744 - 148*p. Let u be i(5). Solve u*v = 35 - 23 for v.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-124"}}
{"id": "dm-algebra__linear_1d_composed-hard-124", "pool": "math", "split": "train", "question": "Suppose 35 = 15*a - 40. Suppose 0 = -39*m + 38*m + a. Solve -8*l + m*l = -12 for l.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-125"}}
{"id": "dm-algebra__linear_1d_composed-hard-125", "pool": "math", "split": "train", "question": "Let j(l) = -l**3 + 6*l**2 + 17*l - 3. Let x be j(8). Suppose -4*p = -x*r + 35, -4*p - 6 = 3*r - p. Let g be ((-1)/(-1))/(-4 + r + 2). Solve 2*w - 7 = g for w.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-126"}}
{"id": "dm-algebra__linear_1d_composed-hard-126", "pool": "math", "split": "train", "question": "Suppose 278*l - 1785 = 99*l - 178*l. Suppose 0*c + 3*c = 27. Solve l*g = 24 - c for g.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-127"}}
{"id": "dm-algebra__linear_1d_composed-hard-127", "pool": "math", "split": "train", "question": "Suppose 0*g + 3480 = -8*g. Let n = -433 - g. Solve -n - 8 = -5*u for u.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-128"}}
{"id": "dm-algebra__linear_1d_composed-hard-128", "pool": "math", "split": "train", "question": "Let y be (3 + 0)/(-3)*0. Suppose -4*n + 4*b = y, -2*n + 23 = 4*b - 7. Let g = 240 - 238. Solve n*o = g*o + 9 for o.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-129"}}
{"id": "dm-algebra__linear_1d_composed-hard-129", "pool": "math", "split": "train", "question": "Let d = 360 - 192. Let w = d + -159. Solve 3 - w = 2*z for z.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-130"}}
{"id": "dm-algebra__linear_1d_composed-hard-130", "pool": "math", "split": "train", "question": "Suppose -3*k + 4*k + 15 = -4*z, -k = -2*z + 33. Let t be k/(-12)*(-24)/(-18). Solve -1 = t*d - 10 for d.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-131"}}
{"id": "dm-algebra__linear_1d_composed-hard-131", "pool": "math", "split": "train", "question": "Suppose -2*g + 4*u = 3*u + 29, -5*g = 2*u + 77. Let z be 3/2 - 81/(-6). Let w = g + z. Solve -2*f + 4 = -w for f.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-132"}}
{"id": "dm-algebra__linear_1d_composed-hard-132", "pool": "math", "split": "train", "question": "Let g = 140 + -107. Suppose -3*y + g = 3. Solve -11*b = -y*b for b.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-133"}}
{"id": "dm-algebra__linear_1d_composed-hard-133", "pool": "math", "split": "train", "question": "Let u(n) = -n**2 + 18*n - 10. Let d be u(3). Solve -9*a = -d + 62 for a.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-134"}}
{"id": "dm-algebra__linear_1d_composed-hard-134", "pool": "math", "split": "train", "question": "Suppose -48 = -9*v + 249. Let y = 74 - 43. Let z = v - y. Solve r + 2 = z*r for r.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-135"}}
{"id": "dm-algebra__linear_1d_composed-hard-135", "pool": "math", "split": "train", "question": "Let p be 1 - (-21)/6 - 114/(-4). Let w = -3 - -12. Solve 6*t + p - w = 0 for t.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-136"}}
{"id": "dm-algebra__linear_1d_composed-hard-136", "pool": "math", "split": "train", "question": "Let f(a) be the second derivative of a**3/6 - 7*a**2/2 + 88*a. Let l be (0 - -2)*(-9)/(-2). Let k be f(l). Solve 0 = -k*s + 5 + 5 for s.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-137"}}
{"id": "dm-algebra__linear_1d_composed-hard-137", "pool": "math", "split": "train", "question": "Suppose -12*u - 678 = -15*u. Let t = u - 146. Let p be ((-1)/5 + 216/t)*2. Solve -2*l + l + p = 0 for l.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-138"}}
{"id": "dm-algebra__linear_1d_composed-hard-138", "pool": "math", "split": "train", "question": "Suppose 173*s + 141*s = 39*s. Solve s = 85*r - 69*r - 16 for r.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-139"}}
{"id": "dm-algebra__linear_1d_composed-hard-139", "pool": "math", "split": "train", "question": "Let k = 34 - 28. Suppose 10*q - k = 8*q. Suppose z - 55 = -q*z + n, 3*n = -4*z + 75. Solve z = 3*m + 2*m for m.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-140"}}
{"id": "dm-algebra__linear_1d_composed-hard-140", "pool": "math", "split": "train", "question": "Let j = 6132 - 6078. Solve 11*c - 65 = -j for c.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-141"}}
{"id": "dm-algebra__linear_1d_composed-hard-141", "pool": "math", "split": "train", "question": "Let f = 29114 + -28834. Solve 59*g = -f - 74 for g.", "unit": "dimensionless", "value": "-6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-142"}}
{"id": "dm-algebra__linear_1d_composed-hard-142", "pool": "math", "split": "train", "question": "Let b = -4 + 9. Let p = -297 + 303. Suppose -7 - 17 = -p*v. Solve -v*r = -5*r - b for r.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-143"}}
{"id": "dm-algebra__linear_1d_composed-hard-143", "pool": "math", "split": "train", "question": "Let x = -403 + 407. Let l be (8/10)/(3/15). Suppose l*t + 2*t = 0. Solve x*c + t - 4 = 0 for c.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-144"}}
{"id": "dm-algebra__linear_1d_composed-hard-144", "pool": "math", "split": "train", "question": "Suppose -2*b + 32 - 26 = 0. Suppose 3 = 2*a + n, -b*a = -a - 2*n - 6. Suppose a*g + w = 1, -26 = 2*g - 4*g + 4*w. Solve 4*h = h + g for h.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-145"}}
{"id": "dm-algebra__linear_1d_composed-hard-145", "pool": "math", "split": "train", "question": "Let r = -26 + 30. Suppose r*s + 60 = 5*p, 3*p = p + 3*s + 24. Solve 8*w - 5*w + p = 0 for w.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-146"}}
{"id": "dm-algebra__linear_1d_composed-hard-146", "pool": "math", "split": "train", "question": "Let l(n) = 27 - 4*n. Let p be l(7). Let m be ((-20)/(-5) - (p - -2)) + -3. Solve 2*t - 6*t - 8 = m for t.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-147"}}
{"id": "dm-algebra__linear_1d_composed-hard-147", "pool": "math", "split": "train", "question": "Suppose -48 = -4*i + 4*t, -2*i - 4*t - 6 = -3*i. Let b be i + -16 + (-6)/(-1). Solve 0 = -b*p + 5 - 1 for p.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-148"}}
{"id": "dm-algebra__linear_1d_composed-hard-148", "pool": "math", "split": "train", "question": "Let z = -3006 + 3006. Solve z = -17*d + 18*d - 5 for d.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-149"}}
{"id": "dm-algebra__linear_1d_composed-hard-149", "pool": "math", "split": "train", "question": "Let a = 220 - 136. Suppose 32*v = 39*v - a. Solve -f + v = -4*f for f.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-150"}}
{"id": "dm-algebra__linear_1d_composed-hard-150", "pool": "math", "split": "train", "question": "Suppose 979 = -11*x - 737. Let o = x + 165. Solve -o = -2*b - 1 for b.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-151"}}
{"id": "dm-algebra__linear_1d_composed-hard-151", "pool": "math", "split": "train", "question": "Let d = -8906 + 8906. Solve d = -20*j + 22*j - 2 for j.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-152"}}
{"id": "dm-algebra__linear_1d_composed-hard-152", "pool": "math", "split": "train", "question": "Suppose 2*g - 2*h = 3*h - 2, 2*h + 28 = 4*g. Solve 4*t = 2*t - g*t for t.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-153"}}
{"id": "dm-algebra__linear_1d_composed-hard-153", "pool": "math", "split": "train", "question": "Let p = -2169 + 2172. Let u(j) = j**3 - 4*j**2 - 5*j + 28. Let t be u(p). Suppose -5 = 2*c - 17. Solve c*b + 2 = t*b for b.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-154"}}
{"id": "dm-algebra__linear_1d_composed-hard-154", "pool": "math", "split": "train", "question": "Let o be (-11 + 12)/(((-2)/1)/6). Let b be (-26)/(-39) + 2/o. Solve 0 = -v - 3 - b for v.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-155"}}
{"id": "dm-algebra__linear_1d_composed-hard-155", "pool": "math", "split": "train", "question": "Let u be (-12)/(-7) + (-10)/(-35). Suppose -5*d + u*d = -6. Let a(g) = -g**2 + 18*g - 20. Let x be a(15). Solve -d*j - 3*j = x for j.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-156"}}
{"id": "dm-algebra__linear_1d_composed-hard-156", "pool": "math", "split": "train", "question": "Let w(i) = i**3 - 2*i**2 + i - 1. Let o(y) = y**2 + 20*y - 30. Let k be o(-21). Let q(n) = 2*n**3 - 4*n**2 + 2*n - 1. Let j(c) = k*w(c) + 4*q(c). Let a be j(0). Solve 12 = -g + a*g for g.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-157"}}
{"id": "dm-algebra__linear_1d_composed-hard-157", "pool": "math", "split": "train", "question": "Suppose -10*x + 70 + 20 = 0. Suppose 3*w - 3*j = 9, 30 = 4*w - 0*w + 5*j. Solve -x*s = -w*s for s.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-158"}}
{"id": "dm-algebra__linear_1d_composed-hard-158", "pool": "math", "split": "train", "question": "Suppose -13*w - 384 + 111 = 0. Let n = -18 - w. Solve -4*l = -n*l + 3 for l.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-159"}}
{"id": "dm-algebra__linear_1d_composed-hard-159", "pool": "math", "split": "train", "question": "Let x(w) = -w - 1. Let o be x(-3). Let n be (-25 - -8)*(0 - o)/2. Suppose -n*l + 16*l = -11. Solve 2*q + 3 = l for q.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-160"}}
{"id": "dm-algebra__linear_1d_composed-hard-160", "pool": "math", "split": "train", "question": "Suppose -3*u + 15 = 0, -8 - 7 = l - 4*u. Suppose -l*d + 25 = 0, 0*i - 4*i = 3*d - 111. Solve w - 9*w = i for w.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-161"}}
{"id": "dm-algebra__linear_1d_composed-hard-161", "pool": "math", "split": "train", "question": "Suppose 0 = -14*x + 7*x + 105. Suppose -72*w + 69*w + x = 0. Solve 5*d = -10 - w for d.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-162"}}
{"id": "dm-algebra__linear_1d_composed-hard-162", "pool": "math", "split": "train", "question": "Suppose -h + 4 = -3*b - 3, -2*b + 18 = 5*h. Suppose -g = -v - 54 + 23, -3*g - 3*v + 69 = 0. Solve -g + 11 = -h*r for r.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-163"}}
{"id": "dm-algebra__linear_1d_composed-hard-163", "pool": "math", "split": "train", "question": "Let b be (-14104)/(-172) - (6 + -2). Solve 162 = 40*k - b for k.", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-164"}}
{"id": "dm-algebra__linear_1d_composed-hard-164", "pool": "math", "split": "train", "question": "Let z = 117 - 67. Suppose 2*n + 3*n + 2*c = 35, -5*n - 5*c + z = 0. Suppose -3*j + 35 = -0*s + s, s + 61 = n*j. Solve x = 4*x - j for x.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-165"}}
{"id": "dm-algebra__linear_1d_composed-hard-165", "pool": "math", "split": "train", "question": "Let s = -14 - -18. Suppose -3*z + 9 = -0*z. Let x = 160 + -160. Solve x = -g + s - z for g.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-166"}}
{"id": "dm-algebra__linear_1d_composed-hard-166", "pool": "math", "split": "train", "question": "Let s = 722 - 646. Solve -s + 60 = 8*t for t.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-167"}}
{"id": "dm-algebra__linear_1d_composed-hard-167", "pool": "math", "split": "train", "question": "Let p(m) = -m**3 + 2*m**2 + 2*m - 4. Suppose -10*v = -9*v + 51. Let w = -49 - v. Let r be p(w). Solve r = -4*s + 18 + 2 for s.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-168"}}
{"id": "dm-algebra__linear_1d_composed-hard-168", "pool": "math", "split": "train", "question": "Suppose 2*f + 77 = 3*g, -f - 92 = -5*g + 34. Let y be (15/(-10))/((-48)/544). Suppose -4*a - y = -j - 15, a - 2 = -j. Solve -7*u = -j*u - g for u.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-169"}}
{"id": "dm-algebra__linear_1d_composed-hard-169", "pool": "math", "split": "train", "question": "Suppose 5*d + 11*d + 592 = 0. Let z = 41 + d. Suppose -20*v + 21*v = 12. Solve -z*n + v = -n for n.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-170"}}
{"id": "dm-algebra__linear_1d_composed-hard-170", "pool": "math", "split": "train", "question": "Let i = -59 - -61. Suppose -45 = -4*c - 5*g, -i*c - 2*c + 3*g = -69. Solve 2*z + 3*z = -c for z.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-171"}}
{"id": "dm-algebra__linear_1d_composed-hard-171", "pool": "math", "split": "train", "question": "Suppose -2*f = -m + 8 - 1, 0 = -3*m + 5*f + 22. Solve -m = -7*s - 30 for s.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-172"}}
{"id": "dm-algebra__linear_1d_composed-hard-172", "pool": "math", "split": "train", "question": "Suppose 3*l - 29 = -4*g, 0*g - 4*l = -3*g + 28. Suppose -4*q = -12, 7 = 3*y - q + 4. Suppose -2*a + y*a = -g*a. Solve 5*u - 14 - 1 = a for u.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-173"}}
{"id": "dm-algebra__linear_1d_composed-hard-173", "pool": "math", "split": "train", "question": "Let f = 96 + -95. Suppose -c + 0*c - 3*r + 13 = 0, f = r. Solve o + c = 6*o for o.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-174"}}
{"id": "dm-algebra__linear_1d_composed-hard-174", "pool": "math", "split": "train", "question": "Suppose 10*g - 456 = -15*g - 51*g. Solve 89 = -g*z + 53 for z.", "unit": "dimensionless", "value": "-6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-175"}}
{"id": "dm-algebra__linear_1d_composed-hard-175", "pool": "math", "split": "train", "question": "Let k = -134 - -138. Let o = 0 + k. Let m be (-12 + o)/(6/(-9)*3). Solve -m*y + 1 + 3 = 0 for y.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-176"}}
{"id": "dm-algebra__linear_1d_composed-hard-176", "pool": "math", "split": "train", "question": "Suppose -z = -3*z + 6. Let v be ((-204)/(-8))/z*-2. Let l = v - -20. Solve 1 - 4 = -l*n for n.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-177"}}
{"id": "dm-algebra__linear_1d_composed-hard-177", "pool": "math", "split": "train", "question": "Suppose -d - 3*d = 5*j + 23, 5*d - 2*j + 4 = 0. Let n be 10/d*1/(20/(-8)). Let l be ((-6)/8)/1*-8*n. Solve -4 + l = 2*c for c.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-178"}}
{"id": "dm-algebra__linear_1d_composed-hard-178", "pool": "math", "split": "train", "question": "Let q(h) = -1280*h - 8906. Let z be q(-7). Solve -z*p + 128*p = -444 for p.", "unit": "dimensionless", "value": "-6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-179"}}
{"id": "dm-algebra__linear_1d_composed-hard-179", "pool": "math", "split": "train", "question": "Suppose -143*a + 349 + 223 = 0. Let l(b) be the first derivative of 5*b**2/2 - 17*b + 1. Let r be l(a). Solve 2*i + r - 1 = 0 for i.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-180"}}
{"id": "dm-algebra__linear_1d_composed-hard-180", "pool": "math", "split": "train", "question": "Let l = 144 - 143. Let c be (-4)/3 - 82/6. Let t = c + 18. Solve -t = -h + l for h.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-181"}}
{"id": "dm-algebra__linear_1d_composed-hard-181", "pool": "math", "split": "train", "question": "Let a = -362 + 367. Let o be 3 - (-3 + -6)/(-3). Solve -a = p - o for p.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-182"}}
{"id": "dm-algebra__linear_1d_composed-hard-182", "pool": "math", "split": "train", "question": "Let r be 2 - (2 + -4 + 1). Suppose 5*p - 86 = r*b, 5*b + 3 = -7. Let h be 52/(-3588)*-115*(-6)/(-5). Solve -h*m - p = 2*m for m.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-183"}}
{"id": "dm-algebra__linear_1d_composed-hard-183", "pool": "math", "split": "train", "question": "Let t(v) = v**3 + 4. Let k be t(0). Suppose k*a - 14 = 2*b, 0 = 4*b - 4 - 0. Solve 0 = 2*s - 3*s + a for s.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-184"}}
{"id": "dm-algebra__linear_1d_composed-hard-184", "pool": "math", "split": "train", "question": "Let v = -123 - -93. Let a(h) = 4*h + 120. Let g be a(v). Solve -4*t + 6*t + 10 = g for t.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-185"}}
{"id": "dm-algebra__linear_1d_composed-hard-185", "pool": "math", "split": "train", "question": "Let y(a) = -13*a**3 + 3*a**2 - 4*a - 7. Let h be y(-1). Suppose -5*s = 2*v - 28, 6*v + 4 = 3*s + 4*v. Solve s*t + 29 - h = 0 for t.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-186"}}
{"id": "dm-algebra__linear_1d_composed-hard-186", "pool": "math", "split": "train", "question": "Let v(l) = -2*l**3 + l**2 - 47*l - 169. Let j be v(-3). Solve 0 = -j*o - 23*o - 406 for o.", "unit": "dimensionless", "value": "-7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-187"}}
{"id": "dm-algebra__linear_1d_composed-hard-187", "pool": "math", "split": "train", "question": "Let i be 3/(3 - 0)*5/5. Let o(c) = 2 - 5*c**2 + 3*c**2 + 3*c**2 + i + 2*c. Let f be o(0). Solve 0 = f*n + 3 + 6 for n.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-188"}}
{"id": "dm-algebra__linear_1d_composed-hard-188", "pool": "math", "split": "train", "question": "Let z(o) be the third derivative of 34*o**2 + 13/6*o**3 + 1/5*o**5 + 0*o + 0 + 1/2*o**4 - 1/120*o**6. Let t be z(13). Solve -3*w + 4*w + 3 = t for w.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-189"}}
{"id": "dm-algebra__linear_1d_composed-hard-189", "pool": "math", "split": "train", "question": "Suppose -n - 2*c = -4*c - 1, -4*n = 3*c - 26. Suppose 2*g - 21 = -n*z, -z + 5*g = 2*z + 6. Let p be 3/(1 + z/(-2) - -1). Solve -d = -p*d - 20 for d.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-190"}}
{"id": "dm-algebra__linear_1d_composed-hard-190", "pool": "math", "split": "train", "question": "Let y = -1821 - -1859. Solve 63*b = 82*b + y for b.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-191"}}
{"id": "dm-algebra__linear_1d_composed-hard-191", "pool": "math", "split": "train", "question": "Suppose 1896 = 116*b - 888. Solve 56*f = 48*f + b for f.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-192"}}
{"id": "dm-algebra__linear_1d_composed-hard-192", "pool": "math", "split": "train", "question": "Let r(s) = 6 + 5 + s**2 - 3 + 4*s - 3. Let h be r(-3). Solve -h*u - 20 = -12 for u.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-193"}}
{"id": "dm-algebra__linear_1d_composed-hard-193", "pool": "math", "split": "train", "question": "Suppose 24 - 1074 = -105*d. Solve d = -10*z - 10 for z.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-194"}}
{"id": "dm-algebra__linear_1d_composed-hard-194", "pool": "math", "split": "train", "question": "Suppose -9*m + 42 = -6*m. Suppose 0 = 13*s - m*s. Let f(g) = 4*g**2 + g. Let q be f(-1). Solve s*t - q*t - 15 = 0 for t.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-195"}}
{"id": "dm-algebra__linear_1d_composed-hard-195", "pool": "math", "split": "train", "question": "Suppose -5*l - 96 = 7*l. Let r be (-9 - l)/(2/(-64)). Suppose -r = -6*z - 2*z. Solve 5*f + 16 = -z for f.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-196"}}
{"id": "dm-algebra__linear_1d_composed-hard-196", "pool": "math", "split": "train", "question": "Let d(g) = g**2 - 10*g - 22. Let p be d(12). Suppose -p*v = -5*n - 30, 2*v + 5*n - 14 = -4. Solve -v = 6*m - 11*m for m.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-197"}}
{"id": "dm-algebra__linear_1d_composed-hard-197", "pool": "math", "split": "train", "question": "Let r = -130 + 88. Let y be -6 + 0 + r/(-7). Solve 5*o + 36 - 11 = y for o.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-198"}}
{"id": "dm-algebra__linear_1d_composed-hard-198", "pool": "math", "split": "train", "question": "Suppose -7*a + 3*a + 96 = 0. Suppose 0 = -4*d + 12*d - a. Let w be (-1)/4 + 1/4. Solve -d = p - w for p.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-199"}}
{"id": "dm-algebra__linear_1d_composed-hard-199", "pool": "math", "split": "train", "question": "Let n(m) = -228*m - 3185. Let k be n(-14). Solve -k*w + 174 = 125 for w.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-200"}}
{"id": "dm-algebra__linear_1d_composed-hard-200", "pool": "math", "split": "train", "question": "Let z(l) = l**3 - 6*l**2 + 6*l + 13. Let x be z(5). Suppose 149 = 4*r + 121. Solve v = r*v + x for v.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-201"}}
{"id": "dm-algebra__linear_1d_composed-hard-201", "pool": "math", "split": "train", "question": "Let q(a) = -a**2 + 24*a - 100. Let s be q(7). Suppose 0 = -n + 2*l + 10, 5*n = 4*l + 19 + s. Solve 0*r - n = -2*r for r.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-202"}}
{"id": "dm-algebra__linear_1d_composed-hard-202", "pool": "math", "split": "train", "question": "Let f be (-3020)/2416*(2 + -1 + -5). Suppose 12 = b + 2*b. Suppose -b*v + 12 = -4*q + 4, 0 = -2*q + 6. Solve -v*d = -0 + f for d.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-203"}}
{"id": "dm-algebra__linear_1d_composed-hard-203", "pool": "math", "split": "train", "question": "Suppose 5*o = 5*x + 200, 0 = 5*x - 42 + 87. Solve -327 = 37*f - o for f.", "unit": "dimensionless", "value": "-8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-204"}}
{"id": "dm-algebra__linear_1d_composed-hard-204", "pool": "math", "split": "train", "question": "Suppose -3*k = 3*l, 2*l + 3*k + 17 = 13. Suppose l*w - 4*r = 36, 17*r + 8 = 13*r. Solve -w = b - 3 for b.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-205"}}
{"id": "dm-algebra__linear_1d_composed-hard-205", "pool": "math", "split": "train", "question": "Suppose 0 = n + 5*a - 19, -6 = 4*n + 2*a - 82. Suppose -h + q = -4*h + n, 0 = 4*h + q - 25. Solve -5*k + h = 6 for k.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-206"}}
{"id": "dm-algebra__linear_1d_composed-hard-206", "pool": "math", "split": "train", "question": "Let a = -153 + 73. Let s be (3 + -2)/(2/a). Let y = 40 + s. Solve 0 = -y*k + k + 5 for k.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-207"}}
{"id": "dm-algebra__linear_1d_composed-hard-207", "pool": "math", "split": "train", "question": "Suppose 4*v - a - 27 = 0, -479*v + 2*a = -480*v. Solve 0 = -v*j - 446 + 452 for j.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-208"}}
{"id": "dm-algebra__linear_1d_composed-hard-208", "pool": "math", "split": "train", "question": "Suppose 10*i - 14*i + 12 = 0. Suppose -2*d = -3*d - 4, 16 = -2*a - 4*d. Suppose 2*z + 2 = k, 3*k - 6 + a = -3*z. Solve -g - i - 2 = z for g.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-209"}}
{"id": "dm-algebra__linear_1d_composed-hard-209", "pool": "math", "split": "train", "question": "Suppose 8 = 4*j + 2*s, 0*s + 20 = 3*j + 5*s. Suppose j = k + 2*a - 41, -200 = k - 6*k - 5*a. Suppose 4*t = -19 + k. Solve -i = -t*i + 4 for i.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-210"}}
{"id": "dm-algebra__linear_1d_composed-hard-210", "pool": "math", "split": "train", "question": "Let y = 29939 + -29935. Solve y*c + 855 - 839 = 0 for c.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-211"}}
{"id": "dm-algebra__linear_1d_composed-hard-211", "pool": "math", "split": "train", "question": "Let d be (2 - 0) + 0 + 1. Suppose 8*v - 9*v + 6 = 0. Let j(q) = -q**2 + 12*q - 34. Let a be j(v). Solve -l = -a*l + d for l.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-212"}}
{"id": "dm-algebra__linear_1d_composed-hard-212", "pool": "math", "split": "train", "question": "Suppose -11*q = -5*q + 30. Let n = q + 7. Let v = 4 - n. Solve 0*r - v = -r for r.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-213"}}
{"id": "dm-algebra__linear_1d_composed-hard-213", "pool": "math", "split": "train", "question": "Let k(l) = 3*l**2 - 20*l - 5. Let g = -9 + 16. Let p be k(g). Solve 0 = 7*f - p + 16 for f.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-214"}}
{"id": "dm-algebra__linear_1d_composed-hard-214", "pool": "math", "split": "train", "question": "Suppose 4*q - 5*c = -99, -5 = -q + 3*c - 35. Let x be 11 + (302 - -1)*(-11)/33. Let g be x/q - 18/63. Solve -g*f + 9 = 1 for f.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-215"}}
{"id": "dm-algebra__linear_1d_composed-hard-215", "pool": "math", "split": "train", "question": "Let o be (-2)/2*(-35 + 2). Let b(g) = g**3 - 24*g**2 - 27. Let s be b(24). Let l = o + s. Solve l = -0*y + 2*y for y.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-216"}}
{"id": "dm-algebra__linear_1d_composed-hard-216", "pool": "math", "split": "train", "question": "Let z = 1 + 2. Let v be 16 - 15*96/180. Solve -a - z = -v for a.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-217"}}
{"id": "dm-algebra__linear_1d_composed-hard-217", "pool": "math", "split": "train", "question": "Let s be 0/(4 + -8)*(-1)/4. Suppose s = 2*a - 0*a + 16. Let p be (-18)/(-5) + a/(-20). Solve p*k = -3 - 5 for k.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-218"}}
{"id": "dm-algebra__linear_1d_composed-hard-218", "pool": "math", "split": "train", "question": "Let o(i) = -i**2 - 5*i + 4. Let g be o(-5). Let c = 176 + -180. Let u be (9/c)/(27/(-36)). Solve -11 = g*q - u for q.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-219"}}
{"id": "dm-algebra__linear_1d_composed-hard-219", "pool": "math", "split": "train", "question": "Let t(n) = 2*n**3 - 10*n**2 - 6*n - 27. Let x be t(6). Let s = 1 + 5. Solve o - x = -s for o.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-220"}}
{"id": "dm-algebra__linear_1d_composed-hard-220", "pool": "math", "split": "train", "question": "Let m = 0 - -121. Let k = -117 + m. Solve -k*d - 4 + 0 = 0 for d.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-221"}}
{"id": "dm-algebra__linear_1d_composed-hard-221", "pool": "math", "split": "train", "question": "Let n be ((-36)/(-16))/((-2)/(-8)). Suppose -3*q = 2*p - 17, 0 = q + 4*p - 0*p - n. Let w be (3 + 33/(-9))*-6. Solve -3 = -w*h + q for h.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-222"}}
{"id": "dm-algebra__linear_1d_composed-hard-222", "pool": "math", "split": "train", "question": "Let x(k) = 31 - 20*k. Let w be x(1). Solve -4*z - w + 23 = 0 for z.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-223"}}
{"id": "dm-algebra__linear_1d_composed-hard-223", "pool": "math", "split": "train", "question": "Let o(k) = -44*k**2 - 304*k + 37. Let n be o(-7). Solve n*z = 23*z + 84 for z.", "unit": "dimensionless", "value": "-6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-224"}}
{"id": "dm-algebra__linear_1d_composed-hard-224", "pool": "math", "split": "train", "question": "Let i be (-321)/(-18) + (-15)/(-90). Solve 4*r = -34 + i for r.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-225"}}
{"id": "dm-algebra__linear_1d_composed-hard-225", "pool": "math", "split": "train", "question": "Suppose 3*x + 216 = 2*m, -5*x - 432 = -4*m - 0*m. Solve -110*u = -m*u + 10 for u.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-226"}}
{"id": "dm-algebra__linear_1d_composed-hard-226", "pool": "math", "split": "train", "question": "Let b be 15/9 + 40/12 + 3. Solve -20 + 60 = -b*w for w.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-227"}}
{"id": "dm-algebra__linear_1d_composed-hard-227", "pool": "math", "split": "train", "question": "Let f(v) = v**2 - 20*v - 57. Let c be f(29). Solve -c = 9*g + 25*g for g.", "unit": "dimensionless", "value": "-6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-228"}}
{"id": "dm-algebra__linear_1d_composed-hard-228", "pool": "math", "split": "train", "question": "Let f = 1471 + -1440. Solve f*a = -51 - 166 for a.", "unit": "dimensionless", "value": "-7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-229"}}
{"id": "dm-algebra__linear_1d_composed-hard-229", "pool": "math", "split": "train", "question": "Suppose -2*m + 3*x - 1024 = -2*x, 2*m = -x - 1000. Let w = 517 + m. Solve -14*u + w*u + 3 = 0 for u.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-230"}}
{"id": "dm-algebra__linear_1d_composed-hard-230", "pool": "math", "split": "train", "question": "Let z(t) be the first derivative of 2*t**3/3 + 3*t**2 - 7*t + 62. Let x be z(1). Solve 0 = -4*s - 3 - x for s.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-231"}}
{"id": "dm-algebra__linear_1d_composed-hard-231", "pool": "math", "split": "train", "question": "Let c be ((5 - 4)/3)/((-61)/(-6039)). Solve 5*j = c*j + 56 for j.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-232"}}
{"id": "dm-algebra__linear_1d_composed-hard-232", "pool": "math", "split": "train", "question": "Let t(z) = -2*z**3 - 8*z**2 - 7*z + 26. Let c be t(-4). Solve c*j = 50*j + 36 for j.", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-233"}}
{"id": "dm-algebra__linear_1d_composed-hard-233", "pool": "math", "split": "train", "question": "Let v = -20 - -25. Let s(n) = -6*n**2 + 23*n - 14. Let a be s(3). Solve 3*o - v - a = 0 for o.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-234"}}
{"id": "dm-algebra__linear_1d_composed-hard-234", "pool": "math", "split": "train", "question": "Let r(d) = 101*d**2 - 321*d + 648. Let k be r(2). Solve 0 = -4*h - k + 430 for h.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-235"}}
{"id": "dm-algebra__linear_1d_composed-hard-235", "pool": "math", "split": "train", "question": "Let p = 48 + -45. Suppose -59*r + 58*r = p*k - 17, -15 = -3*k. Solve 3*z + r*z - 10 = 0 for z.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-236"}}
{"id": "dm-algebra__linear_1d_composed-hard-236", "pool": "math", "split": "train", "question": "Let j be 17 - (1 - (1 - 4)). Let n = 128 + j. Let g = n + -138. Solve 0*w = g*w + 3 for w.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-237"}}
{"id": "dm-algebra__linear_1d_composed-hard-237", "pool": "math", "split": "train", "question": "Suppose 4*q - 2*j = -5*j + 2698, 2*q - j - 1354 = 0. Let r = 679 - q. Solve 7*x = r*x - 20 for x.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-238"}}
{"id": "dm-algebra__linear_1d_composed-hard-238", "pool": "math", "split": "train", "question": "Let i = 16 - 48. Let c = -17 - i. Let u(j) = 36 - 2*j. Let w be u(c). Solve -2*d = 2 + w for d.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-239"}}
{"id": "dm-algebra__linear_1d_composed-hard-239", "pool": "math", "split": "train", "question": "Let k(w) = 4*w + 26. Let o be k(18). Suppose n + 6*n = o. Suppose -j - 5*l - 18 = -10*l, -5*j + n = l. Solve 7 + j = 3*m for m.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-240"}}
{"id": "dm-algebra__linear_1d_composed-hard-240", "pool": "math", "split": "train", "question": "Let h(x) = -10*x - 23. Let a be h(-9). Suppose -172 = -21*i - a. Suppose -3*d + 0*d = 3*u - 39, 4*d - 2*u = 34. Solve -d = -i*j + 10 for j.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-241"}}
{"id": "dm-algebra__linear_1d_composed-hard-241", "pool": "math", "split": "train", "question": "Let k(c) = -3*c**2 + 4*c - 1. Let u(r) be the third derivative of -r**5/60 + 16*r**2. Let b(m) = -k(m) + 2*u(m). Let o be b(4). Solve -1 = -t + o for t.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-242"}}
{"id": "dm-algebra__linear_1d_composed-hard-242", "pool": "math", "split": "train", "question": "Suppose 616*l - 622*l = -504. Suppose l = 30*j - 6. Solve 0 = -2*m + m + j for m.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-243"}}
{"id": "dm-algebra__linear_1d_composed-hard-243", "pool": "math", "split": "train", "question": "Let y(h) = h**2 + 22*h + 37. Let o be y(-21). Let l be (-1)/(-8) + 142/o. Solve l*i + 12 = 3*i for i.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-244"}}
{"id": "dm-algebra__linear_1d_composed-hard-244", "pool": "math", "split": "train", "question": "Suppose 5*w + 53 = -2*t, -2*w - 30 = 5*t - 2*t. Suppose 2*j + j = 5*x - 48, 0 = -5*j + 3*x - 64. Let a be (-3)/w - j/((-132)/(-56)). Solve a - 1 = 4*k for k.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-245"}}
{"id": "dm-algebra__linear_1d_composed-hard-245", "pool": "math", "split": "train", "question": "Let z(x) be the first derivative of -5/3*x**3 - 15 - 1/2*x**2 - 1/2*x**4 + 3*x. Let q be z(-3). Solve -q = s - 4*s for s.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-246"}}
{"id": "dm-algebra__linear_1d_composed-hard-246", "pool": "math", "split": "train", "question": "Suppose -15*c + 15872 = 16*c. Let s = c - 511. Solve s = k - 0*k for k.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-247"}}
{"id": "dm-algebra__linear_1d_composed-hard-247", "pool": "math", "split": "train", "question": "Let j(l) = l**3 - 12*l + 22. Let i be j(2). Solve -4*s - i = 2 for s.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-248"}}
{"id": "dm-algebra__linear_1d_composed-hard-248", "pool": "math", "split": "train", "question": "Let z = 100 + -95. Suppose -5*f - 15 = -z*a - 0*a, -2*a + 4*f = 2. Let j(w) = -w**3 + 5*w**2 + 17*w - 15. Let l be j(a). Solve l = -s + 3 for s.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-249"}}
{"id": "dm-algebra__linear_1d_composed-hard-249", "pool": "math", "split": "train", "question": "Suppose 3*z = -3, -o + 5*o + 3*z = -3. Let b = -58 + 93. Let f(l) = l**2 - 35*l + 3. Let m be f(b). Solve -j - m + 1 = o for j.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-250"}}
{"id": "dm-algebra__linear_1d_composed-hard-250", "pool": "math", "split": "train", "question": "Suppose 515 = -22*c + 27*c. Let r = c - 102. Solve k = 3 + r for k.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-251"}}
{"id": "dm-algebra__linear_1d_composed-hard-251", "pool": "math", "split": "train", "question": "Let k(g) = -g**3 + 8*g**2 - 2*g + 19. Let y = 40 + -32. Let h be k(y). Suppose n = j + j - 32, -j = -3*n - 6. Solve h = 5*a + j for a.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-252"}}
{"id": "dm-algebra__linear_1d_composed-hard-252", "pool": "math", "split": "train", "question": "Let n(l) = -2122 - 2117 - l + 4242. Let h be n(-6). Solve -g - 5 = -h for g.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-253"}}
{"id": "dm-algebra__linear_1d_composed-hard-253", "pool": "math", "split": "train", "question": "Let g = -254 - -218. Let p(l) = 3*l**2 + 108*l. Let v be p(g). Solve -6*o + 43 - 13 = v for o.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-254"}}
{"id": "dm-algebra__linear_1d_composed-hard-254", "pool": "math", "split": "train", "question": "Let w = 14994 - 14994. Solve -27*x - 70 - 146 = w for x.", "unit": "dimensionless", "value": "-8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-255"}}
{"id": "dm-algebra__linear_1d_composed-hard-255", "pool": "math", "split": "train", "question": "Let z(p) = 37 - 18*p. Let r be z(2). Let v(f) = 7*f**2 - f - 2. Let y be v(r). Solve -4*q = -2*q + y for q.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-256"}}
{"id": "dm-algebra__linear_1d_composed-hard-256", "pool": "math", "split": "train", "question": "Let u(x) = -145*x - 3. Let s be u(-2). Suppose 10*g - s + 167 = 0. Let t = 4 - 0. Solve -t*v - g = -0*v for v.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-257"}}
{"id": "dm-algebra__linear_1d_composed-hard-257", "pool": "math", "split": "train", "question": "Let q = -226 + 277. Let a = -46 + q. Solve a*g - 6*g = -4 for g.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-258"}}
{"id": "dm-algebra__linear_1d_composed-hard-258", "pool": "math", "split": "train", "question": "Suppose 2*f = -5*f + 21. Suppose -8 = -f*w - 2. Suppose 5*z = -5*k + 25, w*k - 29 = -2*k + 5*z. Solve -g + 3*g + k = 0 for g.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-259"}}
{"id": "dm-algebra__linear_1d_composed-hard-259", "pool": "math", "split": "train", "question": "Suppose 709*k = 3*q + 712*k - 231, 0 = 5*q - 5*k - 335. Solve 52*f = q*f + 140 for f.", "unit": "dimensionless", "value": "-7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-260"}}
{"id": "dm-algebra__linear_1d_composed-hard-260", "pool": "math", "split": "train", "question": "Let d(n) = n**2 - 5*n + 6. Let r be d(3). Let b(x) = -x**3 + 73*x**2 + 149*x + 77. Let f be b(75). Solve -f*p + 6*p - 12 = r for p.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-261"}}
{"id": "dm-algebra__linear_1d_composed-hard-261", "pool": "math", "split": "train", "question": "Suppose -77*t + 25 = -82*t. Let w = -18 - -11. Let l = t - w. Solve -3*p = -4*p + l for p.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-262"}}
{"id": "dm-algebra__linear_1d_composed-hard-262", "pool": "math", "split": "train", "question": "Suppose 5*n + 100 = 9*n. Let g(q) = -3*q - 23. Let v be g(-11). Solve v = -3*p + n for p.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-263"}}
{"id": "dm-algebra__linear_1d_composed-hard-263", "pool": "math", "split": "train", "question": "Let t(q) be the first derivative of q**4/4 + 4*q**3 + 7*q**2/2 - 44*q + 82. Let g be t(-11). Solve 0 = 3*z - g for z.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-264"}}
{"id": "dm-algebra__linear_1d_composed-hard-264", "pool": "math", "split": "train", "question": "Let y = -10509 + 10551. Solve 725*o - y = 732*o for o.", "unit": "dimensionless", "value": "-6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-265"}}
{"id": "dm-algebra__linear_1d_composed-hard-265", "pool": "math", "split": "train", "question": "Let q be (8/6)/(132/297). Let x = -10 + 14. Suppose -h + 6 = -x. Solve q*p - h = p for p.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-266"}}
{"id": "dm-algebra__linear_1d_composed-hard-266", "pool": "math", "split": "train", "question": "Suppose 94*c - 55*c - 1989 = 0. Solve 0 = 26*m - c - 1 for m.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-267"}}
{"id": "dm-algebra__linear_1d_composed-hard-267", "pool": "math", "split": "train", "question": "Suppose -2*l = 3*l + 3*a + 46, -4*l + a - 30 = 0. Let d be (l/(-6))/((-8)/(-72)). Let k = -3 + d. Solve 4*p - k = -1 for p.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-268"}}
{"id": "dm-algebra__linear_1d_composed-hard-268", "pool": "math", "split": "train", "question": "Suppose -l = 6*l - 42. Suppose -l = -4*g + g. Suppose 2*o = -g*o + 5*o. Solve o*r + 2 = r for r.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-269"}}
{"id": "dm-algebra__linear_1d_composed-hard-269", "pool": "math", "split": "train", "question": "Let t(d) = 6*d - 14. Let s be 0 - -1 - 7/((-35)/15). Let i be t(s). Suppose 4 - 2 = w. Solve -i = w*z - 7*z for z.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-270"}}
{"id": "dm-algebra__linear_1d_composed-hard-270", "pool": "math", "split": "train", "question": "Suppose 0 = -38*i + 90*i - 624. Solve 40 = i*m + 4 for m.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-271"}}
{"id": "dm-algebra__linear_1d_composed-hard-271", "pool": "math", "split": "train", "question": "Let b(g) = -5*g**2 + 20*g + 2. Let p(s) = 2*s**2 + 13*s - 4. Let v(m) = 3*m**2 + 13*m - 5. Let o(d) = 6*p(d) - 5*v(d). Let l(n) = 5*b(n) - 8*o(n). Let y be l(-3). Solve -y*i = 15 - 40 for i.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-272"}}
{"id": "dm-algebra__linear_1d_composed-hard-272", "pool": "math", "split": "train", "question": "Let m(f) = -56*f**2 + f + 3. Let d be m(2). Let r = d - -230. Solve 5*q - 26 + r = 0 for q.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-273"}}
{"id": "dm-algebra__linear_1d_composed-hard-273", "pool": "math", "split": "train", "question": "Let s = -19 - -79. Suppose -44 = -4*v - 24, 5*g - 5*v - 425 = 0. Suppose s + g = 6*i. Solve i = -t - 4*t for t.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-274"}}
{"id": "dm-algebra__linear_1d_composed-hard-274", "pool": "math", "split": "train", "question": "Let l be 5 + 1301 - (-63 + 76). Solve -1294*x = -l*x - 4 for x.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-275"}}
{"id": "dm-algebra__linear_1d_composed-hard-275", "pool": "math", "split": "train", "question": "Suppose 5*z - 6 = -n - n, 4*n = z + 12. Let y be -3*(225/27)/(-5). Suppose y*s - 48*u - 34 = -52*u, -3*u - 32 = -2*s. Solve z = 4*k - s - 6 for k.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-276"}}
{"id": "dm-algebra__linear_1d_composed-hard-276", "pool": "math", "split": "train", "question": "Let w(v) = -v**3 + 11*v**2 - 2. Suppose 2*d = 2*q - 3*d - 17, -2*d = q - 13. Let m be w(q). Let a = m - -14. Solve -3*c = c + a for c.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-277"}}
{"id": "dm-algebra__linear_1d_composed-hard-277", "pool": "math", "split": "train", "question": "Let y be (6 - 0)/(-2 - -3). Suppose -2*v = 2*g - 18, 0 = 2*g + 12*v - 9*v - 23. Solve -y = -2*j + g*j for j.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-278"}}
{"id": "dm-algebra__linear_1d_composed-hard-278", "pool": "math", "split": "train", "question": "Let g(q) = 9*q - 79. Let i(s) = 118 - 13*s. Let o = 2 - -5. Let w(t) = o*g(t) + 5*i(t). Let b be w(18). Solve -j = -0*j + b for j.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-279"}}
{"id": "dm-algebra__linear_1d_composed-hard-279", "pool": "math", "split": "train", "question": "Let i(l) = 228 - 6*l. Let v be i(36). Solve v*b - 147 = -123 for b.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-280"}}
{"id": "dm-algebra__linear_1d_composed-hard-280", "pool": "math", "split": "train", "question": "Let z(a) = 10*a**2 + 50*a + 41. Let o(r) = -3*r**2 - 17*r - 14. Let c(f) = 7*o(f) + 2*z(f). Let l be c(-18). Solve -4*b = -l*b for b.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-281"}}
{"id": "dm-algebra__linear_1d_composed-hard-281", "pool": "math", "split": "train", "question": "Let j(r) = 198*r - 367. Let c be j(2). Solve -5*a - 4 = -c for a.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-282"}}
{"id": "dm-algebra__linear_1d_composed-hard-282", "pool": "math", "split": "train", "question": "Suppose 5*r = 5*m - 28 - 32, -m - 20 = 3*r. Suppose 0 = -5*n - 5*b - 170, 5*n - b = 22 - 168. Let f be n/120 + (-58)/r. Solve -f*i = -2*i for i.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-283"}}
{"id": "dm-algebra__linear_1d_composed-hard-283", "pool": "math", "split": "train", "question": "Let w = 15609 - 15566. Solve -18*z - w = 11 for z.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-284"}}
{"id": "dm-algebra__linear_1d_composed-hard-284", "pool": "math", "split": "train", "question": "Let a = 28 + -25. Let g(w) = -w**2 - 7*w + 2. Let p be g(-7). Let l = 157 - 152. Solve p + a = -l*t for t.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-285"}}
{"id": "dm-algebra__linear_1d_composed-hard-285", "pool": "math", "split": "train", "question": "Suppose w - 4*l + 12*l = 54, 0 = -4*w + 5*l + 68. Solve 50 = -7*z + w for z.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-286"}}
{"id": "dm-algebra__linear_1d_composed-hard-286", "pool": "math", "split": "train", "question": "Let q(i) = i**3 + 14*i**2 - 104*i - 159. Let c be q(-19). Let y = -11 + 13. Solve 2*w = -y*w - c for w.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-287"}}
{"id": "dm-algebra__linear_1d_composed-hard-287", "pool": "math", "split": "train", "question": "Let n be 257 - ((-2)/12)/(((-14)/(-12))/(-7)). Solve -53*g + n + 9 = 0 for g.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-288"}}
{"id": "dm-algebra__linear_1d_composed-hard-288", "pool": "math", "split": "train", "question": "Let c(l) = -2*l - 37. Let x be c(-18). Let j be (x/(-3))/((-3)/(-27)). Solve -1 - 8 = j*t for t.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-289"}}
{"id": "dm-algebra__linear_1d_composed-hard-289", "pool": "math", "split": "train", "question": "Let q = -51 - -56. Let d be (64/(-128))/((-1)/20). Solve 0 = d*s - q*s - 5 for s.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-290"}}
{"id": "dm-algebra__linear_1d_composed-hard-290", "pool": "math", "split": "train", "question": "Suppose -r = -2*r + 22. Let j = -20 + r. Let m(b) = -b**3 + 12*b**2 - 12*b + 14. Let c be m(11). Solve c*p = j*p + 3 for p.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-291"}}
{"id": "dm-algebra__linear_1d_composed-hard-291", "pool": "math", "split": "train", "question": "Let w be (-196)/245*(-1 - -11)/(-2). Solve 0 = 33*s + w*s - 2*s for s.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-292"}}
{"id": "dm-algebra__linear_1d_composed-hard-292", "pool": "math", "split": "train", "question": "Suppose 9 = -74*o + 71*o, -3*a + 288 = -o. Solve 97*g - 6 = a*g for g.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-293"}}
{"id": "dm-algebra__linear_1d_composed-hard-293", "pool": "math", "split": "train", "question": "Let q be (24/(27 - 3))/((-2)/(-122)). Solve 10*k + 31 - q = 0 for k.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-294"}}
{"id": "dm-algebra__linear_1d_composed-hard-294", "pool": "math", "split": "train", "question": "Let g(h) = 81*h + 97*h - 16 - h**2 - 188*h. Let k be g(-8). Solve k*d + 2*d = -8 for d.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-295"}}
{"id": "dm-algebra__linear_1d_composed-hard-295", "pool": "math", "split": "train", "question": "Let w = -1151 + 546. Let x be 5/35 + w/(-77). Let t = -1 - -3. Solve 2*u - x = -t for u.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-296"}}
{"id": "dm-algebra__linear_1d_composed-hard-296", "pool": "math", "split": "train", "question": "Suppose 3*l - 86 = -5*x, 4*l - 24*x = -25*x + 109. Suppose 6*j = l + 15. Solve 0 = -i - j*i - 40 for i.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-297"}}
{"id": "dm-algebra__linear_1d_composed-hard-297", "pool": "math", "split": "train", "question": "Let w = -6510 + 6570. Solve -w*o - 9 = -69*o for o.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-298"}}
{"id": "dm-algebra__linear_1d_composed-hard-298", "pool": "math", "split": "train", "question": "Let y(p) = -12*p**3 - 2*p**2 - 47*p - 102. Let q be y(-2). Solve q = -13*u + 119 for u.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-299"}}
{"id": "dm-algebra__linear_1d_composed-hard-299", "pool": "math", "split": "train", "question": "Let x(l) = 6 - l. Let i be x(6). Suppose -2*y = -2, -5*y + 1 = -4*k - i. Suppose 2*c + k = s + c, -2*s - c = -2. Solve -s = -3*m + 5 for m.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-300"}}
{"id": "dm-algebra__linear_1d_composed-hard-300", "pool": "math", "split": "train", "question": "Suppose -3*q + 5*f + 13 = 0, -8*f = q - 4*f + 7. Let u be 21 + -1 + 2 + (q - -2). Solve 6*a - u = a for a.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-301"}}
{"id": "dm-algebra__linear_1d_composed-hard-301", "pool": "math", "split": "train", "question": "Let x = 25873 + -25387. Solve x = 21*q + 318 for q.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-302"}}
{"id": "dm-algebra__linear_1d_composed-hard-302", "pool": "math", "split": "train", "question": "Let n = -520 + 541. Suppose 3*l + 5*m = 82, 2*l - 2*m - 3*m = 38. Solve n*s = l*s for s.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-303"}}
{"id": "dm-algebra__linear_1d_composed-hard-303", "pool": "math", "split": "train", "question": "Let a = 4358 + -4358. Solve 3*v - 185 + 194 = a for v.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-304"}}
{"id": "dm-algebra__linear_1d_composed-hard-304", "pool": "math", "split": "train", "question": "Let d(v) = 44*v + 816. Let f be d(-18). Solve 3*q + 27 = f for q.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-305"}}
{"id": "dm-algebra__linear_1d_composed-hard-305", "pool": "math", "split": "train", "question": "Suppose -2*q - y = -70, 5*q = 5*y - 53 + 258. Solve -32*x = -q*x - 35 for x.", "unit": "dimensionless", "value": "-7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-306"}}
{"id": "dm-algebra__linear_1d_composed-hard-306", "pool": "math", "split": "train", "question": "Let g be (3 + (-14)/(-5) - 5)*50/10. Let z(s) = 2*s - 3. Let c be z(4). Let w = c - 5. Solve w = -g*q + 4 - 0 for q.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-307"}}
{"id": "dm-algebra__linear_1d_composed-hard-307", "pool": "math", "split": "train", "question": "Suppose -s - 1 = 0, -33 = -2*o + 4*s + 25. Let t = o + -23. Solve -2*h - t = -3*h for h.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-308"}}
{"id": "dm-algebra__linear_1d_composed-hard-308", "pool": "math", "split": "train", "question": "Let l be 252/336 + 74/8. Solve 23*d = -l*d - 231 for d.", "unit": "dimensionless", "value": "-7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-309"}}
{"id": "dm-algebra__linear_1d_composed-hard-309", "pool": "math", "split": "train", "question": "Suppose -71*n - 46 = -94*n. Solve 3*w - n*w = 2 for w.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-310"}}
{"id": "dm-algebra__linear_1d_composed-hard-310", "pool": "math", "split": "train", "question": "Suppose -168 = 18*l - 2886. Solve 6*o + 205 - l = 0 for o.", "unit": "dimensionless", "value": "-9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-311"}}
{"id": "dm-algebra__linear_1d_composed-hard-311", "pool": "math", "split": "train", "question": "Let z = 6311 + -6309. Solve z*d - 11 + 7 = 0 for d.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-312"}}
{"id": "dm-algebra__linear_1d_composed-hard-312", "pool": "math", "split": "train", "question": "Suppose -198*p = -90*p - 90*p - 1530. Solve p*k - 116*k - 155 = 0 for k.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-313"}}
{"id": "dm-algebra__linear_1d_composed-hard-313", "pool": "math", "split": "train", "question": "Suppose 2*q - 9 = 4*a - 1, 0 = -5*q - 2*a - 4. Suppose q = -7*g - 11 + 74. Solve -6 = -5*o + g for o.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-314"}}
{"id": "dm-algebra__linear_1d_composed-hard-314", "pool": "math", "split": "train", "question": "Let w(s) = -s**2 - 6*s + 3. Let p be w(-6). Let q = -5700 - -5700. Solve -3 = -p*g - q*g for g.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-315"}}
{"id": "dm-algebra__linear_1d_composed-hard-315", "pool": "math", "split": "train", "question": "Let r be ((-6)/(-5) + -2)*-5. Suppose -23*c + 21*c - 2 = 0. Let j be c + (4 - r) - -4. Solve 0 = -u - j*u for u.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-316"}}
{"id": "dm-algebra__linear_1d_composed-hard-316", "pool": "math", "split": "train", "question": "Let b = -32642 + 32698. Solve 0 = a - b + 57 for a.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-317"}}
{"id": "dm-algebra__linear_1d_composed-hard-317", "pool": "math", "split": "train", "question": "Let t be (136/12)/((-6)/54). Let p = 105 + t. Solve -p*q + 20 = -8*q for q.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-318"}}
{"id": "dm-algebra__linear_1d_composed-hard-318", "pool": "math", "split": "train", "question": "Let f = -132 - -134. Suppose -3*s + 228 = 5*c, -f*s + 4*c = -3*s + 76. Let b = s - 61. Solve 4*n = n + b for n.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-319"}}
{"id": "dm-algebra__linear_1d_composed-hard-319", "pool": "math", "split": "train", "question": "Suppose 6*t = 1161 - 105. Let g be ((-30)/(-20))/(6/t). Let c be -2 + (-3)/((-6)/g). Solve -7*x - c = -3*x for x.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-320"}}
{"id": "dm-algebra__linear_1d_composed-hard-320", "pool": "math", "split": "train", "question": "Suppose -12 = 4*a, 5*o + 34*a - 37*a - 24 = 0. Solve 82 = -o*k + 73 for k.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-321"}}
{"id": "dm-algebra__linear_1d_composed-hard-321", "pool": "math", "split": "train", "question": "Suppose n = -4*n + 6050. Let g be (-8)/(-10)*n/44. Suppose -f - g = -5*w, 0 = 5*f + 10 - 0. Solve 0*t = t - w for t.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-322"}}
{"id": "dm-algebra__linear_1d_composed-hard-322", "pool": "math", "split": "train", "question": "Let c(s) = s - 2. Let j be c(6). Let y(h) be the third derivative of -h**6/40 + 13*h**5/60 - h**4/6 + h**2 - h. Let k be y(4). Solve k = -d - 3 + j for d.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-323"}}
{"id": "dm-algebra__linear_1d_composed-hard-323", "pool": "math", "split": "train", "question": "Let t be (-403)/(0 - -1) - -8. Let g = 395 + t. Solve g = 84*l - 85*l - 1 for l.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-324"}}
{"id": "dm-algebra__linear_1d_composed-hard-324", "pool": "math", "split": "train", "question": "Let v be (1/(-4))/((-2)/16). Let s(m) = -m**3 + 4*m**2 - 4*m + 2. Let g be s(v). Suppose 2*h - 4*r = 8, 8*h - 4 = 7*h - 2*r. Solve g*k + h = 12 for k.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-325"}}
{"id": "dm-algebra__linear_1d_composed-hard-325", "pool": "math", "split": "train", "question": "Suppose 8*u - 35 = u. Suppose 19 = 5*b - 2*r, -u*b - 4*r = -4 - 3. Suppose -4 = -b*y + 8. Solve 3 = -y*f - 17 for f.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-326"}}
{"id": "dm-algebra__linear_1d_composed-hard-326", "pool": "math", "split": "train", "question": "Suppose -2*n - n - 10 = -4*w, -5*w = 5*n - 30. Let m = -142 + 161. Suppose 0 = m*a - 80 - 15. Solve w*o = a*o + 4 for o.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-327"}}
{"id": "dm-algebra__linear_1d_composed-hard-327", "pool": "math", "split": "train", "question": "Suppose -217*t + 237 + 429 = 5*t. Suppose -3*u - 2*r - 18 = -4*u, -5*r + 45 = 2*u. Let j(i) = 2*i**2 + i - 1. Let g be j(1). Solve -g*v = t*v - u for v.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-328"}}
{"id": "dm-algebra__linear_1d_composed-hard-328", "pool": "math", "split": "train", "question": "Let b = -22740 - -22752. Solve 6*i - b*i - 18 = 0 for i.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-329"}}
{"id": "dm-algebra__linear_1d_composed-hard-329", "pool": "math", "split": "train", "question": "Suppose -10*n + 838 + 1512 = 0. Suppose 0 = -243*x + n*x. Solve x = -5*q - q + 30 for q.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-330"}}
{"id": "dm-algebra__linear_1d_composed-hard-330", "pool": "math", "split": "train", "question": "Let v(p) = 7*p**3 - p**2 - 30*p - 23. Let n(w) = -3*w**3 + 14*w + 12. Let x(f) = -5*n(f) - 2*v(f). Let g be x(-3). Solve -5*y - g = -7 for y.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-331"}}
{"id": "dm-algebra__linear_1d_composed-hard-331", "pool": "math", "split": "train", "question": "Let t(b) = -b**3 + 6*b**2 - 2*b + 8. Let w be t(6). Let d = 2433 - 2514. Let k be (w/(-6))/((-18)/d). Solve 8 = k*j - 5*j for j.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-332"}}
{"id": "dm-algebra__linear_1d_composed-hard-332", "pool": "math", "split": "train", "question": "Let p(r) = r**2 + 18*r + 42. Let z(x) = -4*x**2 - 73*x - 168. Let h(n) = 9*p(n) + 2*z(n). Let i be h(-14). Suppose -4*c + 8 = -8. Solve i - 34 = -c*y for y.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-333"}}
{"id": "dm-algebra__linear_1d_composed-hard-333", "pool": "math", "split": "train", "question": "Suppose 9*a = -0*a + 18. Solve a + 9 = -11*s for s.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-334"}}
{"id": "dm-algebra__linear_1d_composed-hard-334", "pool": "math", "split": "train", "question": "Suppose 21*l = 28*l - 28. Let u be 8 - 6/(-5)*(-10)/l. Suppose -n + 0 = 5*i + 8, 5*n = 5*i + 20. Solve n*m + u = m for m.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-335"}}
{"id": "dm-algebra__linear_1d_composed-hard-335", "pool": "math", "split": "train", "question": "Suppose -73*f - 4888 + 15003 = 12*f. Solve f - 7 = 28*y for y.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-336"}}
{"id": "dm-algebra__linear_1d_composed-hard-336", "pool": "math", "split": "train", "question": "Let o be (616/(-224))/(2/(-8)). Let g(u) = -u**3 + 6*u**2 - u + 1. Let x be g(6). Let v = x + o. Solve -4*l = -v*l - 2 for l.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-337"}}
{"id": "dm-algebra__linear_1d_composed-hard-337", "pool": "math", "split": "train", "question": "Let i = -393 - -403. Solve 13*v + i = 10 for v.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-338"}}
{"id": "dm-algebra__linear_1d_composed-hard-338", "pool": "math", "split": "train", "question": "Let h be (0/(-5))/((-1)/1). Suppose -332*r + 331*r + 16 = h. Let l be 1/(-2) + 2/4. Solve 0 = -4*d - l*d + r for d.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-339"}}
{"id": "dm-algebra__linear_1d_composed-hard-339", "pool": "math", "split": "train", "question": "Suppose -10*k - 27 = -77. Suppose f + a = 2*a + 101, -f - a + 97 = 0. Suppose f = 2*t + 3*t + 2*v, -81 = -4*t - v. Solve -k*x - t - 4 = 0 for x.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-340"}}
{"id": "dm-algebra__linear_1d_composed-hard-340", "pool": "math", "split": "train", "question": "Let x = 63 - 31. Suppose -x = n - 5*n. Suppose 6*s + n = 20. Solve 4 = -2*z - s*z for z.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-341"}}
{"id": "dm-algebra__linear_1d_composed-hard-341", "pool": "math", "split": "train", "question": "Let a be -1*(19 - 1)*(-80)/30. Suppose -12*s = -0*s - a. Solve s*y + y - 20 = 0 for y.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-342"}}
{"id": "dm-algebra__linear_1d_composed-hard-342", "pool": "math", "split": "train", "question": "Let x(d) = -d**2 + 47*d - 504. Let z be x(17). Solve 20 = z*l + 14*l for l.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-343"}}
{"id": "dm-algebra__linear_1d_composed-hard-343", "pool": "math", "split": "train", "question": "Let m(d) = -2*d**2 + 27*d + 18. Let j be m(14). Solve -5*y = 34 - j for y.", "unit": "dimensionless", "value": "-6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-344"}}
{"id": "dm-algebra__linear_1d_composed-hard-344", "pool": "math", "split": "train", "question": "Let j = -19 - -1. Let y be 0/j + (-12)/(-1). Suppose -y = -4*z - 0. Solve -i + z*i = -10 for i.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-345"}}
{"id": "dm-algebra__linear_1d_composed-hard-345", "pool": "math", "split": "train", "question": "Let q = 3548 + -3068. Solve -q = 3*p - 492 for p.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-346"}}
{"id": "dm-algebra__linear_1d_composed-hard-346", "pool": "math", "split": "train", "question": "Let r = -4042 - -4044. Solve -12 = 5*u - r for u.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-347"}}
{"id": "dm-algebra__linear_1d_composed-hard-347", "pool": "math", "split": "train", "question": "Let f = 144 - 129. Let t be -3*(4/(-15))/(6/f). Solve o - 1 - t = 0 for o.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-348"}}
{"id": "dm-algebra__linear_1d_composed-hard-348", "pool": "math", "split": "train", "question": "Let v be ((-60)/5)/(12/(-8)). Let x be (-10)/v + 25/(-40)*-2. Solve 3*l + 2 - 5 = x for l.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-349"}}
{"id": "dm-algebra__linear_1d_composed-hard-349", "pool": "math", "split": "train", "question": "Let z be (3 - 0)/(21/91). Solve 7*k + z = -8 for k.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-350"}}
{"id": "dm-algebra__linear_1d_composed-hard-350", "pool": "math", "split": "train", "question": "Let i = -9390 - -9395. Let r = -2 + 4. Solve -8 - r = i*g for g.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-351"}}
{"id": "dm-algebra__linear_1d_composed-hard-351", "pool": "math", "split": "train", "question": "Let b(k) = k**3 - 56*k**2 - 117*k + 88. Let c be b(58). Solve 32*x - c*x = 0 for x.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-352"}}
{"id": "dm-algebra__linear_1d_composed-hard-352", "pool": "math", "split": "train", "question": "Suppose -16285*i + 98 = -16283*i. Solve 30*q - i = 37*q for q.", "unit": "dimensionless", "value": "-7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-353"}}
{"id": "dm-algebra__linear_1d_composed-hard-353", "pool": "math", "split": "train", "question": "Suppose -7 = 2*h - 3. Let q be (-1)/3*27*h/2. Suppose 0 = -5*s + 4*s + 2*j + q, -45 = -5*s - 2*j. Solve -4*b - s = 3 for b.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-354"}}
{"id": "dm-algebra__linear_1d_composed-hard-354", "pool": "math", "split": "train", "question": "Let n(k) = 49*k - 3*k**3 - 45*k + 2 + 0*k**3 + k**2 + k**2. Let g be n(-1). Suppose 16 - 10 = g*s. Solve -s*t + 15 - 5 = 0 for t.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-355"}}
{"id": "dm-algebra__linear_1d_composed-hard-355", "pool": "math", "split": "train", "question": "Let f be (-2)/24 - 459296/(-384). Solve -7*w = f - 1210 for w.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-356"}}
{"id": "dm-algebra__linear_1d_composed-hard-356", "pool": "math", "split": "train", "question": "Let g = 169 - 140. Suppose 2*y = -2*f + 66, y - 2*f + f - 29 = 0. Solve -2*n = -y + g for n.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-357"}}
{"id": "dm-algebra__linear_1d_composed-hard-357", "pool": "math", "split": "train", "question": "Let r(p) = 0 + 1 - 4*p + 5*p. Let k be r(1). Suppose -33*d + 55 = -28*d - 4*h, 0 = 2*d - 3*h - 15. Solve -o = k*o - d for o.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-358"}}
{"id": "dm-algebra__linear_1d_composed-hard-358", "pool": "math", "split": "train", "question": "Let x(t) = -t**3 + 17*t**2 + 20*t - 31. Let j be x(18). Suppose -j*b + 54 = -3*p, b + 4*p + p = -6. Solve b = 30*h - 33*h for h.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-359"}}
{"id": "dm-algebra__linear_1d_composed-hard-359", "pool": "math", "split": "train", "question": "Let q(k) be the third derivative of -1/12*k**4 + 1/60*k**5 + 0*k + 1/120*k**6 + 0 - 8*k**2 - 1/6*k**3. Let l be q(-1). Solve 5*s + l = 11 for s.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-360"}}
{"id": "dm-algebra__linear_1d_composed-hard-360", "pool": "math", "split": "train", "question": "Suppose -7*n + 17 - 87 = 0. Let y be 3410/95 - n/95. Solve -10*o + o + y = 0 for o.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-361"}}
{"id": "dm-algebra__linear_1d_composed-hard-361", "pool": "math", "split": "train", "question": "Let w be -1 - 6*(-40)/15. Let g = w + -12. Let k = -140 + 160. Solve k = -g*d + 8 for d.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-362"}}
{"id": "dm-algebra__linear_1d_composed-hard-362", "pool": "math", "split": "train", "question": "Suppose -g - 17*g = -252. Suppose 19*n = 33*n - g. Solve -2*p = -3*p + n for p.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-363"}}
{"id": "dm-algebra__linear_1d_composed-hard-363", "pool": "math", "split": "train", "question": "Suppose 4*d - 270 = -22. Suppose 2*l = -k + d, -7*k = l - 8*k - 28. Let b be 13/3 - 40/l. Solve 0 = -b*h + 1 + 2 for h.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-364"}}
{"id": "dm-algebra__linear_1d_composed-hard-364", "pool": "math", "split": "train", "question": "Let l(q) = 16 - 11*q. Let k be l(0). Let a be 4*(-1*4 + 72/k). Solve 4*h - 10 = -a for h.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-365"}}
{"id": "dm-algebra__linear_1d_composed-hard-365", "pool": "math", "split": "train", "question": "Let o be (624/(-2))/((11 - 24) + (-392)/(-32)). Solve 24 = 419*k - o*k for k.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-366"}}
{"id": "dm-algebra__linear_1d_composed-hard-366", "pool": "math", "split": "train", "question": "Suppose 5*p + 3*b = 351, -1816*b = 3*p - 1820*b - 170. Solve -32*i + 10*i + p = 0 for i.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-367"}}
{"id": "dm-algebra__linear_1d_composed-hard-367", "pool": "math", "split": "train", "question": "Let c be (-6)/(-13) + 215712/1092. Solve -k - c = 65*k for k.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-368"}}
{"id": "dm-algebra__linear_1d_composed-hard-368", "pool": "math", "split": "train", "question": "Suppose 214 = 5*a + 204. Suppose 16*c = a*c. Solve -w + 2*w = c for w.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-369"}}
{"id": "dm-algebra__linear_1d_composed-hard-369", "pool": "math", "split": "train", "question": "Let n(v) = -5*v**3 - 13*v**2 + 16*v + 1. Let p(r) = 4*r**3 + 13*r**2 - 15*r - 1. Let q(i) = -6*n(i) - 7*p(i). Let s be 30/(-105) - (-3 - (-46)/(-14)). Let a be q(s). Solve -a - 6 = 5*u for u.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-370"}}
{"id": "dm-algebra__linear_1d_composed-hard-370", "pool": "math", "split": "train", "question": "Let z be 30 - (-7 + 4)*1. Solve -59*c = -z*c - 78 for c.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-371"}}
{"id": "dm-algebra__linear_1d_composed-hard-371", "pool": "math", "split": "train", "question": "Let l(z) = 5012*z**2 - 4 - 5*z - 5015*z**2 + 7. Let a be l(-2). Solve 3*c - a = 11 for c.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-372"}}
{"id": "dm-algebra__linear_1d_composed-hard-372", "pool": "math", "split": "train", "question": "Let c = 3904 + -3842. Solve 5*i - c = -26*i for i.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-373"}}
{"id": "dm-algebra__linear_1d_composed-hard-373", "pool": "math", "split": "train", "question": "Let c be (-6)/8 + 847/308. Suppose 2*d - 3 + 1 = 0. Solve -d = -y + c*y for y.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-374"}}
{"id": "dm-algebra__linear_1d_composed-hard-374", "pool": "math", "split": "train", "question": "Let u(v) = -v**3 - 30*v**2 - 220*v - 44. Let a be u(-12). Let s be (-4)/(-14) + 66/14. Solve a*c - s*c - 4 = 0 for c.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-375"}}
{"id": "dm-algebra__linear_1d_composed-hard-375", "pool": "math", "split": "train", "question": "Let t be 10*(4 - (-3)/(-12)*14). Let r = -5 - -6. Suppose -3*f + y = -1, -t*f + r = -2*y + y. Solve 0 = -f*h + 4*h for h.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-376"}}
{"id": "dm-algebra__linear_1d_composed-hard-376", "pool": "math", "split": "train", "question": "Let s be 2/1 + 0/4. Suppose 5*w = 12 + 8. Suppose s*x = z, -5*z + w*x = -x. Solve z = -2*n + n - 4 for n.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-377"}}
{"id": "dm-algebra__linear_1d_composed-hard-377", "pool": "math", "split": "train", "question": "Suppose 2*b + 8 = 3*u, -3*b = -3*u + 10 - 4. Suppose -4*y - 19 = -b*l - 7*y, -y = -5*l + 22. Solve -l*n + 2 = -3 for n.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-378"}}
{"id": "dm-algebra__linear_1d_composed-hard-378", "pool": "math", "split": "train", "question": "Let v = 1955 - 1829. Solve -v = -11*s - 82 for s.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-379"}}
{"id": "dm-algebra__linear_1d_composed-hard-379", "pool": "math", "split": "train", "question": "Suppose 0 = -0*d + 46*d - 1278 - 792. Solve 113*b = 122*b + d for b.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-380"}}
{"id": "dm-algebra__linear_1d_composed-hard-380", "pool": "math", "split": "train", "question": "Let v = 191 - -9. Let z = -197 + v. Solve -z = 2*g - 1 for g.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-381"}}
{"id": "dm-algebra__linear_1d_composed-hard-381", "pool": "math", "split": "train", "question": "Suppose 2*q - 474 = -124. Let n = 179 - q. Solve -2 = -2*j + n*j for j.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-382"}}
{"id": "dm-algebra__linear_1d_composed-hard-382", "pool": "math", "split": "train", "question": "Let v(t) = t**3 - 6*t**2 + 4*t + 5. Let m be v(5). Let k(l) be the first derivative of -2*l**3/3 + 3*l**2 + 4*l + 5. Let j be k(3). Solve m = -j*r + r + 12 for r.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-383"}}
{"id": "dm-algebra__linear_1d_composed-hard-383", "pool": "math", "split": "train", "question": "Suppose -3*z = s - 577, z - 580 = -2*z - 4*s. Let q = z + -190. Solve -q*p = -p - 3 for p.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-384"}}
{"id": "dm-algebra__linear_1d_composed-hard-384", "pool": "math", "split": "train", "question": "Suppose -63*x + 76 = 4*h - 55*x, 2*h - 34 = -2*x. Solve -9*o + 33 = h for o.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-385"}}
{"id": "dm-algebra__linear_1d_composed-hard-385", "pool": "math", "split": "train", "question": "Suppose -k - 13 = 2*k - w, -25 = 5*k - 5*w. Let n be 16/k*2/(-8). Let c(l) = 3*l**2 + l. Let v be c(-1). Solve h = n - v for h.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-386"}}
{"id": "dm-algebra__linear_1d_composed-hard-386", "pool": "math", "split": "train", "question": "Let b(s) = 332*s + 2027. Let c be b(-6). Solve c*d - 47 = 58 for d.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-387"}}
{"id": "dm-algebra__linear_1d_composed-hard-387", "pool": "math", "split": "train", "question": "Let b = -41 + 89. Let c = b - -42. Let i = -87 + c. Solve w - i = -0 for w.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-388"}}
{"id": "dm-algebra__linear_1d_composed-hard-388", "pool": "math", "split": "train", "question": "Suppose 0 = -2*s + 7*s - 45. Let a(h) = -h**2 + 10*h + 16. Let l be a(s). Let y(b) = -b**2 + 7*b - 3. Let t be y(6). Solve 0 = 2*j + t*j - l for j.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-389"}}
{"id": "dm-algebra__linear_1d_composed-hard-389", "pool": "math", "split": "train", "question": "Suppose -36*l = -43*l + 28. Suppose -5*d + 9 = -16. Suppose d*r - 2*k = -6*k + 21, 4*r - 2*k + l = 0. Solve -r = y + 2 for y.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-390"}}
{"id": "dm-algebra__linear_1d_composed-hard-390", "pool": "math", "split": "train", "question": "Let o(r) = r**2 + 4*r - 1. Let a be o(-4). Let z be a - 1*(-5 + 1). Let g(u) = -u**2 + 256*u - 12535. Let l be g(66). Solve z = l*i - 2 for i.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-391"}}
{"id": "dm-algebra__linear_1d_composed-hard-391", "pool": "math", "split": "train", "question": "Let t = -380 - -566. Let h = t + -183. Solve -3*n - 3 = -h for n.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-392"}}
{"id": "dm-algebra__linear_1d_composed-hard-392", "pool": "math", "split": "train", "question": "Let y = -1934 - -1956. Solve 12 = -17*n - y for n.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-393"}}
{"id": "dm-algebra__linear_1d_composed-hard-393", "pool": "math", "split": "train", "question": "Let h be (-30)/((-6)/(-48)*-20). Solve -h*n + 0*n - 48 = 0 for n.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-394"}}
{"id": "dm-algebra__linear_1d_composed-hard-394", "pool": "math", "split": "train", "question": "Let d(q) = -q**3 + 95*q**2 - 500*q - 6. Let r be d(6). Solve -13*n - 20*n = r for n.", "unit": "dimensionless", "value": "-6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-395"}}
{"id": "dm-algebra__linear_1d_composed-hard-395", "pool": "math", "split": "train", "question": "Suppose -35 = -4*n - 1 + 10. Solve 7*r + 12 = n*r for r.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-396"}}
{"id": "dm-algebra__linear_1d_composed-hard-396", "pool": "math", "split": "train", "question": "Let q = -1621 + 1645. Solve q = 382*f - 386*f for f.", "unit": "dimensionless", "value": "-6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-397"}}
{"id": "dm-algebra__linear_1d_composed-hard-397", "pool": "math", "split": "train", "question": "Let t = -52 - -50. Let n be (-12 - -12)/(8/t). Solve 3*g = 3 - n for g.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-398"}}
{"id": "dm-algebra__linear_1d_composed-hard-398", "pool": "math", "split": "train", "question": "Let q(b) = 311*b**2 - 1864*b + 36. Let n be q(6). Solve 7158*a - 7150*a = n for a.", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-399"}}
{"id": "dm-algebra__linear_1d_composed-hard-399", "pool": "math", "split": "train", "question": "Suppose 5*s + 5*l = 340, -2*l = -s + 24 + 35. Suppose s - 16 = 7*p. Suppose -15*a + p*a + 16 = 0. Solve 0 = a*y - 6 + 2 for y.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-400"}}
{"id": "dm-algebra__linear_1d_composed-hard-400", "pool": "math", "split": "train", "question": "Suppose -4 = -5*i - 4*t, -95*t - 3 = -2*i - 98*t. Solve 23*s - 22*s - 2 = i for s.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-401"}}
{"id": "dm-algebra__linear_1d_composed-hard-401", "pool": "math", "split": "train", "question": "Let l = -8258 + 8294. Solve l*b - 70 = 50*b for b.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-402"}}
{"id": "dm-algebra__linear_1d_composed-hard-402", "pool": "math", "split": "train", "question": "Let i be (60/(-24))/(5/(-124)). Suppose 0 = -i*w + 53*w + 9. Solve 7*t + w = 8*t for t.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-403"}}
{"id": "dm-algebra__linear_1d_composed-hard-403", "pool": "math", "split": "train", "question": "Let n be (-1)/(((16/98)/(-8))/1). Suppose 49 = 5*u - 3*a - 91, 0 = -u - 5*a. Let r = n - u. Solve -5*m = r - 4 for m.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-404"}}
{"id": "dm-algebra__linear_1d_composed-hard-404", "pool": "math", "split": "train", "question": "Let y be (-1)/5 + ((-96)/20 - 3). Let l be ((-12)/9)/(y/12). Suppose -2*i + 9 = 5*o, i - l*o + 0 - 9 = 0. Solve 0 = -5*z - i + 22 for z.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-405"}}
{"id": "dm-algebra__linear_1d_composed-hard-405", "pool": "math", "split": "train", "question": "Let h = -65 + 69. Suppose 10*v + h*v = 28. Suppose 4*i - 7*i + 6 = 0, v*d - 2*i = 0. Solve d = r - 3 for r.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-406"}}
{"id": "dm-algebra__linear_1d_composed-hard-406", "pool": "math", "split": "train", "question": "Let d(q) = -q**3 - 4*q**2 + 3. Let z be d(-4). Suppose 0 = -17*o + 20 - 3. Suppose -4*m + 4*k = 8, 3*k + o = 2*m + 7. Solve -z*h = -m - 6 for h.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-407"}}
{"id": "dm-algebra__linear_1d_composed-hard-407", "pool": "math", "split": "train", "question": "Let w = -5854 - -5854. Solve 44*p - 10*p - 204 = w for p.", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-408"}}
{"id": "dm-algebra__linear_1d_composed-hard-408", "pool": "math", "split": "train", "question": "Suppose 15 = -z - 5*m, 4*m - 3 = -3*z - 4. Let v be -1 + (7 - z) + 8/2. Solve 3*f + 2*f = v for f.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-409"}}
{"id": "dm-algebra__linear_1d_composed-hard-409", "pool": "math", "split": "train", "question": "Let c be (9 - -2)/(-2 + 3). Let x be (-5)/(-2)*12/15. Suppose k + 5 + x = 4*v, 4*k + 11 = -v. Solve 0 = 3*q - c - v for q.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_1d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_1d_composed", "level": "hard", "seed": "algebra__linear_1d_composed-hard-410"}}
{"id": "dm-algebra__linear_2d_composed-hard-0", "pool": "math", "split": "train", "question": "Let c(x) = x**2 + 29*x - 40. Let y be c(-21). Let m = y - -208. Solve m = 2*s - 4, 3*s + 3 = -4*k - 3 for k.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-1"}}
{"id": "dm-algebra__linear_2d_composed-hard-1", "pool": "math", "split": "train", "question": "Let a = 15 - 10. Let k = 382 + -2268. Let l = k + 1886. Solve -4*n - a*b + 26 = 0, l*n + 2*b + 12 = 4*n for n.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-2"}}
{"id": "dm-algebra__linear_2d_composed-hard-2", "pool": "math", "split": "train", "question": "Suppose -3*l = -2*l - 4*b - 4, -l = 3*b + 3. Let f be 10/8 - (-6)/8. Suppose -2 = -g, 2*g + 1 = s + f. Solve 5*m = 25, -u - s*m + m + 7 = l for u.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-3"}}
{"id": "dm-algebra__linear_2d_composed-hard-3", "pool": "math", "split": "train", "question": "Suppose 5*r + c - 14 = 3*c, 0 = -3*r - 5*c - 4. Suppose -5*x = -2 - 3. Let j = 0 - -9. Solve j = 3*p - r*f, -p = p + f + x for p.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-4"}}
{"id": "dm-algebra__linear_2d_composed-hard-4", "pool": "math", "split": "train", "question": "Suppose 298 = -87*k + 1429. Let n be 2 - -3 - (0 + 1). Suppose l - n*x - 36 = 0, x = 3*l - k - 51. Solve 4*w + 40 = 5*m, -l = -3*m - 2*m for w.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-5"}}
{"id": "dm-algebra__linear_2d_composed-hard-5", "pool": "math", "split": "train", "question": "Suppose -13*q = 3*u - 16*q - 69, -8 = -u - 2*q. Solve 5*t - 52 = -47, 3*x - 3*t = -u for x.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-6"}}
{"id": "dm-algebra__linear_2d_composed-hard-6", "pool": "math", "split": "train", "question": "Let z(r) = r**3 + r**2 + 3*r + 6. Let y be z(4). Suppose -15*x + y = -7. Solve -4*a = -h + x, 2*a = 2*h + 4 - 12 for a.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-7"}}
{"id": "dm-algebra__linear_2d_composed-hard-7", "pool": "math", "split": "train", "question": "Suppose -37*s = -43*s + 48. Suppose 3*q - s = -q + 4*g, 14 = 4*q + 2*g. Solve -2*y - u = -3, -8 = q*y + u - 2*u for y.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-8"}}
{"id": "dm-algebra__linear_2d_composed-hard-8", "pool": "math", "split": "train", "question": "Suppose 22*t + 71 = -0*t + 93*t. Let p(h) = -h**3 - 4*h**2 + 4*h - 1. Let i be p(-5). Suppose -4*a - 16 = 4*u, 0 = 2*u - i*a - 0*a - 22. Solve 4*z + 5*m = -t, 0*m + u = -z - m for z.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-9"}}
{"id": "dm-algebra__linear_2d_composed-hard-9", "pool": "math", "split": "train", "question": "Suppose -18*k + 6*k = 19*k - 4*k. Solve 2*u - 2*x + 18 - 24 = k, x + 1 = 0 for u.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-10"}}
{"id": "dm-algebra__linear_2d_composed-hard-10", "pool": "math", "split": "train", "question": "Suppose 44 = -2*s + 13*s. Suppose -91 + 106 = 5*h. Solve l + s*l + 25 = h*x, x - 5 = 0 for l.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-11"}}
{"id": "dm-algebra__linear_2d_composed-hard-11", "pool": "math", "split": "train", "question": "Let t be (-60)/(-24)*(-18)/15*-115. Let l = -345 + t. Solve -4*w - 18 = z - 3*z, l = -5*w + z - 21 for w.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-12"}}
{"id": "dm-algebra__linear_2d_composed-hard-12", "pool": "math", "split": "train", "question": "Suppose 84*h - 23*h = 10*h. Solve -4*t - 2*z + 4*z = h, -3*z = -2*t - 4 for t.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-13"}}
{"id": "dm-algebra__linear_2d_composed-hard-13", "pool": "math", "split": "train", "question": "Let v = 5 - 0. Let a(q) = -8 + q - v + 0*q. Let n be a(15). Solve 8 = -4*y - 4*i, 0*y + n*y + i = -2 for y.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-14"}}
{"id": "dm-algebra__linear_2d_composed-hard-14", "pool": "math", "split": "train", "question": "Let i be (4 - -3 - 12) + 21/3. Solve i = j, -3*n - 4*j - 8 + 1 = 0 for n.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-15"}}
{"id": "dm-algebra__linear_2d_composed-hard-15", "pool": "math", "split": "train", "question": "Suppose -c - 4*i + 7 = 0, -5 = i - 6*i. Solve 4*d + 9 = -5*a + 24, a = c*d + 3 for a.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-16"}}
{"id": "dm-algebra__linear_2d_composed-hard-16", "pool": "math", "split": "train", "question": "Suppose 4*m - 15*m = -3*m + 19*m. Solve -5*z - 2 = 4*s, m = -s + 3*z + 8 for s.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-17"}}
{"id": "dm-algebra__linear_2d_composed-hard-17", "pool": "math", "split": "train", "question": "Suppose 0 = -0*y + y - 3. Suppose l = y*l - 6. Let x be (66/(-132))/(1/(-6)). Solve -2*d = 2*g, 3*g + l*d - x = -d for g.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-18"}}
{"id": "dm-algebra__linear_2d_composed-hard-18", "pool": "math", "split": "train", "question": "Let p = -3575 - -3575. Solve 0*w + 6 = -3*w + 3*n, p = w + 5*n - 16 for w.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-19"}}
{"id": "dm-algebra__linear_2d_composed-hard-19", "pool": "math", "split": "train", "question": "Suppose -14*i = -3*i - 1155. Suppose 0*k - 2*k + 136 = 0. Let g = i - k. Solve 2*u = 2*h - 18, -u + 4*u + g = 5*h for u.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-20"}}
{"id": "dm-algebra__linear_2d_composed-hard-20", "pool": "math", "split": "train", "question": "Suppose -184*u + 290 = -155*u. Solve -2*k + 1 = -u*r + 9*r, 0 = 5*k - 5*r + 5 for k.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-21"}}
{"id": "dm-algebra__linear_2d_composed-hard-21", "pool": "math", "split": "train", "question": "Let m(w) = w**3 + 54*w**2 - 59*w - 214. Let b be m(-55). Solve 4*h + b = y, -4*h = -2*h + 4 for y.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-22"}}
{"id": "dm-algebra__linear_2d_composed-hard-22", "pool": "math", "split": "train", "question": "Let b be 1/(-1)*(-6 - 2/(-1)). Suppose 3*p = 4*d - 24, 29*d - b = 33*d + 4*p. Solve -s = -d*w - 14, -3*s + 8*s - 25 = 0 for w.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-23"}}
{"id": "dm-algebra__linear_2d_composed-hard-23", "pool": "math", "split": "train", "question": "Let k(i) = 9*i + 588. Let a be k(-65). Solve -2*g - 5 = -5*w, a*w - 12 = -3 for g.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-24"}}
{"id": "dm-algebra__linear_2d_composed-hard-24", "pool": "math", "split": "train", "question": "Let b be 4/3 + (3/(-12))/(75/(-10100)). Solve -2*w = 5*k - b, -4*k + 9*k + 5*w = 50 for k.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-25"}}
{"id": "dm-algebra__linear_2d_composed-hard-25", "pool": "math", "split": "train", "question": "Let y(b) = -b**2 + 36*b - 313. Let t be y(21). Solve -3*d = 3*l - d - t, 21 = 4*l - d for l.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-26"}}
{"id": "dm-algebra__linear_2d_composed-hard-26", "pool": "math", "split": "train", "question": "Suppose -m = 2*m, 5*t + 2*m = 15. Suppose j - 6 = 2*u - 8, 3*j = -t*u - 6. Solve 2*d + 2 = 4*w, u = 2*d - 3*d - 1 for w.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-27"}}
{"id": "dm-algebra__linear_2d_composed-hard-27", "pool": "math", "split": "train", "question": "Let t be 7/18*290 - (-22)/99. Suppose 5 = -4*r + t. Suppose -21 = -r*l + 20*l. Solve 0 = -5*v + 2*z - 4*z, z = -l*v for v.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-28"}}
{"id": "dm-algebra__linear_2d_composed-hard-28", "pool": "math", "split": "train", "question": "Let i(h) = h**3 - 13*h**2 + 21*h + 38. Let l be i(11). Suppose 85 = 4*r - l. Suppose 5*g = -3 + 13. Solve -f = -g*n + 3*f + r, f + 5 = 0 for n.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-29"}}
{"id": "dm-algebra__linear_2d_composed-hard-29", "pool": "math", "split": "train", "question": "Suppose 3*g - 1 = -5*b + 4, 4*g - 26 = 3*b. Suppose g*n + 2*z - 40 = 0, -16 = -2*n + 2*z + z. Suppose -5*q + 3*q - x + n = 0, 2*q - 5*x - 20 = 0. Solve 0*p - 5*p + 30 = q*v, -p - 3*v = -8 for p.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-30"}}
{"id": "dm-algebra__linear_2d_composed-hard-30", "pool": "math", "split": "train", "question": "Let y = -6004 - -6017. Solve 5*x - 4*d + 17 = 0, x + 8*d - y*d - 5 = 0 for x.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-31"}}
{"id": "dm-algebra__linear_2d_composed-hard-31", "pool": "math", "split": "train", "question": "Let p(w) = -w**3 - 11*w**2 - 8*w + 22. Let c be p(-10). Let n be 50*((-15)/10)/((-9)/6). Suppose -i - 2*b = 7, 19 = -c*i + 5*b + n. Solve 0 = i*r - 5*q - 10, q - 8 = -r - 2 for r.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-32"}}
{"id": "dm-algebra__linear_2d_composed-hard-32", "pool": "math", "split": "train", "question": "Let f(s) = s**2 - 39*s - 270. Let l = -875 - -920. Let j be f(l). Solve 2*t - 6*d - 9 = -5*d, j = 2*t - 3*d - 7 for t.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-33"}}
{"id": "dm-algebra__linear_2d_composed-hard-33", "pool": "math", "split": "train", "question": "Let w = -2 + 5. Let b(p) = 72 - 7*p. Suppose -35 = 4*z - 7*z - 5*v, 0 = 4*z - v - 39. Let f be b(z). Solve -k - w = f*t, -k + 45 = 4*k - 5*t for k.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-34"}}
{"id": "dm-algebra__linear_2d_composed-hard-34", "pool": "math", "split": "train", "question": "Let c be (-3)/((-42)/(-4)) - (-320)/140. Suppose c = 16*y - 15*y, -10 = j - 5*y. Solve -2*r = 4*l + 2*r + 4, j = 2*r + 8 for l.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-35"}}
{"id": "dm-algebra__linear_2d_composed-hard-35", "pool": "math", "split": "train", "question": "Let s = 9 - 7. Let z = 50 + -66. Let n = 3 - z. Solve 10 = 4*q - 3*u - n, -s*u - 11 = -q for q.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-36"}}
{"id": "dm-algebra__linear_2d_composed-hard-36", "pool": "math", "split": "train", "question": "Suppose 40 = 3*z - 2*z. Let c = z - 26. Suppose -4*j + 6 = -2*v, -9*v + 5 = -5*j - 4*v. Solve w = -3*g + c, -j*w + 2*w = -10 for g.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-37"}}
{"id": "dm-algebra__linear_2d_composed-hard-37", "pool": "math", "split": "train", "question": "Let o(m) = 26*m - 67. Let k be o(3). Let f(s) = -2*s**3 - 19*s**2 - 8*s + 16. Let q be f(-9). Solve 2*b - k - q = 4*l, 0 = 4*b - 4 for l.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-38"}}
{"id": "dm-algebra__linear_2d_composed-hard-38", "pool": "math", "split": "train", "question": "Suppose -16*h = -21*h + 15. Suppose 0*u + 2*i = u - 9, -u = i - h. Solve -2*a + 3*r - u = 0, a + 1 = -0*r + 3*r for a.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-39"}}
{"id": "dm-algebra__linear_2d_composed-hard-39", "pool": "math", "split": "train", "question": "Let f be (4/20 + (-2)/(-10))*5. Suppose f*w + 8*n - 4*n - 26 = 0, 1 = w - 2*n. Solve -5*s = -2*c + 7, -5*c = -s - s - w for c.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-40"}}
{"id": "dm-algebra__linear_2d_composed-hard-40", "pool": "math", "split": "train", "question": "Suppose 4*l = 4*q + 120, 0 = -0*l + 2*l - 8*q - 84. Solve l*j + 25 = 5*g + 21*j, 0 = g - 5*j - 25 for g.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-41"}}
{"id": "dm-algebra__linear_2d_composed-hard-41", "pool": "math", "split": "train", "question": "Let i(k) = k**2 + 3*k - 5. Let s be i(-5). Let f(r) = 3*r + 31. Let d be f(13). Let c be -2 + 13/(65/d). Solve -4*o - c = s*v, 5 = -2*v - o + 2 for v.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-42"}}
{"id": "dm-algebra__linear_2d_composed-hard-42", "pool": "math", "split": "train", "question": "Let h(d) be the third derivative of d**5/60 - d**4/12 - 2*d**3 - 309*d**2. Suppose 13 - 33 = -4*k. Let f be h(k). Solve -5*l - 15 = 5*q, -f*l = 2*q - 0*q + 11 for l.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-43"}}
{"id": "dm-algebra__linear_2d_composed-hard-43", "pool": "math", "split": "train", "question": "Let a = 1079 + -1079. Suppose -m = -5*b - 12, 3*m - 5*b = -0*m + 16. Solve 0 = v - m*y - 2, a = 3*v + 2*y + y + 12 for v.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-44"}}
{"id": "dm-algebra__linear_2d_composed-hard-44", "pool": "math", "split": "train", "question": "Let h(f) be the third derivative of 0*f + 0*f**4 + 0*f**3 + 1/60*f**5 - f**2 + 0. Let y be h(-2). Solve -5*u = -0*v + y*v - 28, 3*v + 4*u = 22 for v.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-45"}}
{"id": "dm-algebra__linear_2d_composed-hard-45", "pool": "math", "split": "train", "question": "Suppose 18 = 45*r - 117. Solve 5*s + 0*m = -3*m + 8, 0 = s - r*m + 2 for s.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-46"}}
{"id": "dm-algebra__linear_2d_composed-hard-46", "pool": "math", "split": "train", "question": "Suppose -21*l = -36*l + 45. Solve r = -7*a + 3*a + 8, 5*r = l*a - 29 for a.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-47"}}
{"id": "dm-algebra__linear_2d_composed-hard-47", "pool": "math", "split": "train", "question": "Let v = -241 - -251. Solve 2*i - r + v = 0, 4*r - 17 = -1 for i.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-48"}}
{"id": "dm-algebra__linear_2d_composed-hard-48", "pool": "math", "split": "train", "question": "Let a be 10/2*561/55. Let l = a - 31. Suppose -2*o + 12*o - l = 0. Solve 0 = 2*s - o*b, -s + 2*b = 4*s - 9 for s.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-49"}}
{"id": "dm-algebra__linear_2d_composed-hard-49", "pool": "math", "split": "train", "question": "Let f = -20605 + 20633. Solve -3*a + 6 = 0, 2*s - 3*a - 12 + f = 0 for s.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-50"}}
{"id": "dm-algebra__linear_2d_composed-hard-50", "pool": "math", "split": "train", "question": "Let b be (-6)/2*236/(-354). Solve 2*l + b*t + 21 = -3*l, 15 = -5*l - 5*t for l.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-51"}}
{"id": "dm-algebra__linear_2d_composed-hard-51", "pool": "math", "split": "train", "question": "Let j = 3281 + -3277. Let m be 2/6 - (-10)/6. Suppose 4*p = 5*n - 7, -m*p + n = j*n - 13. Solve 0 = -p*g + y - 3, 0 = 2*y - 6*y + 4 for g.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-52"}}
{"id": "dm-algebra__linear_2d_composed-hard-52", "pool": "math", "split": "train", "question": "Suppose -6183 = 11*p - 1178. Let k = 458 + p. Solve 4*u + 4 = k*s - 7, -3*u = s + 18 for u.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-53"}}
{"id": "dm-algebra__linear_2d_composed-hard-53", "pool": "math", "split": "train", "question": "Let l = 344 - 256. Suppose -l + 88 = 2*b. Solve -16 + 6 = 3*h - 2*w, -4*h - w - 17 = b for h.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-54"}}
{"id": "dm-algebra__linear_2d_composed-hard-54", "pool": "math", "split": "train", "question": "Let y(c) = c**3 + 8*c**2 + 6*c + 8. Suppose 12 = -4*i - 16. Let f be y(i). Suppose 2*r + 9 = f. Solve -v - a = 8, 2*v - r*a + 4 = -a for v.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-55"}}
{"id": "dm-algebra__linear_2d_composed-hard-55", "pool": "math", "split": "train", "question": "Suppose -31*c = -101*c + 399*c - 987. Solve 0 = -c*y - 2*a - 7, 63*y = 67*y + 5*a + 14 for y.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-56"}}
{"id": "dm-algebra__linear_2d_composed-hard-56", "pool": "math", "split": "train", "question": "Let f = -1 + 2. Let b(s) = 81*s - 1059. Let k be b(13). Let n be f + 2 + (-9 - k). Solve 0 = -2*t - w - 2, -3*t + w - 8 = -n*t for t.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-57"}}
{"id": "dm-algebra__linear_2d_composed-hard-57", "pool": "math", "split": "train", "question": "Suppose 33 = 3*l - 4*o + 153, 0 = 3*l - 3*o + 117. Let s = 64 + l. Suppose -6*k = -10*k + s. Solve 5*g - 10 = -z - 3, -3*g + 5*z - k = 0 for g.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-58"}}
{"id": "dm-algebra__linear_2d_composed-hard-58", "pool": "math", "split": "train", "question": "Let p = 231 - 220. Solve p*n = 13*n + 4*c + 8, -3*n - 3*c = 12 for n.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-59"}}
{"id": "dm-algebra__linear_2d_composed-hard-59", "pool": "math", "split": "train", "question": "Suppose -510 + 1680 = 5*k + 34*k. Solve m + 22 = 3*c + k, -2*c = 5*m - 23 for m.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-60"}}
{"id": "dm-algebra__linear_2d_composed-hard-60", "pool": "math", "split": "train", "question": "Let a(c) = -126*c - 1887. Let i be a(-15). Solve w = 5*x - 10, 3*x + i = -3*w - 9 for w.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-61"}}
{"id": "dm-algebra__linear_2d_composed-hard-61", "pool": "math", "split": "train", "question": "Suppose -290 = -84*u - 38. Solve -h + 2 = -n - 2*n, -u*h + 6 = 2*n for n.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-62"}}
{"id": "dm-algebra__linear_2d_composed-hard-62", "pool": "math", "split": "train", "question": "Suppose -3*m + 264 = 5*r, -2*r + 7 + 99 = m. Suppose 3*f + 15*f - r = 0. Solve 2*a - 4 = f*z, 2*a - 8 = -2*a - 3*z for a.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-63"}}
{"id": "dm-algebra__linear_2d_composed-hard-63", "pool": "math", "split": "train", "question": "Suppose c + 4 = 2*t, -3*c - c + t + 12 = 0. Let b(w) = w**2 - 16*w + 52. Let a be b(c). Solve -4*p = 5*y + 13, -2*p - a*y + 0*y = 8 for p.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-64"}}
{"id": "dm-algebra__linear_2d_composed-hard-64", "pool": "math", "split": "train", "question": "Suppose -3*w + 5*b = -37, 0 = 2*w - 2*b - 17 - 1. Suppose -8 = -4*t + w. Solve -6 = h - t*h, 4*k + 5*h - 11 = 0 for k.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-65"}}
{"id": "dm-algebra__linear_2d_composed-hard-65", "pool": "math", "split": "train", "question": "Let n = 20210 - 20205. Solve -x + 9*c - 2 = 6*c, 3*c - 10 = n*x for x.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-66"}}
{"id": "dm-algebra__linear_2d_composed-hard-66", "pool": "math", "split": "train", "question": "Let w be 3*(-2)/12*-4. Suppose -187*l = -141*l - 138. Solve l*g - 5*h = -10, 3 - 9 = -w*g - 3*h for g.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-67"}}
{"id": "dm-algebra__linear_2d_composed-hard-67", "pool": "math", "split": "train", "question": "Let r(t) = t**2 - 14*t - 146. Let m be r(-7). Solve -4*f - m = -2*j + 7, 5*j + 2*f + 16 = 0 for j.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-68"}}
{"id": "dm-algebra__linear_2d_composed-hard-68", "pool": "math", "split": "train", "question": "Suppose -q + 19 = -2*n, 35*q - 28 = 31*q + 2*n. Solve 0 = q*w + 4*g + 27, 5*w = 6*w - g + 2 for w.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-69"}}
{"id": "dm-algebra__linear_2d_composed-hard-69", "pool": "math", "split": "train", "question": "Suppose 54349*l = 54334*l + 45. Solve 0 = -z - l*z - 4*y + 28, -5*z + 30 = 4*y for z.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-70"}}
{"id": "dm-algebra__linear_2d_composed-hard-70", "pool": "math", "split": "train", "question": "Let u(m) = 64 - 3*m. Let r be u(-12). Let s = r - 98. Suppose -3*v = x - 7*v + 11, 0 = s*x + 4*v - 26. Solve 11*c - 12 = -3*p + 6*c, c + 2 = -x*p for p.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-71"}}
{"id": "dm-algebra__linear_2d_composed-hard-71", "pool": "math", "split": "train", "question": "Let p be (56/(-18))/((-50)/225). Let h(n) = n + 10. Let v be h(-7). Suppose 24 = y + v*y - 2*t, -4*y - 3*t = -p. Solve -2*w - 11 = -y*j + 2*j, -w + 4*j = 18 for w.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-72"}}
{"id": "dm-algebra__linear_2d_composed-hard-72", "pool": "math", "split": "train", "question": "Let l(c) = -21*c**3 - 3*c**2 + 6*c + 19. Let n be l(-3). Let q = n - 539. Solve -2*t - 24 = -6*s + 2*s, 8 = q*s + t for s.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-73"}}
{"id": "dm-algebra__linear_2d_composed-hard-73", "pool": "math", "split": "train", "question": "Suppose -1 = 8*n - 1. Suppose n = 2*u - 8, -6*f + 2*f = u - 252. Let m = 64 - f. Solve b = -3*h - 11, 1 = m*b - 2*h - 1 for b.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-74"}}
{"id": "dm-algebra__linear_2d_composed-hard-74", "pool": "math", "split": "train", "question": "Let s be ((624/20)/13)/((-9)/(-120)). Solve -4*k - 2*p = 20, -s = 5*k - p - 7 for k.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-75"}}
{"id": "dm-algebra__linear_2d_composed-hard-75", "pool": "math", "split": "train", "question": "Let k(f) = f**3 - 8*f**2 + 15*f - 9. Let z be k(6). Suppose 9 = -p - 4*s, 2*p + 0*s - z = s. Solve -4*t + d = -11, p*t = -2*d - 0*d for t.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-76"}}
{"id": "dm-algebra__linear_2d_composed-hard-76", "pool": "math", "split": "train", "question": "Suppose -5*a = -5*b + 15 + 25, 3*b = -3*a - 12. Solve -2*n + b = 3*s - 6*s, -2*n - 6 = s for n.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-77"}}
{"id": "dm-algebra__linear_2d_composed-hard-77", "pool": "math", "split": "train", "question": "Let q(w) = w**3 + 14*w**2 - 93*w - 2. Let i be q(5). Solve 5*t - 2 + i = -a, -20 = -5*a for t.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-78"}}
{"id": "dm-algebra__linear_2d_composed-hard-78", "pool": "math", "split": "train", "question": "Let h = -302 + 268. Let u be (-2)/9 + (-858)/27. Let c = u - h. Solve -2*d - c*i + 9 = 1, 20 = 2*d + 5*i for d.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-79"}}
{"id": "dm-algebra__linear_2d_composed-hard-79", "pool": "math", "split": "train", "question": "Let q = -3 + 5. Let g be 411/9*-3 - -1. Let y = -133 - g. Solve 0 = 4*n + 4*h, -y*n = 2*h - q - 3 for n.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-80"}}
{"id": "dm-algebra__linear_2d_composed-hard-80", "pool": "math", "split": "train", "question": "Let r(w) = 213 - 16*w. Let p be r(13). Suppose 2*v + 24 = p*u - 0*v, 21 = 2*u + 3*v. Solve 3*j - 3*x = -u, -3*j + 3*x - 16 = 2*j for j.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-81"}}
{"id": "dm-algebra__linear_2d_composed-hard-81", "pool": "math", "split": "train", "question": "Let t(h) = h**3 - 10*h**2 + 7*h + 12. Let f be t(10). Let m be (1 + -83)*(9 + -10). Let y = f - m. Solve 2 = -2*w, -6*o + 3*o - w - 4 = y for o.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-82"}}
{"id": "dm-algebra__linear_2d_composed-hard-82", "pool": "math", "split": "train", "question": "Suppose -4*q + x + 32 = 0, 0 = 6*q - 2*q + 2*x - 44. Let y be 20/90 - (-88)/q. Let g = -301 + 305. Solve -g*r + 2*p + 16 = 0, y - 4 = r - p for r.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-83"}}
{"id": "dm-algebra__linear_2d_composed-hard-83", "pool": "math", "split": "train", "question": "Let s be 12/(-4) - ((-2176)/84 + 18/(-189)). Solve -4*p - 4*n + s = 35, p + 3 = 3*n for p.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-84"}}
{"id": "dm-algebra__linear_2d_composed-hard-84", "pool": "math", "split": "train", "question": "Suppose 2025 + 1665 = -5*t + 5*s, 0 = t + 3*s + 722. Let x = -734 - t. Solve -5*u = 5*i - 30, -2*i - 3*u - u + 16 = x for i.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-85"}}
{"id": "dm-algebra__linear_2d_composed-hard-85", "pool": "math", "split": "train", "question": "Let c = 68 - 68. Suppose c = 2*k - 5*o + 68, -3*o - 237 = 4*k - 49. Let g = k - -61. Solve m + 3*w = 0, -4*w - g = -4*m + w for m.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-86"}}
{"id": "dm-algebra__linear_2d_composed-hard-86", "pool": "math", "split": "train", "question": "Suppose 5*l - 46 = 4. Suppose -102*n - 125*n + 213*n = 0. Solve n = 5*c + k - 13, c - l = 2*c - 4*k for c.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-87"}}
{"id": "dm-algebra__linear_2d_composed-hard-87", "pool": "math", "split": "train", "question": "Let z(p) = 794*p + 17473. Let f be z(-22). Solve -3*j = 5*m + 5, -m + f*j = 2 - 1 for m.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-88"}}
{"id": "dm-algebra__linear_2d_composed-hard-88", "pool": "math", "split": "train", "question": "Let m be (-1)/(0 + (-4)/16). Suppose v - 6*v + 2*p = -9, -2*v - 6 = -m*p. Suppose 0 = -d + g + v, 4*d + 2*g + 2*g = 28. Solve -d*b + 2*n + 19 = 0, 3 - 20 = -3*b + 4*n for b.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-89"}}
{"id": "dm-algebra__linear_2d_composed-hard-89", "pool": "math", "split": "train", "question": "Let v(k) = k**3 + 5*k**2 - 11*k + 3. Let j be v(-6). Let b = j - 8. Let h = b - 11. Solve 2*p - g + h = g, 5*p + 2*g + 21 = 0 for p.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-90"}}
{"id": "dm-algebra__linear_2d_composed-hard-90", "pool": "math", "split": "train", "question": "Let d(j) = -20*j**2 - 182*j + 15. Let s be d(-9). Solve 3*f + 7 = c, 3*f = 29*c - s*c + 13 for c.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-91"}}
{"id": "dm-algebra__linear_2d_composed-hard-91", "pool": "math", "split": "train", "question": "Suppose g = 5*g + 4. Let l = g - -4. Let q = -20230 - -20233. Solve 0*h + q*i = 3*h + 12, l*i = -4*h - 2 for h.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-92"}}
{"id": "dm-algebra__linear_2d_composed-hard-92", "pool": "math", "split": "train", "question": "Suppose -3*x = r + x - 76, 4*r - 4*x = 244. Let g = r - 61. Solve 4*v = 5*m - 0*v - 1, 0 = m - g*v + 2 for m.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-93"}}
{"id": "dm-algebra__linear_2d_composed-hard-93", "pool": "math", "split": "train", "question": "Let k = -6 - -80. Suppose 2*g - 131 = 5*c, 2*g = -g - c + 239. Let x = g - k. Solve -x*o + 2*q = 0, 5*o - 8 = -2*q + 1 for o.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-94"}}
{"id": "dm-algebra__linear_2d_composed-hard-94", "pool": "math", "split": "train", "question": "Let u(s) = 2 - 3*s + 3*s + 2*s + 6. Let y be u(-5). Let v be 5/y*198/(-55). Solve f + 10 = -5*m + 2*f, -2*m + 3*f + v = 0 for m.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-95"}}
{"id": "dm-algebra__linear_2d_composed-hard-95", "pool": "math", "split": "train", "question": "Let n(t) be the first derivative of -t**3/3 - 7*t**2/2 - t - 9. Let q be n(-7). Let l be 9/(-3)*(8/(-4) - q). Solve 2*x + 3*o - 2 = o, -l*x - 9 = -o for x.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-96"}}
{"id": "dm-algebra__linear_2d_composed-hard-96", "pool": "math", "split": "train", "question": "Suppose b - 5*n = 30, 406*b + 30 = 404*b - 5*n. Solve b = 3*w + 4*z + 3 + 5, -w - 6 = -2*z for w.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-97"}}
{"id": "dm-algebra__linear_2d_composed-hard-97", "pool": "math", "split": "train", "question": "Suppose 28*t - 27*t = -5. Let b = 0 - t. Suppose 2*z = 3*x + 65 - 20, b*z = x + 80. Solve -4*w = 4*f - 12 - 20, -5*w + z = 0 for f.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-98"}}
{"id": "dm-algebra__linear_2d_composed-hard-98", "pool": "math", "split": "train", "question": "Suppose -5*w = -w + 32. Let r be 69*(w/12)/((-4)/6). Let m = r + -67. Solve 0 = f + 2*k - 1, -3*k - 10 = m*k for f.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-99"}}
{"id": "dm-algebra__linear_2d_composed-hard-99", "pool": "math", "split": "train", "question": "Let d(a) be the third derivative of a**6/60 - a**5/20 - 5*a**4/24 + 4*a**3/3 - 99*a**2. Let i be d(2). Solve 10*x - 5*x + 21 = l, 0 = 4*x + i*l + 28 for x.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-100"}}
{"id": "dm-algebra__linear_2d_composed-hard-100", "pool": "math", "split": "train", "question": "Let x(c) = 476 - 59*c. Let b be x(8). Solve -3*q + 5*q = u + 12, -b*q + 12 = u for u.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-101"}}
{"id": "dm-algebra__linear_2d_composed-hard-101", "pool": "math", "split": "train", "question": "Suppose 3*n - 365 = -59. Let c = n - 112. Let q be (32/c - 0)/((-3)/15). Solve 0 = -2*s + 2*t + 4, 2*t - 6 + q = 5*s for s.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-102"}}
{"id": "dm-algebra__linear_2d_composed-hard-102", "pool": "math", "split": "train", "question": "Let b(d) = -d**2 - 13*d - 18. Let y be b(-11). Let c(v) = v**3 - 15*v**2 - 5*v + 15. Let z be c(15). Let r be (2/(-3))/(8/z). Solve -3*h - 3*p = 12, 0 = -y*h + r*h + 3*p + 14 for h.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-103"}}
{"id": "dm-algebra__linear_2d_composed-hard-103", "pool": "math", "split": "train", "question": "Suppose 5*n = -2*m + 2 - 6, 0 = -4*n - 2*m - 4. Let v = 60 - 57. Suppose -v*x + 19 = p, -3*p = -0*x - 4*x - 57. Solve -2*o - 1 = c - 6*o, n = 4*c - o + p for c.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-104"}}
{"id": "dm-algebra__linear_2d_composed-hard-104", "pool": "math", "split": "train", "question": "Let y be 536/76 + 32/(-608). Solve -y*s + 11*s - 4*a + 20 = 0, s = -2*a - 5 for s.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-105"}}
{"id": "dm-algebra__linear_2d_composed-hard-105", "pool": "math", "split": "train", "question": "Let z = -19900 - -19907. Solve -w + 9 = 2*m, -7*w - 2*m + z = -8*w for w.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-106"}}
{"id": "dm-algebra__linear_2d_composed-hard-106", "pool": "math", "split": "train", "question": "Suppose 0*i = -i + 4. Suppose -122 = -3*d - 86. Let m(z) = z - 9. Let o be m(d). Solve -i*c = l + 13, -2*l + 7 + o = -c for l.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-107"}}
{"id": "dm-algebra__linear_2d_composed-hard-107", "pool": "math", "split": "train", "question": "Let f(w) = 38*w**3 - 4*w**2 - w - 1. Let r be f(2). Let l = r - 283. Solve 5*s = -3*h + 17, 0*h - l*h + 12 = 4*s for s.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-108"}}
{"id": "dm-algebra__linear_2d_composed-hard-108", "pool": "math", "split": "train", "question": "Suppose 0 = -x + 3, 4*p + 4*x + 272 = 308. Solve 2*s - p = 4*j - 3*j, 0 = -2*s - 2*j + 12 for s.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-109"}}
{"id": "dm-algebra__linear_2d_composed-hard-109", "pool": "math", "split": "train", "question": "Let c(f) = -2*f**2 - 38*f + 242. Let x be c(5). Solve x*w = -4*d + 12, 8*d + 3*w = 11*d + 9 for d.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-110"}}
{"id": "dm-algebra__linear_2d_composed-hard-110", "pool": "math", "split": "train", "question": "Let n(l) = l + 14. Suppose -2*u = -3*u - 11. Let k be n(u). Suppose -s = k*s. Solve 0 = 3*b + 15, s = 2*q + 5*b + 21 - 6 for q.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-111"}}
{"id": "dm-algebra__linear_2d_composed-hard-111", "pool": "math", "split": "train", "question": "Let j(v) = 41*v - 1226. Let n be j(30). Solve -n*s = a - 15 - 3, -5*a + 2*s = -2 for a.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-112"}}
{"id": "dm-algebra__linear_2d_composed-hard-112", "pool": "math", "split": "train", "question": "Suppose -h - 3*v + 4 + 25 = 0, 4*h - 3*v = 146. Let l be h/(-28)*(1 + -13). Solve 0 = 4*f - 12, -f = b + 3*f - l for b.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-113"}}
{"id": "dm-algebra__linear_2d_composed-hard-113", "pool": "math", "split": "train", "question": "Let s(k) = k**2 + 154*k + 4635. Let v be s(-113). Solve 0 = -5*t - g - 2*g - v, g = 1 for t.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-114"}}
{"id": "dm-algebra__linear_2d_composed-hard-114", "pool": "math", "split": "train", "question": "Let i(y) = 9*y**3 + y**2 + 2*y - 3. Let o be i(1). Let f(j) = j**2 - 11*j + 17. Let b be f(o). Let p be (135/(-18))/(b/2). Solve 0 = u - 3*n - n - 12, -5*n = 3*u + p for u.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-115"}}
{"id": "dm-algebra__linear_2d_composed-hard-115", "pool": "math", "split": "train", "question": "Let r be 7 + 2 + ((-2 + 20)/(-3) - -1). Solve 0 = 4*a + 2*p - 18, -3*a + r*p + 5 = -3 for a.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-116"}}
{"id": "dm-algebra__linear_2d_composed-hard-116", "pool": "math", "split": "train", "question": "Let k be 2 - (2 + -5)/1. Let r(u) = u**2 - u - 15. Let q be r(k). Solve -c - 3*c - 4 = -5*a, q*c = -5 for a.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-117"}}
{"id": "dm-algebra__linear_2d_composed-hard-117", "pool": "math", "split": "train", "question": "Let h be (-124)/7 + 6/(-21). Let z be -6*2*3/h. Let o = -31163 + 31167. Solve -2 = -u - o*g, -4*u - z + 10 = -4*g for u.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-118"}}
{"id": "dm-algebra__linear_2d_composed-hard-118", "pool": "math", "split": "train", "question": "Suppose 58*t + 78*t - 83 = 189. Solve 0 = 2*h + 6, -3 + 0 = -t*l + h for l.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-119"}}
{"id": "dm-algebra__linear_2d_composed-hard-119", "pool": "math", "split": "train", "question": "Let x be 15/(-9)*(3 - 6). Suppose -5*w = x*m - 10*w - 55, 4*m + w - 54 = 0. Suppose -257 = 30*i - 1277. Solve -3*o - m = -4*o - 2*t, 3*o + 5*t = i for o.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-120"}}
{"id": "dm-algebra__linear_2d_composed-hard-120", "pool": "math", "split": "train", "question": "Let w = -4215 - -4218. Solve 0 = w*h + 2*h + 4*b + 19, 5*h + 16 = -b for h.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-121"}}
{"id": "dm-algebra__linear_2d_composed-hard-121", "pool": "math", "split": "train", "question": "Let t = -18415 + 18420. Solve -2*m + 50 - 40 = -t*v, 0 = -4*v - 3*m - 8 for v.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-122"}}
{"id": "dm-algebra__linear_2d_composed-hard-122", "pool": "math", "split": "train", "question": "Suppose 5*h = -5*f + 900, -2*f + 2*h = -117 - 231. Suppose f = j + 172. Suppose -5*d = 5*p - 15, 1 = -3*p + 3*d + 4. Solve s + o - 15 = j*o, -4*o - 10 = -p*s for s.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-123"}}
{"id": "dm-algebra__linear_2d_composed-hard-123", "pool": "math", "split": "train", "question": "Suppose 5*q - 10 = -0*q. Let r(p) = 6*p**2 - 7*p + 8. Let w be r(2). Let g be 32/6 - (-9 - (-168)/w). Solve d + 2*d - q = -t, -4*t = -d + g for d.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-124"}}
{"id": "dm-algebra__linear_2d_composed-hard-124", "pool": "math", "split": "train", "question": "Let j(w) = -6*w**3 + 4*w**2 + 11*w + 9. Let p be j(-1). Solve 0 = -4*d - 2*t + p, -d + 4*t = -14 - 6 for d.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-125"}}
{"id": "dm-algebra__linear_2d_composed-hard-125", "pool": "math", "split": "train", "question": "Suppose -68 + 26 = -14*r. Let z be 10/r*(-2628)/(-365). Solve -15 + 0 = 3*u, -i = -4*u - z for i.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-126"}}
{"id": "dm-algebra__linear_2d_composed-hard-126", "pool": "math", "split": "train", "question": "Suppose 2*z + 22 = -2*b - b, -2*z + b = 14. Let m(p) = -16*p - 128. Let f be m(z). Solve f = -4*w - 5*k + 5 - 0, -2*w + 4*k = -22 for w.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-127"}}
{"id": "dm-algebra__linear_2d_composed-hard-127", "pool": "math", "split": "train", "question": "Let j be 4/(-7) - (-3 + 36/(-14)). Suppose -2*f = -6*f + 4*u, j*f + 4*u - 45 = 0. Solve 3*q - 1 - 2 = 0, 0 = f*x + 4*q + 16 for x.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-128"}}
{"id": "dm-algebra__linear_2d_composed-hard-128", "pool": "math", "split": "train", "question": "Suppose 0 = 68*c - 78*c + 190. Let k(r) = r**3 - 20*r**2 + 22*r - 53. Let f be k(c). Solve -2*t - 11 = 3*x, 2 = -f*t - 2 for x.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-129"}}
{"id": "dm-algebra__linear_2d_composed-hard-129", "pool": "math", "split": "train", "question": "Suppose -434 + 434 = -27*j. Solve p + 3 = v, j = 13*p - 18*p - 5*v - 5 for p.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-130"}}
{"id": "dm-algebra__linear_2d_composed-hard-130", "pool": "math", "split": "train", "question": "Let t = -314 - -357. Suppose -2*b + 14 = -5*y + t, -y + b = -7. Solve -5*n - 22 = -y*q - 7, -n = -4*q for n.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-131"}}
{"id": "dm-algebra__linear_2d_composed-hard-131", "pool": "math", "split": "train", "question": "Let f(y) = 2*y**2 + 51*y + 324. Let b be f(-10). Solve 0 = -2*p - 2*p + 3*n + 7, -5*p + 2*n = -b for p.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-132"}}
{"id": "dm-algebra__linear_2d_composed-hard-132", "pool": "math", "split": "train", "question": "Suppose 0 = -2*x + 56 - 42. Let y be (-6 + x)*(-1)/(-2)*2. Solve 5*f - 8 - y = 3*r, 0 = -3*r - 4*f - 9 for r.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-133"}}
{"id": "dm-algebra__linear_2d_composed-hard-133", "pool": "math", "split": "train", "question": "Suppose -65*n + 209 + 15 = -9*n. Suppose r + 0 - 7 = 0. Solve 2*l = 2*u - 18, n*u + 6*l - r*l - 21 = 0 for u.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-134"}}
{"id": "dm-algebra__linear_2d_composed-hard-134", "pool": "math", "split": "train", "question": "Suppose 9*h - 15*h + 840 = 0. Suppose 0 = -6*s + 11*s - h. Suppose -10*i - s = -78. Solve 2*l - 2 = 5*o + i, 0 = o - 5*l - 17 for o.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-135"}}
{"id": "dm-algebra__linear_2d_composed-hard-135", "pool": "math", "split": "train", "question": "Suppose -1597 = -5*b - 19*b - 925. Solve b = 4*c + 4*q, 3*q - 5 - 1 = 2*c for c.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-136"}}
{"id": "dm-algebra__linear_2d_composed-hard-136", "pool": "math", "split": "train", "question": "Let w(y) = -2*y**2 - 32*y + 4. Let i be w(-16). Let v be (2 - -4) + -8 + i. Solve g = -2*j + 2, 5*j - v = -2*g + 2 for g.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-137"}}
{"id": "dm-algebra__linear_2d_composed-hard-137", "pool": "math", "split": "train", "question": "Let w = -2299 - -2316. Solve -3*x = 2*m - 7, 2*m = 23*x - 18*x - w for x.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-138"}}
{"id": "dm-algebra__linear_2d_composed-hard-138", "pool": "math", "split": "train", "question": "Suppose 2*x + 256 + 974 = -3*o, -o - 420 = 4*x. Let k = o + 411. Solve -5*l - 13 = 3*d - k*l, -l + 26 = -5*d for d.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-139"}}
{"id": "dm-algebra__linear_2d_composed-hard-139", "pool": "math", "split": "train", "question": "Suppose 1424 + 2513 = 64*c + 63*c. Solve s - c = -p - 28, -2*s = 4 for p.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-140"}}
{"id": "dm-algebra__linear_2d_composed-hard-140", "pool": "math", "split": "train", "question": "Let b = 449407 + -449387. Let y = 3 + 6. Let w = -5 + y. Solve 2*s - 5*d = -3*s + b, -w*s + d = -4 for s.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-141"}}
{"id": "dm-algebra__linear_2d_composed-hard-141", "pool": "math", "split": "train", "question": "Let g be 1*33 - 140/(42 + -22). Solve 8 = -2*l - 3*w, -5*l + 64*w - 60*w = -g for l.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-142"}}
{"id": "dm-algebra__linear_2d_composed-hard-142", "pool": "math", "split": "train", "question": "Let t(f) be the third derivative of -5*f**4/24 - 11*f**3/6 + 14*f**2. Let l(u) = -7*u - 17. Let b(a) = -5*l(a) + 8*t(a). Let m be b(-3). Solve 2*r - 4*r - 2 = 0, -3*r - m = -3*k for k.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-143"}}
{"id": "dm-algebra__linear_2d_composed-hard-143", "pool": "math", "split": "train", "question": "Let b(q) = q**2 + q + 5. Let j be b(0). Suppose j = -w + 2*h, 7 = 4*h - 9. Solve 4*y - 3*o + 0 = -5, -y = -w*o + 8 for y.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-144"}}
{"id": "dm-algebra__linear_2d_composed-hard-144", "pool": "math", "split": "train", "question": "Let q(n) = 2*n**3 - n. Let w(g) = 7*g**3 + 14*g**2 - 37*g - 34. Let x(p) = 3*q(p) - w(p). Let b be x(-16). Solve -2*m = 5*o - o - 6, -o - b*m - 3 = 0 for o.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-145"}}
{"id": "dm-algebra__linear_2d_composed-hard-145", "pool": "math", "split": "train", "question": "Let j = 6 + -1. Suppose 6*q + 162 - 174 = 0. Solve -2*c = -4*z - c - j, 2 = q*z + 4*c for z.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-146"}}
{"id": "dm-algebra__linear_2d_composed-hard-146", "pool": "math", "split": "train", "question": "Suppose g = 6 + 1. Let z be (2/4)/(9/4 + -2). Suppose 5*q = 5*s + 40, 1 = -2*q - q - z*s. Solve 4*a - 30 = -q*w - g, 4*w = 20 for a.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-147"}}
{"id": "dm-algebra__linear_2d_composed-hard-147", "pool": "math", "split": "train", "question": "Let m = -5724 - -5726. Solve 0 = 4*x - 6*x + m*o, -3*o - 5 = -2*x for x.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-148"}}
{"id": "dm-algebra__linear_2d_composed-hard-148", "pool": "math", "split": "train", "question": "Suppose 4*y - 3*w - 29 = 0, -2*y + 37 = 3*y - 4*w. Let n be (2 + -1)*(2/4)/((-17)/(-408)). Solve 3*j = -z + y*z - 16, 4*j - n = -3*z for j.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-149"}}
{"id": "dm-algebra__linear_2d_composed-hard-149", "pool": "math", "split": "train", "question": "Let i(d) be the second derivative of -d**3/6 - 5*d**2/2 - 2*d - 261. Let c = 0 + -9. Let j be i(c). Solve -5*y - 4*x = 28, x = -j*y - 16 - 2 for y.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-150"}}
{"id": "dm-algebra__linear_2d_composed-hard-150", "pool": "math", "split": "train", "question": "Let a(i) = -7*i - 60. Let g be ((-56)/(-24) + -2)*-27. Let q be a(g). Suppose 0*b = 5*b. Solve 1 = n + q*f - b, 0 = -3*n + 3*f - 21 for n.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-151"}}
{"id": "dm-algebra__linear_2d_composed-hard-151", "pool": "math", "split": "train", "question": "Suppose 0 = -25*t + 1583 - 508. Suppose -t*j = -50*j + 126. Solve -4*k + 2*g - 5*g = -26, -2*k - 4*g + j = 0 for k.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-152"}}
{"id": "dm-algebra__linear_2d_composed-hard-152", "pool": "math", "split": "train", "question": "Let r = 116 - 64. Let j = 56 - r. Solve -25 = -5*o, j*d - 4*o + 22 = 2*d for d.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-153"}}
{"id": "dm-algebra__linear_2d_composed-hard-153", "pool": "math", "split": "train", "question": "Suppose -3*j - 3*x = 6, 125*j + 5*x = 130*j - 50. Let u(k) = 5*k**3 - 3*k**2 + k - 6. Let t(f) = 6*f**3 - 3*f**2 + 2*f - 6. Let m(g) = 4*t(g) - 5*u(g). Let c be m(j). Solve -2*p + 8 = -c, 10 = 5*q + 4*p for q.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-154"}}
{"id": "dm-algebra__linear_2d_composed-hard-154", "pool": "math", "split": "train", "question": "Let j be 675/75*2/6. Solve -m - 9 = k, j*k = 5*m + 133 - 120 for m.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-155"}}
{"id": "dm-algebra__linear_2d_composed-hard-155", "pool": "math", "split": "train", "question": "Let c = -37841 + 37852. Solve 0 = -5*w + 20, 5*b - 16*w = -c*w - 45 for b.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-156"}}
{"id": "dm-algebra__linear_2d_composed-hard-156", "pool": "math", "split": "train", "question": "Let c(x) = -4*x - 23. Let u be c(-7). Let j be (-142)/(5 + 12/(-4)). Let a = j - -74. Solve u*i + 5 = -3*d, 2*d + 3*i - 13 = -a*d for d.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-157"}}
{"id": "dm-algebra__linear_2d_composed-hard-157", "pool": "math", "split": "train", "question": "Let g = -2 - -2. Suppose 0 = 4*w - 4*t - 36, 2*w - 5*t + 7 = 40. Suppose w*d - 13 = -s, 2*d + 3*s + 7 = -2*s. Solve d*i + 4*b + 16 = 0, 4*i + 6 = -2*b - g*b for i.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-158"}}
{"id": "dm-algebra__linear_2d_composed-hard-158", "pool": "math", "split": "train", "question": "Let w = -6358 + 6361. Solve -4*z - w*a - 20 = 0, -4*z - a = a + 16 for z.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-159"}}
{"id": "dm-algebra__linear_2d_composed-hard-159", "pool": "math", "split": "train", "question": "Let c = -12561 - -12565. Solve 0 = c*v + 11*o - 6*o + 5, 3*o - 5 = -4*v for v.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-160"}}
{"id": "dm-algebra__linear_2d_composed-hard-160", "pool": "math", "split": "train", "question": "Suppose 0*q + 6*q - 12 = 0. Suppose q*d = 18 - 8. Solve 3*o - x + 6 = 22, d*x - 15 = -4*o for o.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-161"}}
{"id": "dm-algebra__linear_2d_composed-hard-161", "pool": "math", "split": "train", "question": "Let b = 161 + -149. Let l be 528/6*3/b. Solve 0 = -4*f + 5*x + l, 3*f + 0*f - x = 11 for f.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-162"}}
{"id": "dm-algebra__linear_2d_composed-hard-162", "pool": "math", "split": "train", "question": "Let k be (5/5 - 1)/(-2). Suppose 0 = -3*o - k*o - 5*r - 11, 0 = 4*o + 3*r + 33. Let p be (-28)/o + 3*(-3)/27. Solve -a + 26 = -i - 4*i, i = -p*a - 3 for i.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-163"}}
{"id": "dm-algebra__linear_2d_composed-hard-163", "pool": "math", "split": "train", "question": "Let d = 27 - 24. Solve 3 = d*t, t = 3*g - 5 - 3 for g.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-164"}}
{"id": "dm-algebra__linear_2d_composed-hard-164", "pool": "math", "split": "train", "question": "Let y(s) = -s**3 - 3*s**2 - 2*s. Let f be y(-2). Let w(k) = k**3 - k**2 + 3. Let o be w(f). Let u(l) = -l**2 - 18*l - 29. Let t be u(-16). Solve -o*g - 24 = t*r, -3*g = -4*r - 0*g - 11 for r.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-165"}}
{"id": "dm-algebra__linear_2d_composed-hard-165", "pool": "math", "split": "train", "question": "Suppose 265 = -4*r - f, -3*r + 5*r + 120 = 2*f. Let o = -49 - r. Solve -2*u = 5*i - o, 0 = -3*u - 2*u + 15 for i.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-166"}}
{"id": "dm-algebra__linear_2d_composed-hard-166", "pool": "math", "split": "train", "question": "Let j be (-8)/5*(2000/96)/25*-3. Suppose -w - w + 6 = 0. Suppose w*f + z - 4 = 3*z, -2*z + 10 = j*f. Solve 0 = -4*m - 4*o - 16, 3*m = -2*o - 10 + f for m.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-167"}}
{"id": "dm-algebra__linear_2d_composed-hard-167", "pool": "math", "split": "train", "question": "Let m(g) = g**3 + 5*g**2 + 2*g + 2. Let k be m(-5). Let b be -3 + 7/((-7)/k). Let s = -68 - -72. Solve 0*f - b*t = -s*f + 5, -t - 1 = -f for f.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-168"}}
{"id": "dm-algebra__linear_2d_composed-hard-168", "pool": "math", "split": "train", "question": "Suppose 16*w = 40*w - 72. Suppose -w*z = 2*n + z, -n + 2*z + 4 = 0. Solve 1 = 3*a + 7*q - 6*q, -n*a - 11 = 3*q for a.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-169"}}
{"id": "dm-algebra__linear_2d_composed-hard-169", "pool": "math", "split": "train", "question": "Let b(q) = 2*q**3 - 31*q**2 - 15*q - 9. Let h be b(16). Solve -3*d + z = -11, 35*d + 2*z = 36*d - h for d.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-170"}}
{"id": "dm-algebra__linear_2d_composed-hard-170", "pool": "math", "split": "train", "question": "Let a = -103 - -74. Let f = a - -34. Let m = -72 + 75. Solve -5*i = f*w + 25, i + 6*w - m = 7*w for i.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-171"}}
{"id": "dm-algebra__linear_2d_composed-hard-171", "pool": "math", "split": "train", "question": "Let i(h) = 2*h + 31. Let c be i(-14). Let s(n) = 73 - 23*n. Let o be s(c). Solve m + 12 = o*x + 2, -2 = -m for x.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-172"}}
{"id": "dm-algebra__linear_2d_composed-hard-172", "pool": "math", "split": "train", "question": "Suppose 23 = 2*m - 4*s - 127, -4*m + 4*s + 304 = 0. Suppose 16*v - m = -29. Solve n = -f - v*n - 1, 2*f - 5*n = -15 for f.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-173"}}
{"id": "dm-algebra__linear_2d_composed-hard-173", "pool": "math", "split": "train", "question": "Let r(j) = 7*j**3 + 2*j**2 + 8*j + 4. Let t(u) = -13*u**3 - 4*u**2 - 14*u - 7. Let h(q) = -11*r(q) - 6*t(q). Let s be h(2). Suppose 0 = 4*b + 2*z - 6, -3*b - s = -2*z. Solve -3*k + 3*n = b, -5*k - 4*n = -k + 32 for k.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-174"}}
{"id": "dm-algebra__linear_2d_composed-hard-174", "pool": "math", "split": "train", "question": "Let r = 9110 + -9103. Solve -r + 2 = -h + 5*w, 10 = 2*h + 2*w for h.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-175"}}
{"id": "dm-algebra__linear_2d_composed-hard-175", "pool": "math", "split": "train", "question": "Let w = -5 - -10. Let u(x) = -x**3 - 9*x**2 + 2. Let c be u(-9). Suppose -47*s + 10*s + 333 = 0. Solve s = p + c*p, t - 17 = -w*p for t.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-176"}}
{"id": "dm-algebra__linear_2d_composed-hard-176", "pool": "math", "split": "train", "question": "Let i(p) = p**2 + 8*p - 39. Let q = -58 - -62. Let m be i(q). Solve 0*s - 2*s + 1 = -3*r, -4*s + m = r for r.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-177"}}
{"id": "dm-algebra__linear_2d_composed-hard-177", "pool": "math", "split": "train", "question": "Let p be 1110/333*3/(0 + -1 - -3). Solve -2*c - 35 + 27 = -2*y, -p*y - 30 = 5*c for y.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-178"}}
{"id": "dm-algebra__linear_2d_composed-hard-178", "pool": "math", "split": "train", "question": "Suppose 144*z = 140*z + 60. Solve 5*r - 7 = b, -5*b - 8 + z = -4*r for b.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-179"}}
{"id": "dm-algebra__linear_2d_composed-hard-179", "pool": "math", "split": "train", "question": "Suppose 7*j - 10 = 2*j. Let a(t) be the third derivative of -3*t**4/4 + 2*t**3/3 - 5*t**2 + 3*t. Let s be a(0). Solve -2 = -3*g + 4*y, -9 = s*g + j*y + 3 for g.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-180"}}
{"id": "dm-algebra__linear_2d_composed-hard-180", "pool": "math", "split": "train", "question": "Let i(s) = 1659 - 414*s. Let j be i(4). Suppose 5*n + y = 84, -60 = -5*n + 3*y + 2*y. Solve 5*p + n = j*q - q, -5*p + 5*q = 10 for p.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-181"}}
{"id": "dm-algebra__linear_2d_composed-hard-181", "pool": "math", "split": "train", "question": "Suppose 30*y - 199 = -27*y - 28. Solve 5*w + 8 = -0*v - y*v, 5*w - 3*v + 2 = 0 for w.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-182"}}
{"id": "dm-algebra__linear_2d_composed-hard-182", "pool": "math", "split": "train", "question": "Let u be 319/99 - (12/27)/2. Suppose 2*c + 24 = u*b - c, -4*b = 4*c + 8. Solve -5*x - 13 = b*f + 2, 0 = 5*x for f.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-183"}}
{"id": "dm-algebra__linear_2d_composed-hard-183", "pool": "math", "split": "train", "question": "Suppose -145*j - 12*j - 213 + 684 = 0. Solve -2*i = -7*k - 3, -j*k - 17 = -8*i + 4*i for k.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-184"}}
{"id": "dm-algebra__linear_2d_composed-hard-184", "pool": "math", "split": "train", "question": "Suppose -5*o = 2*g - 658, -5*o + 664 = -0*o - 4*g. Suppose -3*r - r + 4*m = -o, -2*m = -5*r + 162. Solve 4*w = 5*l + 5 + 4, -4*l = 3*w + r for l.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-185"}}
{"id": "dm-algebra__linear_2d_composed-hard-185", "pool": "math", "split": "train", "question": "Let b = 16324 - 16307. Solve 90*c - 3*t - 24 = 93*c, -b = 2*c + 3*t for c.", "unit": "dimensionless", "value": "-7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-186"}}
{"id": "dm-algebra__linear_2d_composed-hard-186", "pool": "math", "split": "train", "question": "Suppose -5*r = -77 - 53. Suppose 2*b = b - 2*b + 9. Suppose -n - 4*w + w - 10 = 0, -b*n + 5*w = -r. Solve -5*x + 2*d - 7 = 0, n*x - 5*d + 4 = -3 for x.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-187"}}
{"id": "dm-algebra__linear_2d_composed-hard-187", "pool": "math", "split": "train", "question": "Suppose 2*t + 30 = 4*p, 5*p - 68*t + 70*t - 6 = 0. Solve -4*w - 11*b = -15*b + 4, 0 = p*w + 4*b + 20 for w.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-188"}}
{"id": "dm-algebra__linear_2d_composed-hard-188", "pool": "math", "split": "train", "question": "Suppose -2*n + 8 = 4*s, -5*s + n - 4*n = -8. Let r(f) = -s*f - 35 + 12*f**2 + f + f + f**3 + 14. Let q be r(-12). Solve 5*p = q*d + 2*d - 30, 0 = 4*p + 8 for d.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-189"}}
{"id": "dm-algebra__linear_2d_composed-hard-189", "pool": "math", "split": "train", "question": "Let n(g) = 30*g**2 - 24*g + 23. Let k be n(1). Solve 24*z - 21 = s + k*z, -s = 2*z + 9 for s.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-190"}}
{"id": "dm-algebra__linear_2d_composed-hard-190", "pool": "math", "split": "train", "question": "Let z = 30648 + -30644. Solve z*h = -5*q + 7, -104*q + 103*q = 3*h + 3 for q.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-191"}}
{"id": "dm-algebra__linear_2d_composed-hard-191", "pool": "math", "split": "train", "question": "Let s be (2*4 + 645/(-86))*0. Solve 12 = 4*i + 30*u - 28*u, 2*i + 5*u - 22 = s for i.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-192"}}
{"id": "dm-algebra__linear_2d_composed-hard-192", "pool": "math", "split": "train", "question": "Let o(p) = 23*p + 211. Let u be o(-9). Solve u*h + 2*n = 2, -7 = -10*h + 6*h - 3*n for h.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-193"}}
{"id": "dm-algebra__linear_2d_composed-hard-193", "pool": "math", "split": "train", "question": "Suppose -3*z + 21 = 3*i, 5*i + z - 5 = 14. Let t(w) = 7*w + 191. Let s be t(-27). Suppose 3*f = 7*f - 4, s*x = f + i. Solve -5*m - 8 = 3*u + 8, x*m - 4 = 4*u for m.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-194"}}
{"id": "dm-algebra__linear_2d_composed-hard-194", "pool": "math", "split": "train", "question": "Suppose -714 - 331 = -3*y + 5*h, 3*y + 4*h = 1054. Let v = 353 - y. Solve 0 = -a + n + 9, 0*a - v*n = 2*a + 2 for a.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-195"}}
{"id": "dm-algebra__linear_2d_composed-hard-195", "pool": "math", "split": "train", "question": "Suppose 74 = -9*v + 11*v + 9*l, -26 = -2*v - l. Let q(s) = s**2 - 6*s + 5. Let m be q(5). Solve m = -2*h + v, -5*d + 11 = -d - h for d.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-196"}}
{"id": "dm-algebra__linear_2d_composed-hard-196", "pool": "math", "split": "train", "question": "Let o be -9 - (-15 - (-11 - -8)). Solve 3*n + 25 - o = 2*w, 2*w - 2 = -2*n for n.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-197"}}
{"id": "dm-algebra__linear_2d_composed-hard-197", "pool": "math", "split": "train", "question": "Suppose -240 = -82*a + 88*a. Let h be a/(-6)*6/8. Solve 4*u + 13 = x, h*u - 8 = -5*x + 7 for x.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-198"}}
{"id": "dm-algebra__linear_2d_composed-hard-198", "pool": "math", "split": "train", "question": "Let j(b) = -b**3 - 65*b**2 - 879*b - 94. Let m be j(-19). Solve 2*t + f + m = 0, 0 = -6*f + 3*f - 3 for t.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-199"}}
{"id": "dm-algebra__linear_2d_composed-hard-199", "pool": "math", "split": "train", "question": "Let t = 504 - 302. Let f = t - 202. Solve f = 2*l - 4*s + 19 + 3, -s + 6 = -l for l.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-200"}}
{"id": "dm-algebra__linear_2d_composed-hard-200", "pool": "math", "split": "train", "question": "Let j(y) = y**2 + 8*y + 7. Let s be j(-7). Suppose 2*d + 3*q - 2*q = 11, -5*d + 5*q - 10 = s. Solve -5*a + 0*p - d = p, -4*p - 12 = 0 for a.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-201"}}
{"id": "dm-algebra__linear_2d_composed-hard-201", "pool": "math", "split": "train", "question": "Let p(j) = 171 - 56*j. Let n be p(3). Solve n*q - 2*w + 10 = 0, 4*q + w = -q - 8 for q.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-202"}}
{"id": "dm-algebra__linear_2d_composed-hard-202", "pool": "math", "split": "train", "question": "Let r be ((-1)/4)/(98/(-784)). Solve -2*s - 4*p = -0*s, 0 = -r*s - p + 3 for s.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-203"}}
{"id": "dm-algebra__linear_2d_composed-hard-203", "pool": "math", "split": "train", "question": "Let j(t) = t**3 + t**2 - 6*t + 28. Let h be j(-4). Let x(n) = -n**3 - 9*n**2 - 2*n + 7. Let r be x(-9). Suppose -10 = 5*f - r. Solve -2*c - f*v - 13 = -4*v, 4*v = -4*c + h for c.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-204"}}
{"id": "dm-algebra__linear_2d_composed-hard-204", "pool": "math", "split": "train", "question": "Let p = 5565 + -5563. Solve 5*g - 18 = q, -p*g + 4 = q - 6 for q.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-205"}}
{"id": "dm-algebra__linear_2d_composed-hard-205", "pool": "math", "split": "train", "question": "Suppose -4*a = 4, 3*a = x - 6*x - 3. Let b = -2219 + 2222. Solve 2*y + x = 4*m - 2, -b*m = -2*y - 2 for y.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-206"}}
{"id": "dm-algebra__linear_2d_composed-hard-206", "pool": "math", "split": "train", "question": "Let q(c) = -c - 3. Let z be q(-7). Let h(i) = 5*i - 19. Let v be h(7). Let u = -130 + 132. Solve 10*f - 5*f = u*y + v, 0 = -z*y - 4*f + 24 for y.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-207"}}
{"id": "dm-algebra__linear_2d_composed-hard-207", "pool": "math", "split": "train", "question": "Let k(o) = 29*o**2 - 758*o + 122. Let h be k(26). Solve 0 = 3*a - 3*m - 12, -9*a + 6*a + h = 3*m for a.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-208"}}
{"id": "dm-algebra__linear_2d_composed-hard-208", "pool": "math", "split": "train", "question": "Let o be (-2 + 21/(-3))/(-20 - (-1406)/76). Solve -k + o*k - 11 = -2*g, -2*g = 4 for k.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-209"}}
{"id": "dm-algebra__linear_2d_composed-hard-209", "pool": "math", "split": "train", "question": "Suppose -1482 + 1500 = 9*n. Solve -2*w + 4*w = n*m, -2*m - 16 = 2*w for m.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-210"}}
{"id": "dm-algebra__linear_2d_composed-hard-210", "pool": "math", "split": "train", "question": "Let h = 5204 + -5202. Solve -u - h = a, 5*a = u - 20 - 2 for a.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-211"}}
{"id": "dm-algebra__linear_2d_composed-hard-211", "pool": "math", "split": "train", "question": "Let f be (4 + 262)/(-8 + 6). Let h = -130 - f. Solve -h*r - 4*x + 2 + 11 = 0, 2*x - 14 = -4*r for r.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-212"}}
{"id": "dm-algebra__linear_2d_composed-hard-212", "pool": "math", "split": "train", "question": "Let k = 7161 - 7157. Solve n = 2*n + 4*q + 25, -4*n - k*q - 40 = 0 for n.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-213"}}
{"id": "dm-algebra__linear_2d_composed-hard-213", "pool": "math", "split": "train", "question": "Suppose 0 = 5*i - z - 22, -i + 4*i = -z + 18. Suppose -45*k + 80 = -i*k. Solve -5*p + k*v = -13, p + 0*v + v + 3 = 0 for p.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-214"}}
{"id": "dm-algebra__linear_2d_composed-hard-214", "pool": "math", "split": "train", "question": "Suppose -4*h = -n, 5*n - 54 = h + 3. Suppose 5*g = -2*f - 2, -3*f - f - 2*g + n = 0. Suppose 0 = -r - f*p - 13, 0 = -4*r - 5*p - 8. Solve 3*i + 0*i + 2*k = 4, -r*i - k = -8 for i.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-215"}}
{"id": "dm-algebra__linear_2d_composed-hard-215", "pool": "math", "split": "train", "question": "Let h be (-3)/2 - 36/(-8). Suppose h*i - 2 = f + 8, 0 = -2*i - 5*f - 16. Solve -2*d + 16 = -2*m + i, 2 = d for m.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-216"}}
{"id": "dm-algebra__linear_2d_composed-hard-216", "pool": "math", "split": "train", "question": "Suppose 9 = 5*f - 11. Suppose -2*g + 0*o = -o - 11, 2*g + f = -4*o. Solve 21 = 5*w - m, m + 2*m - 13 = -g*w for w.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-217"}}
{"id": "dm-algebra__linear_2d_composed-hard-217", "pool": "math", "split": "train", "question": "Suppose 157*b - 146*b = 165. Solve -3*a - 3*n + 6 = 33, b = -5*n for a.", "unit": "dimensionless", "value": "-6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-218"}}
{"id": "dm-algebra__linear_2d_composed-hard-218", "pool": "math", "split": "train", "question": "Let f = 136 + -126. Suppose 38 = 9*v + f*v. Solve 5*c = 4*h + 37, -v*c = 4 - 14 for h.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-219"}}
{"id": "dm-algebra__linear_2d_composed-hard-219", "pool": "math", "split": "train", "question": "Suppose 3*q = 4*o - 360, q + 352 = 4*o - 0*q. Suppose o = -4*t - 53. Let w = -19 - t. Solve -5*v + 9 = -2*a, 4*v - 40 + w = -4*a for a.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-220"}}
{"id": "dm-algebra__linear_2d_composed-hard-220", "pool": "math", "split": "train", "question": "Suppose -12 = -42*p + 39*p. Let a be ((-56)/(-21))/(p/6). Suppose b + 3*w + 0 - 1 = 0, b - 3*w = 7. Solve 16 = -3*k + a*v, v = 2*k + b*v - 12 for k.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-221"}}
{"id": "dm-algebra__linear_2d_composed-hard-221", "pool": "math", "split": "train", "question": "Let s(r) = -2*r**3 - 7*r**2 - 3*r - 7. Let q be s(-5). Let b = -123 + q. Let g = -40 - b. Solve 0 = h - 2*h + x, g = 2*x - 4 for h.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-222"}}
{"id": "dm-algebra__linear_2d_composed-hard-222", "pool": "math", "split": "train", "question": "Suppose -2*m + 7*h = 8*h - 9, h = -1. Let y(i) = i**3 - i**2 - 22*i + 14. Let q be y(m). Solve c + 5*f = 13 + 7, c = q*f - 7 for c.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-223"}}
{"id": "dm-algebra__linear_2d_composed-hard-223", "pool": "math", "split": "train", "question": "Let x be -2*175/(-50)*(-36)/(-21). Solve -5*k = m - 2*k + x, 15 = -3*k for m.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-224"}}
{"id": "dm-algebra__linear_2d_composed-hard-224", "pool": "math", "split": "train", "question": "Suppose 3*h = 4*s + 72, h + 10 - 34 = -5*s. Suppose h*o - 28*o = 8. Let w = o + 11. Solve 5*l + 4*n - 15 = 0, 2*n + w = -0*l + 3*l for l.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-225"}}
{"id": "dm-algebra__linear_2d_composed-hard-225", "pool": "math", "split": "train", "question": "Let n = 17786 - 17784. Solve -8 = -5*r + 2*p, 191*r = 192*r - n*p for r.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-226"}}
{"id": "dm-algebra__linear_2d_composed-hard-226", "pool": "math", "split": "train", "question": "Let t = 397 - 395. Suppose 0 = -t*y - 8, -5*y - 16 = 4*k - 2*k. Solve 5*x - 2*l - 24 = 0, -6*l - 20 = -3*x - k*l for x.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-227"}}
{"id": "dm-algebra__linear_2d_composed-hard-227", "pool": "math", "split": "train", "question": "Suppose -1361 + 1342 = -3*f + r, -4*r = 2*f - 50. Solve n - f*d = -7*d + 15, 3*n - 5 = -4*d for n.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-228"}}
{"id": "dm-algebra__linear_2d_composed-hard-228", "pool": "math", "split": "train", "question": "Let h(y) = -y**3 - 27*y**2 + 32*y - 16. Let t be h(-28). Let u = -124 - t. Solve -3*g - u*q + 40 = g, 2*q = -4*g + 30 for g.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-229"}}
{"id": "dm-algebra__linear_2d_composed-hard-229", "pool": "math", "split": "train", "question": "Suppose -6 = -3*l, 41 = 5*g - 4*l + 49. Solve -5*m - 22*i + 17*i + 50 = g, 0 = -2*i + 10 for m.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-230"}}
{"id": "dm-algebra__linear_2d_composed-hard-230", "pool": "math", "split": "train", "question": "Let r(j) = -j**3 - 3*j**2 + j + 11. Let g be r(-4). Suppose 2*n + 19*f = g*f + 26, 4*n - 27 = 3*f. Let y(k) = 11*k**2 + k - 1. Let u be y(1). Solve -2*t + u = -3*d - 3*t, 3*t + 21 = -n*d for d.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-231"}}
{"id": "dm-algebra__linear_2d_composed-hard-231", "pool": "math", "split": "train", "question": "Let b(s) = -s**2 + 8*s + 2. Let m be b(8). Solve 12 = -2*v + m*r, 56*v + 14 = 52*v + 2*r for v.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-232"}}
{"id": "dm-algebra__linear_2d_composed-hard-232", "pool": "math", "split": "train", "question": "Let j = 12 - -10. Let r be (2/11 - 4/j)/1. Solve r*f = -5*f - 4*s + 6, 6 = f + 2*s for f.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-233"}}
{"id": "dm-algebra__linear_2d_composed-hard-233", "pool": "math", "split": "train", "question": "Let o(m) = m**3 - 14*m**2 - m + 16. Let x be ((-30)/(-20))/(5/140*3). Let i be o(x). Solve -1 = 3*w - i*a - 10, 5*w + 4*a + 7 = 0 for w.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-234"}}
{"id": "dm-algebra__linear_2d_composed-hard-234", "pool": "math", "split": "train", "question": "Let i(b) = -99*b**2 - b - 1. Let z be i(-1). Let j be ((-3)/(-2))/(6 + z/18). Solve -4*f - p - 9 = 0, 5*p + 0 - 1 = j*f for f.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-235"}}
{"id": "dm-algebra__linear_2d_composed-hard-235", "pool": "math", "split": "train", "question": "Let o = 156 + -151. Solve -4*f + 2*i = -0*f + 10, -4*f = -o*i + 19 for f.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-236"}}
{"id": "dm-algebra__linear_2d_composed-hard-236", "pool": "math", "split": "train", "question": "Let c(b) be the third derivative of b**6/120 + b**5/60 + 7*b**4/24 - 11*b**3/3 + 82*b**2. Let y be c(2). Solve y*j - 2*q - 12 = j, 2*q = 5*j - 20 for j.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-237"}}
{"id": "dm-algebra__linear_2d_composed-hard-237", "pool": "math", "split": "train", "question": "Let d(b) = 28*b**2 + 624*b + 185. Let r be d(-22). Solve 3*x + r = -4*g, 9 + 0 = -3*x - 5*g for x.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-238"}}
{"id": "dm-algebra__linear_2d_composed-hard-238", "pool": "math", "split": "train", "question": "Let c = 330 + -729. Let z be (-19)/(c/14) + 2/6. Solve 1 = -v - a, -3*v - 4*a = -z + 5 for v.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-239"}}
{"id": "dm-algebra__linear_2d_composed-hard-239", "pool": "math", "split": "train", "question": "Let c be (7/49*-3)/(((-91)/(-49))/(-13)). Solve 3*n + o - 11 = 0, 0 = 15*o - 18*o - c for n.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-240"}}
{"id": "dm-algebra__linear_2d_composed-hard-240", "pool": "math", "split": "train", "question": "Suppose 6*f - 393 = -21. Let p = 66 - f. Solve 0 = -4*h - p, -5*b + h - 22 = 3*h for b.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-241"}}
{"id": "dm-algebra__linear_2d_composed-hard-241", "pool": "math", "split": "train", "question": "Let i(w) = w**2 - 6*w + 7. Let q be i(5). Solve 0 = -3*o + 6, 142 - 134 = q*k + 4*o for k.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-242"}}
{"id": "dm-algebra__linear_2d_composed-hard-242", "pool": "math", "split": "train", "question": "Let j be ((-9)/12 - (-4)/(-16))*-120. Suppose 35*b - 41*b + j = 0. Solve 3*a = -5*u - 25, 4*a - u = -5*u - b for a.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-243"}}
{"id": "dm-algebra__linear_2d_composed-hard-243", "pool": "math", "split": "train", "question": "Suppose -90 = -17*z + 12*z. Suppose 4*r - g - z = 0, -g - 2*g - 22 = -4*r. Solve r*l = -2*f, 3 = f + 1 for l.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-244"}}
{"id": "dm-algebra__linear_2d_composed-hard-244", "pool": "math", "split": "train", "question": "Let y(c) = 9*c + 48. Let a be y(-5). Let n be (-1)/((4 + -5)/a). Solve 5*m = -4*l, -n*m = -7*l + 3*l + 32 for l.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-245"}}
{"id": "dm-algebra__linear_2d_composed-hard-245", "pool": "math", "split": "train", "question": "Let z(s) = 19 - 3*s + 2*s**2 - 9 - 13. Let b be z(-1). Let n be 6/b - (-12 + 13). Solve -n = 2*w, -3*v + 4*v + w = 2 for v.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-246"}}
{"id": "dm-algebra__linear_2d_composed-hard-246", "pool": "math", "split": "train", "question": "Let v(l) = 2*l**2 - 4*l + 4. Suppose 2*u - 6 = -u. Let t be v(u). Let h be (-5)/(-5 - (t - 8)). Solve -2*d + j + 14 = d, 5*d = h*j + 40 for d.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-247"}}
{"id": "dm-algebra__linear_2d_composed-hard-247", "pool": "math", "split": "train", "question": "Suppose 15 + 11 = r + 5*h, 3*r = -h + 22. Let g = -23872 - -23877. Solve 2*n + r + 3 = -a, g*n = 4*a - 16 for n.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-248"}}
{"id": "dm-algebra__linear_2d_composed-hard-248", "pool": "math", "split": "train", "question": "Suppose -20*t - t + 567 = 0. Suppose 5*o - 3 = -3*l + 9, -2*l + 3*o = -t. Solve -3*f + 4 = 2*y + 3, 3*y = 3*f + l for y.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-249"}}
{"id": "dm-algebra__linear_2d_composed-hard-249", "pool": "math", "split": "train", "question": "Let z = -4363 - -4380. Solve -5*g = 2*p - 4, -z*g - p + 7 = -12*g for g.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-250"}}
{"id": "dm-algebra__linear_2d_composed-hard-250", "pool": "math", "split": "train", "question": "Let s(l) = l**3 + 28*l**2 - 63*l - 85. Let m be s(-30). Solve 7 = 3*k - 2*k + m*o, 0 = 2*k + 3*o - 7 for k.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-251"}}
{"id": "dm-algebra__linear_2d_composed-hard-251", "pool": "math", "split": "train", "question": "Let a(y) = -y**3 - 6*y**2 - 6*y + 7. Let m be a(-5). Let d(l) = 2 - 211*l. Let u be d(-3). Let w = u + -635. Solve -4*b = -2*r + m, w*b + b - 3*r + 13 = 0 for b.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-252"}}
{"id": "dm-algebra__linear_2d_composed-hard-252", "pool": "math", "split": "train", "question": "Let s be 4/(1/(90/(-66)) - -1). Let w(o) = o**2 - 25*o + 155. Let i be w(s). Solve -18 = i*z + 2*u, -3*u + 4 = 1 for z.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-253"}}
{"id": "dm-algebra__linear_2d_composed-hard-253", "pool": "math", "split": "train", "question": "Let t = 45 - 47. Let p be -1*((-6)/t + -5). Suppose 0*a - a + p*z = -16, 3*a = z + 23. Solve -3*i + 6 + a = 3*h, -i + 2 = 0 for h.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-254"}}
{"id": "dm-algebra__linear_2d_composed-hard-254", "pool": "math", "split": "train", "question": "Let g(v) = 2*v**2 - 26*v + 87. Let c be g(5). Solve -6*s = -3*o - 4*s - c, 15 = 3*s for o.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-255"}}
{"id": "dm-algebra__linear_2d_composed-hard-255", "pool": "math", "split": "train", "question": "Let b be 19 - 90/(-10) - 1. Solve -5*o = -3*a - b, 5*o + 6 = 21 for a.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-256"}}
{"id": "dm-algebra__linear_2d_composed-hard-256", "pool": "math", "split": "train", "question": "Let z(l) = 616 - 26*l. Let n be z(23). Solve 2*r + 4*a - n = 0, -5*r - 14 = -5*a + 16 for r.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-257"}}
{"id": "dm-algebra__linear_2d_composed-hard-257", "pool": "math", "split": "train", "question": "Let j = 9244 - 9240. Solve j*d = -5*t - 13, 53*t + 3 = 52*t - d for t.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-258"}}
{"id": "dm-algebra__linear_2d_composed-hard-258", "pool": "math", "split": "train", "question": "Suppose -l - 3*l + 180 = 0. Let s(m) = m**2 - 10*m + 57. Let d be s(11). Suppose 4*z - l = -b - 9, 3*b + 4*z = d. Solve 4*v + 2*p + 8 = 0, 0*p + 4*p + b = -2*v for v.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-259"}}
{"id": "dm-algebra__linear_2d_composed-hard-259", "pool": "math", "split": "train", "question": "Let f(v) = -5*v - 35. Let r be f(-7). Suppose -j + 5*g = -17, r*j = j - 2*g - 20. Solve -i - 2*m = -2, 0*i - j = 4*i - 2*m for i.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-260"}}
{"id": "dm-algebra__linear_2d_composed-hard-260", "pool": "math", "split": "train", "question": "Let p(r) = -r**2 + 27*r - 57. Let h be p(23). Suppose -m - 3*g = 13 - 33, 2*g = -5*m + h. Solve w + 4*b + 2 = 0, 4*w - m*b = 9*w - 5 for w.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-261"}}
{"id": "dm-algebra__linear_2d_composed-hard-261", "pool": "math", "split": "train", "question": "Let a be 30/4*(20 + -18). Solve -8*i = -3*i + a, -3*n - 5*i = 27 for n.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-262"}}
{"id": "dm-algebra__linear_2d_composed-hard-262", "pool": "math", "split": "train", "question": "Let v = 5 + 0. Suppose 0 = 4*b + v*o + 2, -10 - 2 = -5*b + o. Suppose 5*u + 254*k - 249*k - 20 = 0, -2*u + 7 = 3*k. Solve 4*p - 5 = -u*j + 7, -b*j + 5*p = 15 for j.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-263"}}
{"id": "dm-algebra__linear_2d_composed-hard-263", "pool": "math", "split": "train", "question": "Let l = 4360 - 4359. Solve 0 = -w + 13*u - 18*u - l, -w - u = 1 for w.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-264"}}
{"id": "dm-algebra__linear_2d_composed-hard-264", "pool": "math", "split": "train", "question": "Suppose 25*i + 20 = 58*i - 23*i. Solve -i*l = -6, 0 = -4*p + 5*p + 3*l - 4 for p.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-265"}}
{"id": "dm-algebra__linear_2d_composed-hard-265", "pool": "math", "split": "train", "question": "Let x be 4*((-9)/(-6) - 1). Let w = 18 - x. Suppose w*j = 18*j - 14. Solve 0 = 3*m - 2*l - 12, -16 = 3*m - j*m - 5*l for m.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-266"}}
{"id": "dm-algebra__linear_2d_composed-hard-266", "pool": "math", "split": "train", "question": "Let d be 1 + 47/(235/10). Solve d*t - 4*n - 19 = 0, -35*t + 37*t - 29 = 5*n for t.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-267"}}
{"id": "dm-algebra__linear_2d_composed-hard-267", "pool": "math", "split": "train", "question": "Suppose 353 + 351 = 4*d. Suppose -181 + d = -q. Solve 5*i - q*b = 0, -15 = -2*i + 6*b - b for i.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-268"}}
{"id": "dm-algebra__linear_2d_composed-hard-268", "pool": "math", "split": "train", "question": "Suppose -4184*z + 2583 + 1917 = -4124*z. Solve z*d + 8 = -2*f + 77*d, -5*f = 5*d - 10 for f.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-269"}}
{"id": "dm-algebra__linear_2d_composed-hard-269", "pool": "math", "split": "train", "question": "Suppose 37 = -4*z - 111. Suppose 1445 = -276*y - 9595. Let t = z - y. Solve -10 = 5*q, -m + q - t*q - 6 = 0 for m.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-270"}}
{"id": "dm-algebra__linear_2d_composed-hard-270", "pool": "math", "split": "train", "question": "Let z be (-220)/(-88)*2/1. Solve -c = -13*a + 17*a - 16, -5*c - 20 = -z*a for c.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-271"}}
{"id": "dm-algebra__linear_2d_composed-hard-271", "pool": "math", "split": "train", "question": "Let p(f) = 7*f**2 + 4*f + 14. Let a be p(-3). Let h = 68 - a. Solve -3*k - 3 = -4*r, 0 = -4*r + k + h*k for r.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-272"}}
{"id": "dm-algebra__linear_2d_composed-hard-272", "pool": "math", "split": "train", "question": "Suppose -979*o + 972*o + 175 = 0. Solve 0 = 5*l - o, 2*l - 22 = 31*m - 34*m for m.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-273"}}
{"id": "dm-algebra__linear_2d_composed-hard-273", "pool": "math", "split": "train", "question": "Let o = -59 + 9. Let l = 52 + o. Let f be -5 + l + -10*(-2)/4. Solve -5*k + f*k = -2*r + 7, -3*k - 2*r = 11 for k.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-274"}}
{"id": "dm-algebra__linear_2d_composed-hard-274", "pool": "math", "split": "train", "question": "Let x = -592 - -596. Solve -3*w - 25 = 5*a, -3*w - 5 = -a - x*a for a.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-275"}}
{"id": "dm-algebra__linear_2d_composed-hard-275", "pool": "math", "split": "train", "question": "Let b(d) = 140*d - 110. Let m be b(4). Suppose -80 = 440*i - m*i. Solve -4*g - 3*c - i = -5*c, -3*c - 6 = 0 for g.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-276"}}
{"id": "dm-algebra__linear_2d_composed-hard-276", "pool": "math", "split": "train", "question": "Let b(h) = h + 8. Let k be b(-6). Let o be (2/3)/((-22)/(-14388)). Let n = -403 + o. Solve -5*j = 5*g + 20, -13 + n = -5*g + k*j for g.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-277"}}
{"id": "dm-algebra__linear_2d_composed-hard-277", "pool": "math", "split": "train", "question": "Let a be 50/4 - 94/(-188). Let b be 2/3*78/a. Solve 3*v - 3 = 2*q - 6, -4*v - b = -5*q for q.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-278"}}
{"id": "dm-algebra__linear_2d_composed-hard-278", "pool": "math", "split": "train", "question": "Suppose 64*f = 9058 - 1762. Let h be f/8 + (147/(-28))/(-7). Solve 0*b = -3*p + 3*b + h, -2*p - b = 5 for p.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-279"}}
{"id": "dm-algebra__linear_2d_composed-hard-279", "pool": "math", "split": "train", "question": "Let s be (-84)/36*-3 + (-45)/(-5). Solve -23 = -3*d + 5*q, 26*q - s = 30*q for d.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-280"}}
{"id": "dm-algebra__linear_2d_composed-hard-280", "pool": "math", "split": "train", "question": "Suppose -57*i - 189 = -120*i. Solve 0 = i*g, 0 = -3*r - 2*r + 5*g - 5 for r.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-281"}}
{"id": "dm-algebra__linear_2d_composed-hard-281", "pool": "math", "split": "train", "question": "Let x = -709 - -711. Solve -2*v + 3*g = -39 + 20, -x*v = -g - 13 for v.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-282"}}
{"id": "dm-algebra__linear_2d_composed-hard-282", "pool": "math", "split": "train", "question": "Let k be 1584/176 - (-1 + -4). Solve -2*i - 4 = -5*p - k, 0 = -5*i - 25 for p.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-283"}}
{"id": "dm-algebra__linear_2d_composed-hard-283", "pool": "math", "split": "train", "question": "Let j(a) = a**3 + a**2 - 12*a + 13. Let l be j(1). Solve -5*w - 5*c = 50, l + 12 = -3*c for w.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-284"}}
{"id": "dm-algebra__linear_2d_composed-hard-284", "pool": "math", "split": "train", "question": "Let x(r) = r**2 - 4*r - 7. Let j be x(6). Let k = 8 - j. Let l(b) = 6*b**2 - 77*b + 125. Let p be l(11). Solve 4*s - 5*n = 6, 3*s + k = -p*n - 8 for s.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-285"}}
{"id": "dm-algebra__linear_2d_composed-hard-285", "pool": "math", "split": "train", "question": "Suppose 0 = -5*r - 5*n - 100, -3*r = -6*n + 3*n + 84. Let d be 9/r - 295/(-40). Solve -3*c - 2 = 2*i + d, 5*c + i + 8 = 0 for c.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-286"}}
{"id": "dm-algebra__linear_2d_composed-hard-286", "pool": "math", "split": "train", "question": "Suppose -5 = -8*w + 9*w. Let p be -1*w/(-15) - 16/(-3). Let b = 59 - 39. Solve b = -5*t - 4*l, p*t + 3*l + 13 + 2 = 0 for t.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-287"}}
{"id": "dm-algebra__linear_2d_composed-hard-287", "pool": "math", "split": "train", "question": "Let s = 9434 - 9432. Solve -n = s, 3*n - n = 4*m for m.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-288"}}
{"id": "dm-algebra__linear_2d_composed-hard-288", "pool": "math", "split": "train", "question": "Let y = 7131 - 7123. Solve 0 = c + 2*i - 9, 0 = -14*c + 12*c - 2*i + y for c.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-289"}}
{"id": "dm-algebra__linear_2d_composed-hard-289", "pool": "math", "split": "train", "question": "Let q be (-3)/(-21) + (-4960)/28. Let d = -166 - q. Solve 4*g + d = -3*f, -2*g = -2*f + 2*g + 6 for f.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-290"}}
{"id": "dm-algebra__linear_2d_composed-hard-290", "pool": "math", "split": "train", "question": "Let q = 71 - 136. Let d = q - -67. Solve 0 = 2*r - 2*j + 6, 2 = -d*r + 4*j - 0 for r.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-291"}}
{"id": "dm-algebra__linear_2d_composed-hard-291", "pool": "math", "split": "train", "question": "Let c(p) = 2*p**3 + 25*p**2 - 21*p - 84. Let a be c(-13). Solve -5*y = a, -5*d = y + y - 7 for d.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-292"}}
{"id": "dm-algebra__linear_2d_composed-hard-292", "pool": "math", "split": "train", "question": "Suppose 5*m + 1 - 21 = 0. Suppose 429 + 181 - 16 = 198*y. Solve y*o + 2*p - 23 = 0, -2*o - m*p - 5 = -31 for o.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-293"}}
{"id": "dm-algebra__linear_2d_composed-hard-293", "pool": "math", "split": "train", "question": "Let m(j) = j + 3. Let r be m(-4). Let w be 14/4 - 42/(-28). Let i = w + r. Solve 0 = i*y - 5*q - 19, 9 = -5*q + 2*q for y.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-294"}}
{"id": "dm-algebra__linear_2d_composed-hard-294", "pool": "math", "split": "train", "question": "Suppose 0 = 6*z + 12, 5*z - 5 - 3 = -2*n. Solve 3*a + n = 0, 32*i = 31*i - 3*a - 11 for i.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-295"}}
{"id": "dm-algebra__linear_2d_composed-hard-295", "pool": "math", "split": "train", "question": "Let s(a) = 95*a - 843. Let x be s(9). Solve 3*m = 4*w + w - 22, 2*m = 2*w - x for w.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-296"}}
{"id": "dm-algebra__linear_2d_composed-hard-296", "pool": "math", "split": "train", "question": "Suppose t + 4*k + 1 = 3*k, 4*k + 16 = 2*t. Suppose 2*y + 4 = 3*j, t*j - 2*y = -0*j + 4. Solve j = -2*q + 3*f - 4, -5*q + 3 = -0*q - f for q.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-297"}}
{"id": "dm-algebra__linear_2d_composed-hard-297", "pool": "math", "split": "train", "question": "Let u = 18506 + -18501. Suppose -3 = -5*o + 12. Solve -5*x - u*w = -30, x + 2*w - o*w = 0 for x.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-298"}}
{"id": "dm-algebra__linear_2d_composed-hard-298", "pool": "math", "split": "train", "question": "Suppose 21 + 127 = b. Let f = -134 + b. Solve 2*i = j + f, i - 2*i = j - 1 for i.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-299"}}
{"id": "dm-algebra__linear_2d_composed-hard-299", "pool": "math", "split": "train", "question": "Suppose 57 - 347 = -2*z. Suppose -12*i = -z + 25. Solve 5*b = 5*a + i, -10 = -5*b + 15 for a.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-300"}}
{"id": "dm-algebra__linear_2d_composed-hard-300", "pool": "math", "split": "train", "question": "Let m(d) = -d**3 - 12*d**2 + 15*d + 28. Let t be m(-13). Suppose 0*k = -k + 8. Let b be k/(-5)*(-15)/6. Solve -2*u + b - 14 = 5*f, -t*f - 4 = 2*u for u.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-301"}}
{"id": "dm-algebra__linear_2d_composed-hard-301", "pool": "math", "split": "train", "question": "Suppose -4*c = -5*r + 40, 0 = -4*c + 46*r - 42*r - 32. Let y(s) = s + 2. Let u be y(-4). Let z be u/(2/4*-2). Solve -z = x - c*x - 3*o, -x + 2*o - 3 = 0 for x.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-302"}}
{"id": "dm-algebra__linear_2d_composed-hard-302", "pool": "math", "split": "train", "question": "Suppose 7210*o + 44 = x + 7215*o, 0 = 3*x - 2*o + 4. Solve -m = 4*u + 7 + 13, 5 = -u + x*m for u.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-303"}}
{"id": "dm-algebra__linear_2d_composed-hard-303", "pool": "math", "split": "train", "question": "Let g = -11954 - -11971. Solve 0 = 3*x - 7*x + 20, -2*y - 5*x = -g for y.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-304"}}
{"id": "dm-algebra__linear_2d_composed-hard-304", "pool": "math", "split": "train", "question": "Suppose -16*v + 273 - 92 = -91. Solve -v*h = -2*j - 12*h + 23, -3*j + 9 = h for j.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-305"}}
{"id": "dm-algebra__linear_2d_composed-hard-305", "pool": "math", "split": "train", "question": "Let l(p) = p**2 + 3*p + 4. Let f be l(-3). Suppose 164*v - 20 = 166*v. Let d be v/4*(-8)/5 - 2. Solve 4*r - d*g + 12 = 2*g, g = f*r for r.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-306"}}
{"id": "dm-algebra__linear_2d_composed-hard-306", "pool": "math", "split": "train", "question": "Let c be 48/888 + 0 - (-218)/74. Solve r - 2*p + 24 = 25, 2*p - 11 = -c*r for r.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-307"}}
{"id": "dm-algebra__linear_2d_composed-hard-307", "pool": "math", "split": "train", "question": "Let i be 8/3*(-18 - 8520/(-320)). Solve 5*r = -3*j + 9, -4*j = 3*r + 11 - i for j.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-308"}}
{"id": "dm-algebra__linear_2d_composed-hard-308", "pool": "math", "split": "train", "question": "Suppose -5*t = -8*t - 51. Let o(z) = z**2 + 15*z - 34. Let r be o(t). Solve 5*b - 4 = -4*g, -3*g + 3 = 4*b - r*g for b.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-309"}}
{"id": "dm-algebra__linear_2d_composed-hard-309", "pool": "math", "split": "train", "question": "Let q(u) = 10*u - 104. Let g be q(5). Let h = g - -59. Solve -3*m - 28 = h*l, 2*m - 8*l = -4*l + 18 for m.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-310"}}
{"id": "dm-algebra__linear_2d_composed-hard-310", "pool": "math", "split": "train", "question": "Suppose -3*n = -17*n - 1652. Let c = -88 - n. Solve m + 2*s - 9 = 0, m = -4*m + 5*s - c for m.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-311"}}
{"id": "dm-algebra__linear_2d_composed-hard-311", "pool": "math", "split": "train", "question": "Let l be -10 + 4 + 1 + 9. Let d be (2 - (l + -2)) + 18 + -15. Solve 2*m - 26 = -3*a - d, m = -3*a + 19 for m.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-312"}}
{"id": "dm-algebra__linear_2d_composed-hard-312", "pool": "math", "split": "train", "question": "Suppose 182 = 2*f + 5*f. Let j be (f/(-3))/(-3*(-6)/(-27)). Let i be (j + -9)*1/2. Solve 8 = -i*d - 3*g, -2*g - 8 = 4*d - 0*g for d.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-313"}}
{"id": "dm-algebra__linear_2d_composed-hard-313", "pool": "math", "split": "train", "question": "Let t = 34522 - 34517. Solve -t*w + 20 - 3 = d, 2*d - 5*w + 26 = 0 for d.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-314"}}
{"id": "dm-algebra__linear_2d_composed-hard-314", "pool": "math", "split": "train", "question": "Let d = 2997 - 2995. Solve -5 = 3*h + 5*t, 5*h - 12*t - d = -10*t for h.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-315"}}
{"id": "dm-algebra__linear_2d_composed-hard-315", "pool": "math", "split": "train", "question": "Let g be (21 + -16)/(1/3 + 0). Suppose 5*o - g = -s, 5*o - 7*s = -4*s + 35. Solve -17 - 3 = -4*w, o*u + 4*w - 16 = 0 for u.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-316"}}
{"id": "dm-algebra__linear_2d_composed-hard-316", "pool": "math", "split": "train", "question": "Suppose -m - 4*a + 29 = 0, 53*a - 58*a + 100 = 5*m. Solve 5*k - m = 11*b - 7*b, -k = 5*b + 14 for k.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-317"}}
{"id": "dm-algebra__linear_2d_composed-hard-317", "pool": "math", "split": "train", "question": "Suppose 7*d + 1 = 4*z, -11 - 4 = -3*d. Solve -x - 7 - z = -5*b, 0 = -3*b + 3*x + 12 for b.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-318"}}
{"id": "dm-algebra__linear_2d_composed-hard-318", "pool": "math", "split": "train", "question": "Let o(i) = i**3 - 10*i**2 + 9*i + 5. Let q be o(9). Suppose q*w + 4*y - 8 = 0, -3*w = -2*w + 2*y - 4. Suppose -2*v - m + 5 = 0, 4*v + 44*m - 4 = 36*m. Solve w*a - v*a - 5*n - 14 = 0, n = -1 for a.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-319"}}
{"id": "dm-algebra__linear_2d_composed-hard-319", "pool": "math", "split": "train", "question": "Let d = -286 + 377. Suppose 0 = 99*i - d*i - 40. Solve 2*s + i = -3*p, 4*p - 2*s - 3*s + 45 = 0 for p.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-320"}}
{"id": "dm-algebra__linear_2d_composed-hard-320", "pool": "math", "split": "train", "question": "Let f = -3481 + 3485. Solve -5*v = x, -v - 3*v - f = 0 for x.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-321"}}
{"id": "dm-algebra__linear_2d_composed-hard-321", "pool": "math", "split": "train", "question": "Suppose -665 = 5*a + 5*b, -3*b - 163 = 4*a + 365. Let v = 131 + a. Solve 3*x - 15 = 2*f - v*x, 0 = 4*f - 5*x + 5 for f.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-322"}}
{"id": "dm-algebra__linear_2d_composed-hard-322", "pool": "math", "split": "train", "question": "Let h be -4*(1 + -7)/6. Let l(x) be the first derivative of x**3/3 - x**2 + 2*x - 1. Let o be l(h). Solve -5*t = -5*c - 50, c = -0*c - 3*t + o for c.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-323"}}
{"id": "dm-algebra__linear_2d_composed-hard-323", "pool": "math", "split": "train", "question": "Let r = -168 - -190. Suppose -1667*f = -1665*f - r. Solve 2*i = -5*y + f, -3*y + 3 = 2*i + i for y.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-324"}}
{"id": "dm-algebra__linear_2d_composed-hard-324", "pool": "math", "split": "train", "question": "Suppose -428 + 266 = -18*n. Solve 2*f - 6 = 0, 4*s = 11*f - n*f + 14 for s.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-325"}}
{"id": "dm-algebra__linear_2d_composed-hard-325", "pool": "math", "split": "train", "question": "Let s be 48/(-10)*(-10)/4. Suppose 3*z = -3*l - s, 2*z + 13 = -3*z + 2*l. Let n be 1 + 12 + z - 0. Solve 3*k - 5*f + 19 = -n*f, -4*k = -4*f + 4 for k.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-326"}}
{"id": "dm-algebra__linear_2d_composed-hard-326", "pool": "math", "split": "train", "question": "Suppose 0 = -2*z + 28*n - 27*n + 19, -5*z = 4*n - 41. Suppose -z = 3*t - 24. Solve t = 5*s, 0 = -3*o - s + 2*s + 5 for o.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-327"}}
{"id": "dm-algebra__linear_2d_composed-hard-327", "pool": "math", "split": "train", "question": "Let v = 464 + -305. Suppose 149 - v = -5*f. Solve 3*c = 3*j, 2*j = j + 2*c + f for j.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-328"}}
{"id": "dm-algebra__linear_2d_composed-hard-328", "pool": "math", "split": "train", "question": "Let t(a) = -a**3 + 3*a**2 + 5*a + 15. Let b(n) = 2*n**2 + 3*n + 7. Let d(r) = -5*b(r) + 2*t(r). Let o be d(-2). Solve -o*j + 10 - 32 = z, -z + 28 = -5*j for j.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-329"}}
{"id": "dm-algebra__linear_2d_composed-hard-329", "pool": "math", "split": "train", "question": "Let n(o) = o**3 + 5*o**2 + 5*o + 71. Let d be n(-6). Suppose 0 = -4*v - d*y + y - 12, 2*v = 3*y + 19. Solve l = -2*m - 5, l - v + 1 = 4*m for l.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-330"}}
{"id": "dm-algebra__linear_2d_composed-hard-330", "pool": "math", "split": "train", "question": "Suppose 5*a = -0*a + 120. Suppose -8*n = -14*n + a. Suppose 5*f - 28 = -2*z, -2*z + 32 = n*f + 2*z. Solve -q - 11 = -3*p, 0 = -0*q + 5*q + f*p - 2 for q.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-331"}}
{"id": "dm-algebra__linear_2d_composed-hard-331", "pool": "math", "split": "train", "question": "Suppose 15 = m - 4*i, -2*m - m + 5*i = -24. Let c be (2/(-4))/(-9 + 10822/1204). Let y(b) = -b**3 + 7*b**2 + 3*b - 6. Let r be y(7). Solve 3*u + m - c = -5*s, -2*s - u = -r for s.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-332"}}
{"id": "dm-algebra__linear_2d_composed-hard-332", "pool": "math", "split": "train", "question": "Let g = 136 - 136. Suppose -i + 4*f - 14 = g, -3*i - 2*i + 4*f = 6. Solve 0 = -4*t - 3*p - 13 + 1, p + 4 = -i*t for t.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-333"}}
{"id": "dm-algebra__linear_2d_composed-hard-333", "pool": "math", "split": "train", "question": "Let x be (0 + 5)*(-116)/(-290). Solve 16 = -4*t, 0*z + 2*z - x = -t for z.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-334"}}
{"id": "dm-algebra__linear_2d_composed-hard-334", "pool": "math", "split": "train", "question": "Suppose 5*c - 5*m = 15, -5*c + 6*m - 3*m = -13. Let p = 56 + -17. Suppose -3*k - 3*x = -p, 5*k - 2*x + 0*x - 30 = 0. Solve 3*l + c*w - 7 = 0, k + 1 = -4*l + w for l.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-335"}}
{"id": "dm-algebra__linear_2d_composed-hard-335", "pool": "math", "split": "train", "question": "Suppose 2*f = -5*h + 4*h + 68, -76 = -2*f + h. Suppose -12*y + 8*y = -f. Let t(q) = q. Let r be t(5). Solve 4*x + r*s = 22 + y, -3*s = -x - 5 for x.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-336"}}
{"id": "dm-algebra__linear_2d_composed-hard-336", "pool": "math", "split": "train", "question": "Suppose 5*l + 291 = -3*d, -4*l - 4*d + 8*d = 252. Let k = l + 54. Let z(c) = c**2 + 6*c + 7. Let o be z(k). Solve -t + 4 = -0, 4*t - o = 3*x for x.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-337"}}
{"id": "dm-algebra__linear_2d_composed-hard-337", "pool": "math", "split": "train", "question": "Let r be (1012/(-33) - (-7 + 0))*-3. Solve -2*z + 3 = k, r*z = 67*z + k + 9 for z.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-338"}}
{"id": "dm-algebra__linear_2d_composed-hard-338", "pool": "math", "split": "train", "question": "Let q(f) = -f**2 - 15*f - 22. Let k be q(-13). Solve -k*a + r = -20, -7*a + 20 = -5*a - 3*r for a.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-339"}}
{"id": "dm-algebra__linear_2d_composed-hard-339", "pool": "math", "split": "train", "question": "Let w = -4450 - -4469. Solve -v + l = -5, -4*l - w = -v - 5 for v.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-340"}}
{"id": "dm-algebra__linear_2d_composed-hard-340", "pool": "math", "split": "train", "question": "Suppose 0 = -129*w + 1068 - 811 + 1420. Solve 3*o - 5*l = -3*l - w, -2*l = -o - 11 for o.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-341"}}
{"id": "dm-algebra__linear_2d_composed-hard-341", "pool": "math", "split": "train", "question": "Suppose 2*a = -w - 6, -3*a - a - 4 = w. Let y = w - -7. Let v be 0/((3 - y) + -5). Solve v = n, -10 = -3*o - 3*n + 5 for o.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-342"}}
{"id": "dm-algebra__linear_2d_composed-hard-342", "pool": "math", "split": "train", "question": "Suppose 4*v - 255 = -939. Let y = 176 + v. Solve -y*q + 25 = 0, z - 4*q + 21 = -0*z for z.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-343"}}
{"id": "dm-algebra__linear_2d_composed-hard-343", "pool": "math", "split": "train", "question": "Let r(v) = -v**3 - 5*v**2 + 7*v + 9. Let s be r(-6). Suppose -s*y - 5 = -5*a + 19, -5*y - 30 = -5*a. Suppose 0*u = -5*u. Solve -2*f = p - a, 5*f + 2*p + u = 10 for f.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-344"}}
{"id": "dm-algebra__linear_2d_composed-hard-344", "pool": "math", "split": "train", "question": "Let k(m) = m**3 - 3*m**2 - 5*m. Let n(o) = -2*o**3 + 6*o**2 + 11*o. Let f(b) = -13*k(b) - 6*n(b). Suppose 14*x + 22 = 25*x. Let l be f(x). Solve 5*a - 24 = -2*z, -l*a + 10 = z - 0*a for z.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-345"}}
{"id": "dm-algebra__linear_2d_composed-hard-345", "pool": "math", "split": "train", "question": "Let m be 0*((-19)/4)/19. Solve m = -3*t + 7*t - 3*r - 12, -4*r + 6 = 2*t for t.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-346"}}
{"id": "dm-algebra__linear_2d_composed-hard-346", "pool": "math", "split": "train", "question": "Let g be (-25 + 3)*(2 - (-22)/(-4)). Suppose -g = -13*r - 259. Let c be ((-2)/7 - 74/r) + -1. Solve -3*j = 5*t + 10, t + c*j = -0*t - 2 for t.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-347"}}
{"id": "dm-algebra__linear_2d_composed-hard-347", "pool": "math", "split": "train", "question": "Let k(z) = 3*z**2 + 10*z - 168. Let j be k(6). Solve l + 3 = 4*v - 7, -2*l - 4*v + 4 = j for l.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-348"}}
{"id": "dm-algebra__linear_2d_composed-hard-348", "pool": "math", "split": "train", "question": "Suppose 3*z - 6 = 3*m, 9*z - 11*z + 22 = -5*m. Let p be m/(2/(-2))*460/276. Solve 13 = -f - 5*j, 4*j + 4 + p = f for f.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-349"}}
{"id": "dm-algebra__linear_2d_composed-hard-349", "pool": "math", "split": "train", "question": "Let w be 9/(-3) - (14*2 + 1). Let n = -31 - w. Suppose 3*t + 2*z = n, -3 - 4 = -t + z. Solve 7 = 2*h - 3, 25 = 2*s + t*h for s.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-350"}}
{"id": "dm-algebra__linear_2d_composed-hard-350", "pool": "math", "split": "train", "question": "Let u(f) = 37*f**3 + 3*f**2 - 2. Let y be u(1). Suppose s + 0*s = -34. Let o = y + s. Solve 3 = -j + o*t, 5*j + 7*t - 35 = 2*t for j.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-351"}}
{"id": "dm-algebra__linear_2d_composed-hard-351", "pool": "math", "split": "train", "question": "Let c = -16959 + 16962. Suppose 0 = -2*j + 4, -2*o + 20 = 5*j. Solve o*f + 25 = -5*p, -2*f - 11 = -0*p + c*p for f.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-352"}}
{"id": "dm-algebra__linear_2d_composed-hard-352", "pool": "math", "split": "train", "question": "Let k = 546 + -470. Suppose -10 = -k*c + 71*c. Solve c*z - 6 = 4*d, -3*z + 27 = 2*d + 2*z for d.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-353"}}
{"id": "dm-algebra__linear_2d_composed-hard-353", "pool": "math", "split": "train", "question": "Suppose -4*w + 297 - 161 = 0. Suppose -16 = 6*l - w. Solve 0 = -5*f - 15, 2*k - 3*f - 11 = l*k for k.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-354"}}
{"id": "dm-algebra__linear_2d_composed-hard-354", "pool": "math", "split": "train", "question": "Let c = 6132 + -6127. Solve -5*x = 3*r - 4, r - 24 = -c*x - 16 for r.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-355"}}
{"id": "dm-algebra__linear_2d_composed-hard-355", "pool": "math", "split": "train", "question": "Let r(a) = a**3 - 17*a**2 - 16*a - 11. Let t be r(20). Let j = 872 - t. Suppose 1 = 4*c - 7. Solve -j*m - 6 = -w, -5*w - c = -6*w + m for w.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-356"}}
{"id": "dm-algebra__linear_2d_composed-hard-356", "pool": "math", "split": "train", "question": "Suppose 0 = -23*i + 26*i - 48. Let n(y) = -y - 4. Let s = 10 - 17. Let t be n(s). Solve t = 2*o - 3*k + i, 4*o = 5*k - 23 for o.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-357"}}
{"id": "dm-algebra__linear_2d_composed-hard-357", "pool": "math", "split": "train", "question": "Let p = 19 + 87. Let w be 28/42 - p/(-3). Let s be (-54)/w + (-14)/(-4). Solve 2*i - 12 = -3*h, 0 = -h + 5*i - s*i + 4 for h.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-358"}}
{"id": "dm-algebra__linear_2d_composed-hard-358", "pool": "math", "split": "train", "question": "Suppose -3*i = -a - 9, -8*i + 11*i = -3*a + 9. Solve -3*o - 5*x = 23, -18*o - 8 = -22*o + i*x for o.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-359"}}
{"id": "dm-algebra__linear_2d_composed-hard-359", "pool": "math", "split": "train", "question": "Let h be (-20)/(-170) + 104/(-17). Let w be 64/(-34) + h/51. Let u be (2 + w)*1/(-2). Solve 0*t = -2*t - 5*g + 4, u = 4*t - 3*g - 8 for t.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-360"}}
{"id": "dm-algebra__linear_2d_composed-hard-360", "pool": "math", "split": "train", "question": "Suppose 385 = -6*l - 575. Let p = l - -187. Solve j + 14 + 5 = 3*n, 3*n - 3*j - p = 0 for n.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-361"}}
{"id": "dm-algebra__linear_2d_composed-hard-361", "pool": "math", "split": "train", "question": "Let r(v) = -v**3 - 5*v**2 + 17*v - 55. Let x be r(-8). Solve 0*c - i = 5*c + 26, 0 = c - 4*i + x for c.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-362"}}
{"id": "dm-algebra__linear_2d_composed-hard-362", "pool": "math", "split": "train", "question": "Let m = -4549 - -4551. Solve 3*i + 5 = 5*b, m*i + b - 4 = 10 for i.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-363"}}
{"id": "dm-algebra__linear_2d_composed-hard-363", "pool": "math", "split": "train", "question": "Let d = -312 + 153. Let z = d - -163. Solve -z*b - 60 = 5*i - 25, -4*i = -b + 7 for i.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-364"}}
{"id": "dm-algebra__linear_2d_composed-hard-364", "pool": "math", "split": "train", "question": "Suppose 3*s + 19 + 19 = 2*i, i - s - 19 = 0. Let z be (2/6)/(8/(48 - 0)). Let q be 2/(z + (-12)/9). Solve 5*y = -2*l - i, -2*l + 0*l - q*y = 9 for l.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-365"}}
{"id": "dm-algebra__linear_2d_composed-hard-365", "pool": "math", "split": "train", "question": "Let b = -420 + 424. Solve -m = -b*m - 5*t - 12, 0 = 4*t for m.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-366"}}
{"id": "dm-algebra__linear_2d_composed-hard-366", "pool": "math", "split": "train", "question": "Let o(v) = 23*v + 283. Let a be o(-8). Let u be 11/a + (-107)/(-9). Solve 4*p + 5*m = 1, -5*p + 5*m = -2 + u for p.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-367"}}
{"id": "dm-algebra__linear_2d_composed-hard-367", "pool": "math", "split": "train", "question": "Let h be 6/(-1) + (1 + -1 - 4). Let d be 3 + 6 + h + 8. Solve -d*o = -3*o - 8, 4*o + 17 = 5*p for p.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-368"}}
{"id": "dm-algebra__linear_2d_composed-hard-368", "pool": "math", "split": "train", "question": "Let j(p) = p**3 - 2*p**2 + 5*p - 3. Suppose 4*d - 2 = 3*g, -d - 3*d = 5*g - 18. Let v be j(d). Suppose -8 - 34 = -v*t. Solve -a = 4*l - t*a - 9, -3*l + a = -4 for l.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-369"}}
{"id": "dm-algebra__linear_2d_composed-hard-369", "pool": "math", "split": "train", "question": "Let u = 288 + -248. Suppose 42*c - u = 32*c. Solve -1 = -w - c, 12 = -3*y - 5*w for y.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-370"}}
{"id": "dm-algebra__linear_2d_composed-hard-370", "pool": "math", "split": "train", "question": "Let m(w) = -4*w**2 + 143*w + 514. Let h be m(39). Solve 23 = t + 5*g + 4, h = t + 2*g for t.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-371"}}
{"id": "dm-algebra__linear_2d_composed-hard-371", "pool": "math", "split": "train", "question": "Suppose 386*o = 373*o + 416. Solve -4*b - 4*r = -o, -13*b + 12 = -10*b - r for b.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-372"}}
{"id": "dm-algebra__linear_2d_composed-hard-372", "pool": "math", "split": "train", "question": "Let h be (-1 + -2)*(-2)/3. Let b = -107 - -105. Let m be 1 + 0*2/(-10) - b. Solve -5*w + m = -h*z - 0*z, -4*w - 2*z - 12 = 0 for w.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-373"}}
{"id": "dm-algebra__linear_2d_composed-hard-373", "pool": "math", "split": "train", "question": "Suppose 120*x - 2949 = -2709. Solve -x*q + 31 = 5*c, -6*q + 3*q - 6 = -3*c for c.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-374"}}
{"id": "dm-algebra__linear_2d_composed-hard-374", "pool": "math", "split": "train", "question": "Let h(v) = -v**2 + 5*v + 8. Let b be h(6). Let d = -9879 - -9886. Solve 0 = -b*w + 2*q - 10, 0 = -4*w + 3*w - 5*q + d for w.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-375"}}
{"id": "dm-algebra__linear_2d_composed-hard-375", "pool": "math", "split": "train", "question": "Let r = 77246 - 77244. Let s(m) = 4*m**2 - 2*m - 1. Let z be s(-1). Solve -8 = -4*g, -z*j + r*g - 3 - 16 = 0 for j.", "unit": "dimensionless", "value": "-3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-376"}}
{"id": "dm-algebra__linear_2d_composed-hard-376", "pool": "math", "split": "train", "question": "Let o(p) = -2*p**2 - 17*p + 5. Let z be o(-9). Let h be 40/4*z/(-2). Let s be ((-12)/h)/(2/(-40)). Solve 2*d - 3 = -3*w + 6, -s = 3*d - 4*w for d.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-377"}}
{"id": "dm-algebra__linear_2d_composed-hard-377", "pool": "math", "split": "train", "question": "Let r be (-4)/2 - (49 - 7)/(-7). Suppose -6*y = -4*y - 2*b, r*b = 2*y + 10. Solve a + y = -3*a + 3*q, 2*a - 2*q + 2 = 0 for a.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-378"}}
{"id": "dm-algebra__linear_2d_composed-hard-378", "pool": "math", "split": "train", "question": "Suppose -236*h + 235*h + 25 = 0. Suppose 5*y = 4*n - n, 5*y - h = -2*n. Let o be 2/(-3) + (-44)/(-12). Solve -7 = -s + 5*s + y*z, 0 = -o*s + 3*z - 21 for s.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-379"}}
{"id": "dm-algebra__linear_2d_composed-hard-379", "pool": "math", "split": "train", "question": "Let r = 14 - 10. Let o be (3 - r) + (14 - 1) + 2. Suppose -o = -j - j. Solve -z - z = 3*n - 9, 4*z - 5*n - j = 0 for z.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-380"}}
{"id": "dm-algebra__linear_2d_composed-hard-380", "pool": "math", "split": "train", "question": "Let r = -422 - -414. Let b be 1/(-3)*(r - -2). Solve -5*j = 0, 0*k = b*k + j + 8 for k.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-381"}}
{"id": "dm-algebra__linear_2d_composed-hard-381", "pool": "math", "split": "train", "question": "Let m(d) = -4 + 148*d**3 + 28 - 11*d**2 + 2*d - 149*d**3. Let j be m(-11). Solve 3*g = 5*q + 3 - 7, -j*g + 2 = -q for q.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-382"}}
{"id": "dm-algebra__linear_2d_composed-hard-382", "pool": "math", "split": "train", "question": "Let n(a) = -7*a - 61. Let l be n(-8). Let y(c) = -c**3 - 4*c**2 + c - 17. Let w be y(l). Solve -w*f - g = 6, -f - 4*g = -g + 2 for f.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-383"}}
{"id": "dm-algebra__linear_2d_composed-hard-383", "pool": "math", "split": "train", "question": "Let t be (-1 - 1)/(2/(-3)). Suppose -122*b = -117*b - 8*n - 58, n + 6 = 0. Solve 0 = 5*d - r - 3 + b, t*r - 10 = 2*d for d.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-384"}}
{"id": "dm-algebra__linear_2d_composed-hard-384", "pool": "math", "split": "train", "question": "Let d be 6/(-5)*1*5/(-2). Suppose 4*y = -d*j + 78, 62 = 3*y - 2*j + 6*j. Suppose -y = -13*u + 10*u. Solve -3*b + u = 3*p - 24, -5 = -p for b.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-385"}}
{"id": "dm-algebra__linear_2d_composed-hard-385", "pool": "math", "split": "train", "question": "Let n = 1529 + -1529. Let x(z) = -z**3 - 5*z**2 + 6*z + 5. Let h be x(-6). Suppose -j + n*a + 32 = -h*a, 3*a = 2*j - 43. Solve -3*o + 2 = -q + 2*q, -3*q = -2*o - j for o.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-386"}}
{"id": "dm-algebra__linear_2d_composed-hard-386", "pool": "math", "split": "train", "question": "Let j(q) = -q**3 + 21*q**2 + 13*q - 5. Let u be j(-1). Solve c - u*v - 23 = -28, 5*v - 8 = c for c.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-387"}}
{"id": "dm-algebra__linear_2d_composed-hard-387", "pool": "math", "split": "train", "question": "Suppose 985 = 75*h - 1265. Solve -q - 15 = -d - 5, -4*q = -2*d + h for q.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-388"}}
{"id": "dm-algebra__linear_2d_composed-hard-388", "pool": "math", "split": "train", "question": "Suppose 34*d - 41*d + 21 = 0. Let k = 335 - 334. Solve -3*t + t + d*m + k = 0, 3*t - 5*m = 2 for t.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-389"}}
{"id": "dm-algebra__linear_2d_composed-hard-389", "pool": "math", "split": "train", "question": "Let a be 309*(-10)/(-15)*4/8. Let n = a + -98. Solve 0 = -n*k - 2*v + 28, -2*v = 3*k - 5*k for k.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-390"}}
{"id": "dm-algebra__linear_2d_composed-hard-390", "pool": "math", "split": "train", "question": "Let m = 43058 - 43029. Solve 0 = -182*y + 186*y + 3*w + m, -3*y - 3*w - 24 = 0 for y.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-391"}}
{"id": "dm-algebra__linear_2d_composed-hard-391", "pool": "math", "split": "train", "question": "Suppose 6*h = 4*h + 56. Let a be (-10)/25 - (-2)/5. Suppose -5*c + 2*b + 14 = a, -2*c = 2*c - b - 13. Solve -d + 9 = -j, -d - c*j = h - 12 for d.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-392"}}
{"id": "dm-algebra__linear_2d_composed-hard-392", "pool": "math", "split": "train", "question": "Suppose -7*y + 8*y - 2 = -q, -3*q + 13 = -4*y. Solve -2*f + s = -s + 2, -4*s = -q*f - 8 for f.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-393"}}
{"id": "dm-algebra__linear_2d_composed-hard-393", "pool": "math", "split": "train", "question": "Suppose o + 2 = -c - c, -4*o = -2*c - 22. Let m(u) = -u**2 - 24 + 6*u**2 - o*u**2 - 32*u + 22*u. Let d be m(12). Solve -3*i = -0*t - t - 13, d = -5*t - 3*i - 11 for t.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-394"}}
{"id": "dm-algebra__linear_2d_composed-hard-394", "pool": "math", "split": "train", "question": "Let q(h) = h**3 - 9*h**2 - 2*h - 62. Let x be q(10). Solve -21*v = -3*p - x*v, -15 = p + 2*v for p.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-395"}}
{"id": "dm-algebra__linear_2d_composed-hard-395", "pool": "math", "split": "train", "question": "Let v(k) = -20*k + 13*k + 4*k + 2*k. Let g be v(0). Solve 4*h - 3*x + 29 = -g*h, -x + 23 = -4*h for h.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-396"}}
{"id": "dm-algebra__linear_2d_composed-hard-396", "pool": "math", "split": "train", "question": "Let g(m) be the second derivative of -m**3/6 + 7*m. Let x be g(-4). Suppose 9*t + 246 = 273. Solve -4*u - 16 = -2*s, x*u - t = -3*s + 1 for u.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-397"}}
{"id": "dm-algebra__linear_2d_composed-hard-397", "pool": "math", "split": "train", "question": "Suppose -5*c - o = 2, c - o - 22 = -20. Suppose c = -3*y - 5*m - 5, 26*m = y + 23*m - 17. Solve 3*v + y = -4*w, -w - 3*v - 2*v - 14 = 0 for w.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-398"}}
{"id": "dm-algebra__linear_2d_composed-hard-398", "pool": "math", "split": "train", "question": "Let f = -101 - -157. Suppose -f + 80 = 8*g. Solve u - g*s = -4, 0 = u + s + 2*s - 8 for u.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-399"}}
{"id": "dm-algebra__linear_2d_composed-hard-399", "pool": "math", "split": "train", "question": "Let t be -11 - -6 - 1 - (-2 - 8). Solve -1 = m - t*a, 0*a = 2*m + 3*a + 2 for m.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-400"}}
{"id": "dm-algebra__linear_2d_composed-hard-400", "pool": "math", "split": "train", "question": "Let x(n) = -n**3 + 19*n**2 + 14*n + 122. Let v be x(20). Let p be v + 6/14 + (-6)/14. Solve -4 = -c + 2*l + 1, 3*c - p*l = 3 for c.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-401"}}
{"id": "dm-algebra__linear_2d_composed-hard-401", "pool": "math", "split": "train", "question": "Let m be (-3 + 3)*26/(-104). Solve m = 2*n + n - 15, 2*r = 2*n - 12 for r.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-402"}}
{"id": "dm-algebra__linear_2d_composed-hard-402", "pool": "math", "split": "train", "question": "Suppose 2910*d = 2907*d - 4*s + 48, -5*d + 3*s = 7. Solve 4*l = -d*q - 24, 2*l = -8*q + 4*q - 14 for q.", "unit": "dimensionless", "value": "-1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-403"}}
{"id": "dm-algebra__linear_2d_composed-hard-403", "pool": "math", "split": "train", "question": "Let n be 8814/351 - 10/90. Solve 6*m + 2*d = m - 31, 2*m + 5*d = -n for m.", "unit": "dimensionless", "value": "-5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-404"}}
{"id": "dm-algebra__linear_2d_composed-hard-404", "pool": "math", "split": "train", "question": "Let v = 148 - -210. Let n = v + -348. Solve -i + 3*i = -n, 3*z = i - 1 for z.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-405"}}
{"id": "dm-algebra__linear_2d_composed-hard-405", "pool": "math", "split": "train", "question": "Suppose 30*i + 8 = -3*a + 26*i, 5*i + 5 = -5*a. Suppose -z - c + 17 = a*z, -5*z + 5*c = -5. Suppose 0 = -4*u + 5*m - 9, -11 = u - 3*m - 0*m. Solve w + w - z*v = u, -3*v = 12 for w.", "unit": "dimensionless", "value": "-4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-406"}}
{"id": "dm-algebra__linear_2d_composed-hard-406", "pool": "math", "split": "train", "question": "Suppose 2*h + w = -3, 0 = 5*h - 3*w - 13 + 4. Suppose h = 2*f - 27 - 29. Suppose 2 = -27*g + f*g. Solve -5*o + 3 = -3*r - 3*o, -g = r - o for r.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-407"}}
{"id": "dm-algebra__linear_2d_composed-hard-407", "pool": "math", "split": "train", "question": "Let c be 84/16*4/3. Suppose -4*l + 6 + 6 = 0, -c = -5*b + l. Solve b*w + 7 = -3*a, 4 + 3 = -5*w + 3*a for w.", "unit": "dimensionless", "value": "-2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-408"}}
{"id": "dm-algebra__linear_2d_composed-hard-408", "pool": "math", "split": "train", "question": "Suppose -4*w - 12 = -w, 0 = -2*x - 2*w + 1064. Let n = x - 531. Solve -5*t + 1 = -l, -5*t + 5 = -n*l + 20 for t.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-409"}}
{"id": "dm-algebra__linear_2d_composed-hard-409", "pool": "math", "split": "train", "question": "Suppose 6 + 12 = -5*x - 2*t, 0 = 2*x + t + 8. Let o be (14/105*3)/(x/(-15)). Solve -o*s - 4 = -4*u - 23, -5*s = 3*u + 7 for s.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "algebra__linear_2d_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "algebra__linear_2d_composed", "level": "hard", "seed": "algebra__linear_2d_composed-hard-410"}}
{"id": "dm-numbers__div_remainder_composed-hard-0", "pool": "math", "split": "train", "question": "Suppose -36 = -60*a + 864. Let c(b) = 4*b**2 + 11*b + 8. What is the remainder when c(5) is divided by a?", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-1"}}
{"id": "dm-numbers__div_remainder_composed-hard-1", "pool": "math", "split": "train", "question": "Let i(n) = 5*n**3 + 14*n**2 + 9*n - 16. Calculate the remainder when 1347 is divided by i(3).", "unit": "dimensionless", "value": "259", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-2"}}
{"id": "dm-numbers__div_remainder_composed-hard-2", "pool": "math", "split": "train", "question": "Suppose -81 = -5*v - q, 0 = -5*v + 3*q - 0*q + 97. Suppose -9*k = -v*k + 144. Let o(s) = 9 - s. Calculate the remainder when k is divided by o(3).", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-3"}}
{"id": "dm-numbers__div_remainder_composed-hard-3", "pool": "math", "split": "train", "question": "Suppose 26*a - 11761 = -295. What is the remainder when a is divided by 15?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-4"}}
{"id": "dm-numbers__div_remainder_composed-hard-4", "pool": "math", "split": "train", "question": "Suppose 5*c - 128 = -q, -6*q = -3*q - c - 432. Let f = q + -118. What is the remainder when 147 is divided by f?", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-5"}}
{"id": "dm-numbers__div_remainder_composed-hard-5", "pool": "math", "split": "train", "question": "Let f = -70 + 73. Let x be 2 + 6*(f - (-21)/(-6)). What is the remainder when 31 is divided by x*3/(-6)*14?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-6"}}
{"id": "dm-numbers__div_remainder_composed-hard-6", "pool": "math", "split": "train", "question": "Suppose 89*b = 78*b. Calculate the remainder when 204 is divided by 204/51 + (b - -9).", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-7"}}
{"id": "dm-numbers__div_remainder_composed-hard-7", "pool": "math", "split": "train", "question": "Suppose t - 13 = g + 47, t - 63 = -2*g. Suppose -18*o + 78 = -17*o. Suppose -2*c + o = 52. What is the remainder when t is divided by c?", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-8"}}
{"id": "dm-numbers__div_remainder_composed-hard-8", "pool": "math", "split": "train", "question": "Let z be (840/(-175))/((-4)/390). Suppose z = -29*p + 33*p. What is the remainder when p is divided by 8?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-9"}}
{"id": "dm-numbers__div_remainder_composed-hard-9", "pool": "math", "split": "train", "question": "Suppose 0 = -8*p + 99 + 13. Suppose -s = -p*s + 390. What is the remainder when s is divided by (-2)/2 + 11*2?", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-10"}}
{"id": "dm-numbers__div_remainder_composed-hard-10", "pool": "math", "split": "train", "question": "Suppose 5*x + 3 = b, -5*x + 1 = b - 2. Suppose -2*w + 65 = b*w. Suppose 0 = 4*j + 17*j - 504. Calculate the remainder when j is divided by w.", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-11"}}
{"id": "dm-numbers__div_remainder_composed-hard-11", "pool": "math", "split": "train", "question": "Let j(q) = 7*q**3 - 33*q**2 + 83*q + 3. What is the remainder when 163 is divided by j(3)?", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-12"}}
{"id": "dm-numbers__div_remainder_composed-hard-12", "pool": "math", "split": "train", "question": "Let u(v) = 13*v**2 + 4*v - 3. Let a be (0 - 3/6)/(1/(-48)). Suppose 0 = c - 27 + a. What is the remainder when u(c) is divided by 26?", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-13"}}
{"id": "dm-numbers__div_remainder_composed-hard-13", "pool": "math", "split": "train", "question": "Let m be ((-1)/2)/(4/(-192)). Suppose -f + 2*o - 3*o + m = 0, 5*f + 2*o = 114. Calculate the remainder when 284 is divided by f.", "unit": "dimensionless", "value": "20", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-14"}}
{"id": "dm-numbers__div_remainder_composed-hard-14", "pool": "math", "split": "train", "question": "Let i(g) = g - 37*g**2 + 59*g**2 - 1 - 6*g - 16*g**2. Let o(r) = -r**3 - 2*r**2 + r - 1. Let j be o(0). What is the remainder when 36 is divided by i(j)?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-15"}}
{"id": "dm-numbers__div_remainder_composed-hard-15", "pool": "math", "split": "train", "question": "Let q = 353 + -269. Let t = -76 + q. Calculate the remainder when 31 is divided by t.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-16"}}
{"id": "dm-numbers__div_remainder_composed-hard-16", "pool": "math", "split": "train", "question": "Let f = -9375 - -9702. What is the remainder when 1201 is divided by f?", "unit": "dimensionless", "value": "220", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-17"}}
{"id": "dm-numbers__div_remainder_composed-hard-17", "pool": "math", "split": "train", "question": "What is the remainder when ((-60)/80 + 118/(-8))/(2/(-124)) is divided by 299?", "unit": "dimensionless", "value": "64", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-18"}}
{"id": "dm-numbers__div_remainder_composed-hard-18", "pool": "math", "split": "train", "question": "Let p(g) be the third derivative of -g**6/120 - g**5/15 - 5*g**4/12 + g**2. Let x(o) be the second derivative of p(o). What is the remainder when 111 is divided by x(-6)?", "unit": "dimensionless", "value": "27", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-19"}}
{"id": "dm-numbers__div_remainder_composed-hard-19", "pool": "math", "split": "train", "question": "Suppose 4*v - 4*s - 3416 = 0, -21*v - 2*s - 3424 = -25*v. Calculate the remainder when v is divided by 61.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-20"}}
{"id": "dm-numbers__div_remainder_composed-hard-20", "pool": "math", "split": "train", "question": "Let g = 5 + 24. Let t(c) = c**3 - 5*c**2 - 102*c + 131. Calculate the remainder when t(-8) is divided by g.", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-21"}}
{"id": "dm-numbers__div_remainder_composed-hard-21", "pool": "math", "split": "train", "question": "Let q(m) = -7*m**3 + m**2 - 3*m + 10. Let p be q(-3). Suppose 4*n - p = 67. Calculate the remainder when n is divided by 1 + 1 - -16 - 0.", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-22"}}
{"id": "dm-numbers__div_remainder_composed-hard-22", "pool": "math", "split": "train", "question": "Let p(r) = 1895*r + 356487. Suppose 3*l - 400 = -2*l. What is the remainder when p(-188) is divided by l?", "unit": "dimensionless", "value": "67", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-23"}}
{"id": "dm-numbers__div_remainder_composed-hard-23", "pool": "math", "split": "train", "question": "Suppose 5*b - 2*x + 120 = 350, 3*b + 3*x - 117 = 0. Let t = -29 + b. What is the remainder when 193 is divided by t?", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-24"}}
{"id": "dm-numbers__div_remainder_composed-hard-24", "pool": "math", "split": "train", "question": "Suppose 2*q = -3*v - 331 + 400, 0 = 2*v + 3*q - 41. Let p = 110 + 13. What is the remainder when p is divided by v?", "unit": "dimensionless", "value": "23", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-25"}}
{"id": "dm-numbers__div_remainder_composed-hard-25", "pool": "math", "split": "train", "question": "Suppose -3*x = -223 + 70. Suppose 5*j - 7*j = -0*j. Suppose j = 29*t - 42*t + 195. What is the remainder when x is divided by t?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-26"}}
{"id": "dm-numbers__div_remainder_composed-hard-26", "pool": "math", "split": "train", "question": "Let w(j) = 55*j**2 - 2*j + 1. What is the remainder when 6/(-66)*2 - (-103740)/660 is divided by w(1)?", "unit": "dimensionless", "value": "49", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-27"}}
{"id": "dm-numbers__div_remainder_composed-hard-27", "pool": "math", "split": "train", "question": "Let c(l) = 8295 - 669*l. What is the remainder when c(12) is divided by 129?", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-28"}}
{"id": "dm-numbers__div_remainder_composed-hard-28", "pool": "math", "split": "train", "question": "Let n = -2396 - -2767. What is the remainder when n is divided by 126?", "unit": "dimensionless", "value": "119", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-29"}}
{"id": "dm-numbers__div_remainder_composed-hard-29", "pool": "math", "split": "train", "question": "Let b = 47 - 45. Suppose -5*r = 5*v - 48 - 387, b*v = -2. Let w = r - 81. Calculate the remainder when 11 is divided by w.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-30"}}
{"id": "dm-numbers__div_remainder_composed-hard-30", "pool": "math", "split": "train", "question": "Let v = 8 - -24. Let s = 1760 - 1757. Suppose -3*y = s*p - 54, y + y = 2*p + v. What is the remainder when 81 is divided by y?", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-31"}}
{"id": "dm-numbers__div_remainder_composed-hard-31", "pool": "math", "split": "train", "question": "Let z = 3 + -7. Let y = 20898 - 20883. Calculate the remainder when (-1)/z + 310/8 is divided by y.", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-32"}}
{"id": "dm-numbers__div_remainder_composed-hard-32", "pool": "math", "split": "train", "question": "Let y(g) = g**3 - 14*g**2 + 25*g - 17. Let v be y(12). Let n(f) = -f + 7 + 6*f**2 - 2*f - 2*f. What is the remainder when n(v) is divided by 46?", "unit": "dimensionless", "value": "44", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-33"}}
{"id": "dm-numbers__div_remainder_composed-hard-33", "pool": "math", "split": "train", "question": "Suppose 3*o + 46 = -4*d, 4*o - d + 53 = 2*d. Let l = 216 + -168. Let p = o + l. Calculate the remainder when 90 is divided by p.", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-34"}}
{"id": "dm-numbers__div_remainder_composed-hard-34", "pool": "math", "split": "train", "question": "Suppose 4*t + t = 2*q - 97, 0 = -5*q + 5*t + 265. Let b = 243 - 243. Suppose b = 2*l - q + 14. Calculate the remainder when 61 is divided by l.", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-35"}}
{"id": "dm-numbers__div_remainder_composed-hard-35", "pool": "math", "split": "train", "question": "Suppose 8*x - 10*x = 2. Let m(j) = 2 - 117*j. Let n be m(x). Suppose 0 = 7*g + 21 - n. What is the remainder when 54 is divided by g?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-36"}}
{"id": "dm-numbers__div_remainder_composed-hard-36", "pool": "math", "split": "train", "question": "Suppose -g = 5*s - 7918, 4*g + 1998 - 406 = s. Calculate the remainder when s is divided by 527.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-37"}}
{"id": "dm-numbers__div_remainder_composed-hard-37", "pool": "math", "split": "train", "question": "Suppose 0 = -g - f + 25, -5*g + 107 = -f + 12. Calculate the remainder when 359 is divided by g.", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-38"}}
{"id": "dm-numbers__div_remainder_composed-hard-38", "pool": "math", "split": "train", "question": "Let d(z) = z**3 - 52*z**2 - 3*z + 157. Calculate the remainder when 22 is divided by d(52).", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-39"}}
{"id": "dm-numbers__div_remainder_composed-hard-39", "pool": "math", "split": "train", "question": "Suppose -2*a = -5*a + 27. Let q = -168 - -284. What is the remainder when q is divided by a?", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-40"}}
{"id": "dm-numbers__div_remainder_composed-hard-40", "pool": "math", "split": "train", "question": "Suppose 3*a + 106 = 115, 3*o + 3*a - 885 = 0. Calculate the remainder when 19561 is divided by o.", "unit": "dimensionless", "value": "289", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-41"}}
{"id": "dm-numbers__div_remainder_composed-hard-41", "pool": "math", "split": "train", "question": "Suppose 9 = 8*j - 15. Suppose -168 = -j*y - 3*y. What is the remainder when y + (-4 - -8) + -1 is divided by 11?", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-42"}}
{"id": "dm-numbers__div_remainder_composed-hard-42", "pool": "math", "split": "train", "question": "Let r(s) = 67 - 35*s. Let d be r(-9). Calculate the remainder when 76/(-209) - d/(-22) is divided by 10.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-43"}}
{"id": "dm-numbers__div_remainder_composed-hard-43", "pool": "math", "split": "train", "question": "Let b(m) = 3*m + 141. Suppose 999 = 18*w + 9*w. Calculate the remainder when w is divided by b(-37).", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-44"}}
{"id": "dm-numbers__div_remainder_composed-hard-44", "pool": "math", "split": "train", "question": "Let w(k) = k**2 - 1229*k + 117. What is the remainder when 942 is divided by w(0)?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-45"}}
{"id": "dm-numbers__div_remainder_composed-hard-45", "pool": "math", "split": "train", "question": "Let v = 432 - 341. Suppose 3*f = -2*z + v, 95 = 7*f - 4*f + 4*z. Calculate the remainder when 63 is divided by f.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-46"}}
{"id": "dm-numbers__div_remainder_composed-hard-46", "pool": "math", "split": "train", "question": "Suppose -5*i = -2*k - 137 + 479, 348 = 2*k - 2*i. What is the remainder when k is divided by 53?", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-47"}}
{"id": "dm-numbers__div_remainder_composed-hard-47", "pool": "math", "split": "train", "question": "Let y(v) = -v**2 + 48*v + 16. What is the remainder when 1305 is divided by y(0)?", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-48"}}
{"id": "dm-numbers__div_remainder_composed-hard-48", "pool": "math", "split": "train", "question": "Suppose 11*b - 8*b + 15 = 0. Let a(n) = 2*n**3 + 10*n**2 + n + 5. Let i be a(b). Let y(m) = 61 - 3*m. What is the remainder when y(i) is divided by 11?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-49"}}
{"id": "dm-numbers__div_remainder_composed-hard-49", "pool": "math", "split": "train", "question": "Let a(x) = x**3 + 2*x**2 - 2*x + 4. Let d(l) = -4*l**2 + 2*l - 4. Let t(k) = 3*a(k) + 4*d(k). Calculate the remainder when t(6) is divided by 60.", "unit": "dimensionless", "value": "56", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-50"}}
{"id": "dm-numbers__div_remainder_composed-hard-50", "pool": "math", "split": "train", "question": "Let h(g) = 3*g**2 + 13*g - 53. Let y be h(-10). Suppose -7*c - y = -313. Calculate the remainder when 44 is divided by c.", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-51"}}
{"id": "dm-numbers__div_remainder_composed-hard-51", "pool": "math", "split": "train", "question": "Suppose g - 2909 = 2*r, -4331 = -2*r + 5*r + 5*g. Calculate the remainder when 5/(70/(-4)) + r/(-84) is divided by 8.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-52"}}
{"id": "dm-numbers__div_remainder_composed-hard-52", "pool": "math", "split": "train", "question": "Suppose -3*g = -5*g + 70. Let q = g + -33. Calculate the remainder when q*4*1*(-15)/(-12) is divided by 7.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-53"}}
{"id": "dm-numbers__div_remainder_composed-hard-53", "pool": "math", "split": "train", "question": "Let v(b) = -76*b - 88. Let d be v(-3). What is the remainder when (-1)/((22/d)/(-11)) is divided by 45?", "unit": "dimensionless", "value": "25", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-54"}}
{"id": "dm-numbers__div_remainder_composed-hard-54", "pool": "math", "split": "train", "question": "Suppose -5*x = 4*y - x - 48, -x - 30 = -2*y. Suppose -768 = 22*u - 3826. Suppose -11*t - 2*c = -6*t - u, 10 = 5*c. Calculate the remainder when t is divided by y.", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-55"}}
{"id": "dm-numbers__div_remainder_composed-hard-55", "pool": "math", "split": "train", "question": "Suppose -i - 14 = -10. Suppose 22 = 8*c - 98. What is the remainder when (-104)/(-4)*(-2 - i) is divided by c?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-56"}}
{"id": "dm-numbers__div_remainder_composed-hard-56", "pool": "math", "split": "train", "question": "Let q(n) = -32*n**3 - n - 1. Calculate the remainder when 102708/1296 + 57/12 is divided by q(-1).", "unit": "dimensionless", "value": "20", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-57"}}
{"id": "dm-numbers__div_remainder_composed-hard-57", "pool": "math", "split": "train", "question": "Suppose -1 - 5 = -t. Let y = -71 + 9. Calculate the remainder when 5/(-10) + -1*y/4 is divided by t.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-58"}}
{"id": "dm-numbers__div_remainder_composed-hard-58", "pool": "math", "split": "train", "question": "Let d(m) = 92 - m. Let g(c) = -15. Let a(s) = 6*d(s) + 34*g(s). Let o = 59 - 36. Calculate the remainder when a(3) is divided by o.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-59"}}
{"id": "dm-numbers__div_remainder_composed-hard-59", "pool": "math", "split": "train", "question": "Let x = 261 + -76. Let v = x + 43. What is the remainder when v is divided by 59?", "unit": "dimensionless", "value": "51", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-60"}}
{"id": "dm-numbers__div_remainder_composed-hard-60", "pool": "math", "split": "train", "question": "Suppose -5*g = -3*f + 1410, -5*g - 32 = -17. Calculate the remainder when f is divided by 32.", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-61"}}
{"id": "dm-numbers__div_remainder_composed-hard-61", "pool": "math", "split": "train", "question": "Let v(s) = 2*s**2 - s + 74. Calculate the remainder when v(-7) is divided by 47.", "unit": "dimensionless", "value": "38", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-62"}}
{"id": "dm-numbers__div_remainder_composed-hard-62", "pool": "math", "split": "train", "question": "Let z = -5050 - -5755. What is the remainder when z is divided by 347?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-63"}}
{"id": "dm-numbers__div_remainder_composed-hard-63", "pool": "math", "split": "train", "question": "Let s(d) = 2*d**2 + 128*d - 896. Calculate the remainder when 215 is divided by s(7).", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-64"}}
{"id": "dm-numbers__div_remainder_composed-hard-64", "pool": "math", "split": "train", "question": "Let f(t) = 11 - 7*t. Let y be f(8). Let m = -10 - y. Calculate the remainder when m is divided by ((-102)/(-12) - -4 - 12)/(2/36).", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-65"}}
{"id": "dm-numbers__div_remainder_composed-hard-65", "pool": "math", "split": "train", "question": "Let n be (3 + (-18)/5)*-65. Let y = n + 1. Suppose j + 0*j - w = 21, 0 = -2*j + 3*w + y. Calculate the remainder when j is divided by 8.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-66"}}
{"id": "dm-numbers__div_remainder_composed-hard-66", "pool": "math", "split": "train", "question": "Suppose 5*w - 102 = 3*f, 3*w + 31 = 3*f + 97. Suppose w*g + 2*k = 15*g + 86, -4*k = 2*g - 44. Calculate the remainder when g is divided by 13.", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-67"}}
{"id": "dm-numbers__div_remainder_composed-hard-67", "pool": "math", "split": "train", "question": "Let x(d) = -2 + 0*d**3 + 9 + 4*d**3 - 1827*d - d**2 + 1821*d. What is the remainder when x(3) is divided by (6/(-4))/((-2)/24)?", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-68"}}
{"id": "dm-numbers__div_remainder_composed-hard-68", "pool": "math", "split": "train", "question": "Let g = 353 + -369. What is the remainder when 42 is divided by g/(-6) + -3 + 1128/36?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-69"}}
{"id": "dm-numbers__div_remainder_composed-hard-69", "pool": "math", "split": "train", "question": "Suppose 7*y + 77 = n + 8*y, -2*y - 308 = -4*n. Calculate the remainder when 328 is divided by n.", "unit": "dimensionless", "value": "20", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-70"}}
{"id": "dm-numbers__div_remainder_composed-hard-70", "pool": "math", "split": "train", "question": "Let w(x) = -62*x - 5453. Calculate the remainder when 255 is divided by w(-90).", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-71"}}
{"id": "dm-numbers__div_remainder_composed-hard-71", "pool": "math", "split": "train", "question": "Suppose 14*x = 1172 + 3224. What is the remainder when x is divided by 45?", "unit": "dimensionless", "value": "44", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-72"}}
{"id": "dm-numbers__div_remainder_composed-hard-72", "pool": "math", "split": "train", "question": "Suppose -2*a = 151*z - 155*z - 84, 0 = a - 4*z - 48. Calculate the remainder when 114 is divided by a.", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-73"}}
{"id": "dm-numbers__div_remainder_composed-hard-73", "pool": "math", "split": "train", "question": "Let h(z) = 5*z**2 + z - 4. Let v(d) = -27*d**2 - 5*d + 20. Let o(f) = 11*h(f) + 2*v(f). Suppose -s - s = -8, 0 = 2*p + 2*s. What is the remainder when 13 is divided by o(p)?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-74"}}
{"id": "dm-numbers__div_remainder_composed-hard-74", "pool": "math", "split": "train", "question": "Suppose 3*u - 2404 = -2*p, -u - 21*p + 802 = -20*p. What is the remainder when u is divided by 261?", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-75"}}
{"id": "dm-numbers__div_remainder_composed-hard-75", "pool": "math", "split": "train", "question": "Let j(l) = 894*l - 14. Let f be j(1). What is the remainder when 101 is divided by f/48 + (-4)/3?", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-76"}}
{"id": "dm-numbers__div_remainder_composed-hard-76", "pool": "math", "split": "train", "question": "Let q(m) = -2*m**2 + 3*m + 1. Let t(y) = 6*y**3 + 11*y**2 - 20*y - 4. Let g(n) = -6*q(n) - t(n). Let z(j) = j**3 + 8*j**2 + 8*j + 5. Let a be z(-7). Calculate the remainder when g(a) is divided by 12.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-77"}}
{"id": "dm-numbers__div_remainder_composed-hard-77", "pool": "math", "split": "train", "question": "Let j = 69 - -54. Let r = j + -103. Calculate the remainder when 32 is divided by r.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-78"}}
{"id": "dm-numbers__div_remainder_composed-hard-78", "pool": "math", "split": "train", "question": "Let i(k) = 9*k**2 - 5*k + 0*k**3 + k + 5*k - 15 - k**3. Suppose -2*j - 420 + 436 = 0. What is the remainder when i(j) is divided by 15?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-79"}}
{"id": "dm-numbers__div_remainder_composed-hard-79", "pool": "math", "split": "train", "question": "Let k be -2 - (-6 + 5 + -3). Suppose -7*d = -k*d - 70. Suppose 97 + 1947 = d*j. Calculate the remainder when j is divided by 49.", "unit": "dimensionless", "value": "48", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-80"}}
{"id": "dm-numbers__div_remainder_composed-hard-80", "pool": "math", "split": "train", "question": "What is the remainder when (-2)/4*(-4 - (717 - 3)) is divided by 170?", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-81"}}
{"id": "dm-numbers__div_remainder_composed-hard-81", "pool": "math", "split": "train", "question": "Suppose 2*y + 500*q - 505*q = 229, -3*y - 5*q + 281 = 0. Suppose 3*n = -n + 4*s + 96, 4*s = -12. Calculate the remainder when y is divided by n.", "unit": "dimensionless", "value": "18", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-82"}}
{"id": "dm-numbers__div_remainder_composed-hard-82", "pool": "math", "split": "train", "question": "Let z(x) = 45*x**2 + 2*x - 2. What is the remainder when z(2) is divided by (-2 + -2)*1/5 + (-154938)/(-2635)?", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-83"}}
{"id": "dm-numbers__div_remainder_composed-hard-83", "pool": "math", "split": "train", "question": "Suppose -3*m + 12 = 0, 10*m - 5*m = -4*h - 7196. Let p be ((-26)/4)/(11/h). Suppose -n = -14*n + p. What is the remainder when n is divided by 17?", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-84"}}
{"id": "dm-numbers__div_remainder_composed-hard-84", "pool": "math", "split": "train", "question": "Suppose -3*j = 5*p - 328, -p = -3*j - 0*j + 352. Let w = j - 18. What is the remainder when w is divided by 50?", "unit": "dimensionless", "value": "48", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-85"}}
{"id": "dm-numbers__div_remainder_composed-hard-85", "pool": "math", "split": "train", "question": "Let r = 24 + -15. Suppose -r*l = -l - 968. Suppose 10*j - 63 = 7*j. What is the remainder when l is divided by j?", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-86"}}
{"id": "dm-numbers__div_remainder_composed-hard-86", "pool": "math", "split": "train", "question": "Let x(v) = v**3 - 6*v**2 - 9*v + 16. Let z be x(7). Suppose 5*d = -5*h + 40, -3*d + 3 = z*h - 17. Calculate the remainder when (-4)/((-32)/(-12))*(7 + -11) is divided by d.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-87"}}
{"id": "dm-numbers__div_remainder_composed-hard-87", "pool": "math", "split": "train", "question": "Let d(b) = -6*b**2 + 10*b - 29. Let r be d(-5). Let n = -176 - r. Calculate the remainder when n is divided by 13.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-88"}}
{"id": "dm-numbers__div_remainder_composed-hard-88", "pool": "math", "split": "train", "question": "Suppose -6*g + 0*g + 882 = 0. Let u = 178 - g. Let v = -8 - -19. What is the remainder when u is divided by v?", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-89"}}
{"id": "dm-numbers__div_remainder_composed-hard-89", "pool": "math", "split": "train", "question": "Let t be ((-1512)/49)/((-1)/7). Let d = -51 + t. Suppose 0 = -40*k + 37*k + d. What is the remainder when k is divided by 20?", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-90"}}
{"id": "dm-numbers__div_remainder_composed-hard-90", "pool": "math", "split": "train", "question": "Let f = -3612 + 3628. Calculate the remainder when 190 is divided by f.", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-91"}}
{"id": "dm-numbers__div_remainder_composed-hard-91", "pool": "math", "split": "train", "question": "Let z(h) = h**2 - 29*h - 18. Let j(o) = 50 - 2*o. Let v be j(10). What is the remainder when 95 is divided by z(v)?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-92"}}
{"id": "dm-numbers__div_remainder_composed-hard-92", "pool": "math", "split": "train", "question": "Suppose -42*k + 26*k = -1904. Calculate the remainder when 587 is divided by k.", "unit": "dimensionless", "value": "111", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-93"}}
{"id": "dm-numbers__div_remainder_composed-hard-93", "pool": "math", "split": "train", "question": "Let z = -37 + 56. Let q(u) = -69*u - 6169. Calculate the remainder when q(-91) is divided by z.", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-94"}}
{"id": "dm-numbers__div_remainder_composed-hard-94", "pool": "math", "split": "train", "question": "Let d be (-120)/(1 - 11)*3/(-4). Calculate the remainder when -4 + (-308)/d - (-2)/(-9) is divided by 20.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-95"}}
{"id": "dm-numbers__div_remainder_composed-hard-95", "pool": "math", "split": "train", "question": "Let d = -119 + 199. Let x(j) be the second derivative of 9*j**4/4 - j**3/2 - 3*j**2/2 - 3*j. What is the remainder when d is divided by x(-1)?", "unit": "dimensionless", "value": "26", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-96"}}
{"id": "dm-numbers__div_remainder_composed-hard-96", "pool": "math", "split": "train", "question": "Let d = -209 + 119. Calculate the remainder when 207 is divided by (-2)/(-9) - (160/d + -14).", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-97"}}
{"id": "dm-numbers__div_remainder_composed-hard-97", "pool": "math", "split": "train", "question": "Let p(n) = 3 - 4*n. Suppose 179*l = 58*l + 70*l + 5457. Calculate the remainder when l is divided by p(-6).", "unit": "dimensionless", "value": "26", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-98"}}
{"id": "dm-numbers__div_remainder_composed-hard-98", "pool": "math", "split": "train", "question": "Suppose a + 169 + 345 = -5*r, 0 = -5*r + 3*a - 498. Let h = 118 + r. Let g = 12 + -5. Calculate the remainder when h is divided by g.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-99"}}
{"id": "dm-numbers__div_remainder_composed-hard-99", "pool": "math", "split": "train", "question": "Let c = 33 - 21. Let o(j) be the second derivative of -j**4/3 + j**3/6 + 47*j**2/2 + 10*j. Calculate the remainder when o(0) is divided by c.", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-100"}}
{"id": "dm-numbers__div_remainder_composed-hard-100", "pool": "math", "split": "train", "question": "Let t(u) = 14*u + 10. Let y be (8/(-3))/(16/(-24)). Suppose y*d - 21 = 3. Calculate the remainder when t(d) is divided by 32.", "unit": "dimensionless", "value": "30", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-101"}}
{"id": "dm-numbers__div_remainder_composed-hard-101", "pool": "math", "split": "train", "question": "Suppose -55*p + 1165 + 429 + 1266 = 0. What is the remainder when 1660 is divided by p?", "unit": "dimensionless", "value": "48", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-102"}}
{"id": "dm-numbers__div_remainder_composed-hard-102", "pool": "math", "split": "train", "question": "Let w(g) = 37*g**2 + 22*g. Let t be w(-1). Let x(b) = b**2 - 9*b + 4. What is the remainder when x(t) is divided by 80?", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-103"}}
{"id": "dm-numbers__div_remainder_composed-hard-103", "pool": "math", "split": "train", "question": "Suppose -p - 3*p = 0, -5*p + 10*p = 4*m. Suppose 2*u + 10*u - 612 = m. Calculate the remainder when 251 is divided by u.", "unit": "dimensionless", "value": "47", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-104"}}
{"id": "dm-numbers__div_remainder_composed-hard-104", "pool": "math", "split": "train", "question": "Let n be 2/7 + ((-99)/21)/(-1). Suppose l = 5*q + 42, -n*l - 4*q + 370 = 102. What is the remainder when l is divided by 30?", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-105"}}
{"id": "dm-numbers__div_remainder_composed-hard-105", "pool": "math", "split": "train", "question": "Let h(m) = -369*m - 3883. What is the remainder when h(-73) is divided by 87?", "unit": "dimensionless", "value": "86", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-106"}}
{"id": "dm-numbers__div_remainder_composed-hard-106", "pool": "math", "split": "train", "question": "Let l be (246 + 6)/7 - -4. Suppose -5*n + 43*j - l*j + 193 = 0, 0 = -5*n - 4*j + 186. What is the remainder when 302 is divided by n?", "unit": "dimensionless", "value": "36", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-107"}}
{"id": "dm-numbers__div_remainder_composed-hard-107", "pool": "math", "split": "train", "question": "Suppose 29*m - 24*m - 165 = 0. Suppose -m*l + 6 = -32*l. Calculate the remainder when ((-9)/(-6))/(261/84 - 3) is divided by l.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-108"}}
{"id": "dm-numbers__div_remainder_composed-hard-108", "pool": "math", "split": "train", "question": "Let y(c) = -c**3 - 2*c**2 - 2*c. Let r be y(0). Let b(q) = 5 - 9*q. Let x(l) = 2*l + 7. What is the remainder when x(5) is divided by b(r)?", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-109"}}
{"id": "dm-numbers__div_remainder_composed-hard-109", "pool": "math", "split": "train", "question": "What is the remainder when 182 is divided by (237/(-102))/(1/(-12)) + 144/1224?", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-110"}}
{"id": "dm-numbers__div_remainder_composed-hard-110", "pool": "math", "split": "train", "question": "Let s = -902 - -1330. Calculate the remainder when s is divided by 143.", "unit": "dimensionless", "value": "142", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-111"}}
{"id": "dm-numbers__div_remainder_composed-hard-111", "pool": "math", "split": "train", "question": "Suppose 6 - 16 = 5*p, 4*n + p = 42. What is the remainder when 1825 is divided by n?", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-112"}}
{"id": "dm-numbers__div_remainder_composed-hard-112", "pool": "math", "split": "train", "question": "Let u = 131 + -97. Suppose 4*t - 2*t = 2*n, -10 = 2*n - 4*t. Suppose 0 = b + 4*p - 3, -4*b + n*p + 12 = 4*p. Calculate the remainder when u is divided by b.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-113"}}
{"id": "dm-numbers__div_remainder_composed-hard-113", "pool": "math", "split": "train", "question": "Let v(k) = -49 + 140 - 48 + 21*k - 48. Calculate the remainder when 24 is divided by v(1).", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-114"}}
{"id": "dm-numbers__div_remainder_composed-hard-114", "pool": "math", "split": "train", "question": "Let k = 98 + -81. Suppose -k = -3*r - 17. What is the remainder when -3 - -5 - 5 - (-120 - r) is divided by 24?", "unit": "dimensionless", "value": "21", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-115"}}
{"id": "dm-numbers__div_remainder_composed-hard-115", "pool": "math", "split": "train", "question": "Let z(c) = -c**3 - 11*c**2 - 17*c + 15. Let k be z(-9). Suppose k*n - 5*n = 2. Suppose 3*y = -0*l - 4*l + 47, -n*y + l = -13. Calculate the remainder when 15 is divided by y.", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-116"}}
{"id": "dm-numbers__div_remainder_composed-hard-116", "pool": "math", "split": "train", "question": "Let p = -136 + 194. Calculate the remainder when (p/(-4))/((-2)/4) is divided by 13.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-117"}}
{"id": "dm-numbers__div_remainder_composed-hard-117", "pool": "math", "split": "train", "question": "Suppose 0*a = -a + 10. Let d be (105/a)/(6/40). Suppose 5*y = -5*w + d, -3*y + 34 + 0 = -5*w. Calculate the remainder when y is divided by 5.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-118"}}
{"id": "dm-numbers__div_remainder_composed-hard-118", "pool": "math", "split": "train", "question": "Let u(b) = 8*b - 1. Let j be u(2). Let w be j*(2 + 6 + -3). Suppose -5*v + w = -0*v. What is the remainder when 28 is divided by v?", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-119"}}
{"id": "dm-numbers__div_remainder_composed-hard-119", "pool": "math", "split": "train", "question": "Let r(d) = -14*d**3 + 39*d**2 + 9*d + 32. Let x(p) = -5*p**3 + 13*p**2 + 3*p + 11. Let j(v) = -3*r(v) + 8*x(v). Suppose 2*u - 30 = -0*k - 2*k, 0 = 4*u - 3*k - 39. Calculate the remainder when j(7) is divided by u.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-120"}}
{"id": "dm-numbers__div_remainder_composed-hard-120", "pool": "math", "split": "train", "question": "Suppose -4*o = -2*n - 1472, -4*o = -3*n - 2199 + 727. Calculate the remainder when o is divided by 18.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-121"}}
{"id": "dm-numbers__div_remainder_composed-hard-121", "pool": "math", "split": "train", "question": "Let k = -97 + 161. Suppose 0 = 4*q - 3*s - 739, 8*q - 2*s = 4*q + 742. What is the remainder when q is divided by k?", "unit": "dimensionless", "value": "59", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-122"}}
{"id": "dm-numbers__div_remainder_composed-hard-122", "pool": "math", "split": "train", "question": "Let l be (88/(-12) - -4)*-9. Let z = 33 - l. What is the remainder when (-325)/(-3) + (-1)/z is divided by 22?", "unit": "dimensionless", "value": "20", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-123"}}
{"id": "dm-numbers__div_remainder_composed-hard-123", "pool": "math", "split": "train", "question": "Let h(l) = l**3 + 10*l**2 - l - 9. Suppose 3*u + k = -39 + 4, 25 = -2*u - k. What is the remainder when h(u) is divided by 1?", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-124"}}
{"id": "dm-numbers__div_remainder_composed-hard-124", "pool": "math", "split": "train", "question": "Let i(k) = -228*k - 1. Let h be i(-1). Suppose -2*f + 1 = 3, h = 5*x - 2*f. Let c = 33 + x. What is the remainder when c is divided by 20?", "unit": "dimensionless", "value": "18", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-125"}}
{"id": "dm-numbers__div_remainder_composed-hard-125", "pool": "math", "split": "train", "question": "Suppose 5*b - 192 = -2*i + 316, 3*b + 476 = 2*i. Let y = i + -141. Let k(c) = 27*c - 1. What is the remainder when y is divided by k(1)?", "unit": "dimensionless", "value": "25", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-126"}}
{"id": "dm-numbers__div_remainder_composed-hard-126", "pool": "math", "split": "train", "question": "Let n(j) = 6*j**2 - 12*j - 19. What is the remainder when 2127 is divided by n(5)?", "unit": "dimensionless", "value": "68", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-127"}}
{"id": "dm-numbers__div_remainder_composed-hard-127", "pool": "math", "split": "train", "question": "Let q = 4182 - 1175. Calculate the remainder when q is divided by 43.", "unit": "dimensionless", "value": "40", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-128"}}
{"id": "dm-numbers__div_remainder_composed-hard-128", "pool": "math", "split": "train", "question": "Suppose 0 = -0*a - 62*a + 30752. Calculate the remainder when a is divided by 83.", "unit": "dimensionless", "value": "81", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-129"}}
{"id": "dm-numbers__div_remainder_composed-hard-129", "pool": "math", "split": "train", "question": "Suppose 20*u + 11592 = 48*u. What is the remainder when 1661 is divided by u?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-130"}}
{"id": "dm-numbers__div_remainder_composed-hard-130", "pool": "math", "split": "train", "question": "Let k = 119 - -14. Suppose 2*o = -5*a + 38, 5*o + 5*a - k = 2*a. Let f = 2 - -6. What is the remainder when o is divided by f?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-131"}}
{"id": "dm-numbers__div_remainder_composed-hard-131", "pool": "math", "split": "train", "question": "Let t(d) = -2*d**3 - d**2 + 2*d. Let m be t(2). Let k(y) = -3*y**2 + 54*y + 91. Let h be k(20). Let g = m - h. Calculate the remainder when 64 is divided by g.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-132"}}
{"id": "dm-numbers__div_remainder_composed-hard-132", "pool": "math", "split": "train", "question": "Let j(r) = 1 - 2*r. Suppose 0 = v - 5*c + 28, 0*v = -3*v - 2*c - 16. Calculate the remainder when 58 is divided by j(v).", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-133"}}
{"id": "dm-numbers__div_remainder_composed-hard-133", "pool": "math", "split": "train", "question": "Suppose 2*q - 5*i + 71 = 0, 0 = -4*q + 2*q - 4*i - 80. Let x be (-1912)/(-20) - (-4)/10. Calculate the remainder when 112 is divided by x/16*q/(-12).", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-134"}}
{"id": "dm-numbers__div_remainder_composed-hard-134", "pool": "math", "split": "train", "question": "Let v(c) = 12*c + 396. Let g(s) = 2*s + 72. Let a(i) = -28*g(i) + 5*v(i). What is the remainder when 29/4*(-4)/(-1) is divided by a(11)?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-135"}}
{"id": "dm-numbers__div_remainder_composed-hard-135", "pool": "math", "split": "train", "question": "Let o = -33 - -99. Let n(y) = -5*y - 58. Let p(k) = -k**3 - 17*k**2 - 14*k + 18. Let t be p(-16). What is the remainder when o is divided by n(t)?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-136"}}
{"id": "dm-numbers__div_remainder_composed-hard-136", "pool": "math", "split": "train", "question": "Suppose 2*z - 15 = -11. Suppose t = -4*l + 6*t + 382, 4 = z*t. Calculate the remainder when l is divided by 35.", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-137"}}
{"id": "dm-numbers__div_remainder_composed-hard-137", "pool": "math", "split": "train", "question": "Suppose -63*i + 68*i = -35, -49 = -2*r + 5*i. Let m be 0 - 1*(-1 - 1). Suppose -1 = -m*b - 3, 0 = -5*a + 3*b + 103. Calculate the remainder when a is divided by r.", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-138"}}
{"id": "dm-numbers__div_remainder_composed-hard-138", "pool": "math", "split": "train", "question": "Suppose -103*v = -100*v. Calculate the remainder when (v - -2)/((-3)/((-2457)/18)) is divided by 23.", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-139"}}
{"id": "dm-numbers__div_remainder_composed-hard-139", "pool": "math", "split": "train", "question": "Let r = -72792 - -72818. Let d = 276 - 183. Calculate the remainder when d is divided by r.", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-140"}}
{"id": "dm-numbers__div_remainder_composed-hard-140", "pool": "math", "split": "train", "question": "Suppose 2*q = 5*d + 5487, -8*d = -5*q - 12*d + 13767. What is the remainder when q is divided by 89?", "unit": "dimensionless", "value": "81", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-141"}}
{"id": "dm-numbers__div_remainder_composed-hard-141", "pool": "math", "split": "train", "question": "Suppose 71*m - 75*m = 108. Let k(y) = -14*y - 319. What is the remainder when 112 is divided by k(m)?", "unit": "dimensionless", "value": "53", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-142"}}
{"id": "dm-numbers__div_remainder_composed-hard-142", "pool": "math", "split": "train", "question": "Suppose -1355*l + 1295*l + 6640 + 3560 = 0. Calculate the remainder when 618 is divided by l.", "unit": "dimensionless", "value": "108", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-143"}}
{"id": "dm-numbers__div_remainder_composed-hard-143", "pool": "math", "split": "train", "question": "Suppose 102*f - 9211 - 6517 = -3896. Calculate the remainder when 2084 is divided by f.", "unit": "dimensionless", "value": "112", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-144"}}
{"id": "dm-numbers__div_remainder_composed-hard-144", "pool": "math", "split": "train", "question": "Let x(z) = z**2 + 26*z + 143. Let s be x(-6). Suppose s = -3*c + 59. Suppose 5*p - y - 180 = 0, 4*p - 5*p - 3*y = -20. What is the remainder when p is divided by c?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-145"}}
{"id": "dm-numbers__div_remainder_composed-hard-145", "pool": "math", "split": "train", "question": "Suppose -4*h + 4*h - 9*h = -4473. Calculate the remainder when h is divided by 25.", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-146"}}
{"id": "dm-numbers__div_remainder_composed-hard-146", "pool": "math", "split": "train", "question": "Suppose -90 = 4*j - 538. Let l = j + -49. Suppose -4*r + 3*r = -l. Calculate the remainder when r is divided by 24.", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-147"}}
{"id": "dm-numbers__div_remainder_composed-hard-147", "pool": "math", "split": "train", "question": "Let t(q) = q**2 - 14*q + 36. Let l be t(17). Suppose l = 14*r - 11*r. Suppose 0 = -d + 2*d - 16. What is the remainder when r is divided by d?", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-148"}}
{"id": "dm-numbers__div_remainder_composed-hard-148", "pool": "math", "split": "train", "question": "Suppose c - 4*f - 19 = 0, c = -c + f + 17. Suppose -5*y + 80 = -4*w - 124, 4*y - 156 = -4*w. Calculate the remainder when y is divided by c.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-149"}}
{"id": "dm-numbers__div_remainder_composed-hard-149", "pool": "math", "split": "train", "question": "Suppose -755 = -4*d + 1077. Let x = 503 - d. Calculate the remainder when 309 is divided by x.", "unit": "dimensionless", "value": "39", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-150"}}
{"id": "dm-numbers__div_remainder_composed-hard-150", "pool": "math", "split": "train", "question": "Calculate the remainder when 173 is divided by (212/(-20))/(((-20)/50)/2).", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-151"}}
{"id": "dm-numbers__div_remainder_composed-hard-151", "pool": "math", "split": "train", "question": "Suppose -17*b - 119 = -425. What is the remainder when (8 - 8 - 4) + 103 is divided by b?", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-152"}}
{"id": "dm-numbers__div_remainder_composed-hard-152", "pool": "math", "split": "train", "question": "Suppose 4*c + 58 = 2*i, -4*i - c = 27 - 152. Calculate the remainder when i is divided by (6/(-11))/(46732/1232 - 38).", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-153"}}
{"id": "dm-numbers__div_remainder_composed-hard-153", "pool": "math", "split": "train", "question": "Let i = -2882 - -3125. Calculate the remainder when 244 is divided by i.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-154"}}
{"id": "dm-numbers__div_remainder_composed-hard-154", "pool": "math", "split": "train", "question": "Let l = -67 + 222. Let q = 20148 + -20109. Calculate the remainder when l is divided by q.", "unit": "dimensionless", "value": "38", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-155"}}
{"id": "dm-numbers__div_remainder_composed-hard-155", "pool": "math", "split": "train", "question": "Let n be (-1 + 2)/((-6)/(-18)). Suppose 5*z = -4*w + w + 31, 5*z = 3*w + 19. Suppose 27 = n*k + i, z*i + 19 = 4*k + 2. Calculate the remainder when 69 is divided by k.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-156"}}
{"id": "dm-numbers__div_remainder_composed-hard-156", "pool": "math", "split": "train", "question": "Let r = -18626 + 18868. What is the remainder when 606 is divided by r?", "unit": "dimensionless", "value": "122", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-157"}}
{"id": "dm-numbers__div_remainder_composed-hard-157", "pool": "math", "split": "train", "question": "Let g(x) = -2*x**2 + 4 - 4 - 4*x + 25 + x + 0*x. What is the remainder when 59 is divided by g(-4)?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-158"}}
{"id": "dm-numbers__div_remainder_composed-hard-158", "pool": "math", "split": "train", "question": "Let u = 25482 - 25428. Calculate the remainder when 2125 is divided by u.", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-159"}}
{"id": "dm-numbers__div_remainder_composed-hard-159", "pool": "math", "split": "train", "question": "Suppose 0*m + 20 = 2*m + 2*c, -2*m = 3*c - 21. Suppose 5*p - 46 = -21. Suppose -p*g = -m - 146. What is the remainder when 60 is divided by g?", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-160"}}
{"id": "dm-numbers__div_remainder_composed-hard-160", "pool": "math", "split": "train", "question": "Let k(l) = l**3 + 7*l**2 - 12*l - 31. Calculate the remainder when 2329 is divided by k(-6).", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-161"}}
{"id": "dm-numbers__div_remainder_composed-hard-161", "pool": "math", "split": "train", "question": "Let b be 2/(-8) - 34/(-8). Suppose 0 = -b*r - 2*s - 22, -4 = -r + 2*r - s. Let t(w) = 3*w**2 - 5*w - 6. Calculate the remainder when t(r) is divided by 16.", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-162"}}
{"id": "dm-numbers__div_remainder_composed-hard-162", "pool": "math", "split": "train", "question": "What is the remainder when (-8)/(-10) + (4060/50 - 2) is divided by 32?", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-163"}}
{"id": "dm-numbers__div_remainder_composed-hard-163", "pool": "math", "split": "train", "question": "Suppose -10837 = -119*c - 101*c + 163. What is the remainder when 495 is divided by c?", "unit": "dimensionless", "value": "45", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-164"}}
{"id": "dm-numbers__div_remainder_composed-hard-164", "pool": "math", "split": "train", "question": "Let r = 5869 - 5582. Calculate the remainder when r is divided by 10.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-165"}}
{"id": "dm-numbers__div_remainder_composed-hard-165", "pool": "math", "split": "train", "question": "Let z = 23279 - 23228. Let v = 23 + -10. What is the remainder when z is divided by v?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-166"}}
{"id": "dm-numbers__div_remainder_composed-hard-166", "pool": "math", "split": "train", "question": "Let x(f) = f**3 + 44*f**2 + 41*f - 81. Let y be x(-43). What is the remainder when 540/y*9/6 is divided by 33?", "unit": "dimensionless", "value": "30", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-167"}}
{"id": "dm-numbers__div_remainder_composed-hard-167", "pool": "math", "split": "train", "question": "Suppose 5*y = -5*r + 435, 0*r - 3*r - 362 = -4*y. Let o = 2104 + -2163. Let f = o + y. Calculate the remainder when f is divided by 16.", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-168"}}
{"id": "dm-numbers__div_remainder_composed-hard-168", "pool": "math", "split": "train", "question": "Let t(z) = z**3 + 8*z**2 - 472*z - 23. What is the remainder when t(-25) is divided by 140?", "unit": "dimensionless", "value": "32", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-169"}}
{"id": "dm-numbers__div_remainder_composed-hard-169", "pool": "math", "split": "train", "question": "Let f(z) = z**2 - 11*z + 18. What is the remainder when f(12) is divided by (10/6)/(-37*(-250)/105450)?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-170"}}
{"id": "dm-numbers__div_remainder_composed-hard-170", "pool": "math", "split": "train", "question": "Suppose 18*m = -17*m - 22*m + 13680. Calculate the remainder when m is divided by 62.", "unit": "dimensionless", "value": "54", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-171"}}
{"id": "dm-numbers__div_remainder_composed-hard-171", "pool": "math", "split": "train", "question": "Let x(w) = 32*w**3 + 3*w**2 - 35*w - 2. Calculate the remainder when 1960 is divided by x(4).", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-172"}}
{"id": "dm-numbers__div_remainder_composed-hard-172", "pool": "math", "split": "train", "question": "What is the remainder when 1279 is divided by ((-15)/(-5))/((-66)/(-220))?", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-173"}}
{"id": "dm-numbers__div_remainder_composed-hard-173", "pool": "math", "split": "train", "question": "Suppose 72 = -6*j + 7*j. Let w = j - 66. Calculate the remainder when 1/5 - w*203/(-35) is divided by 20.", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-174"}}
{"id": "dm-numbers__div_remainder_composed-hard-174", "pool": "math", "split": "train", "question": "Let z(b) = b**3 - 12*b**2 + 46*b - 527. Let j(w) = 70*w**3 + w**2 - w. Calculate the remainder when j(1) is divided by z(12).", "unit": "dimensionless", "value": "20", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-175"}}
{"id": "dm-numbers__div_remainder_composed-hard-175", "pool": "math", "split": "train", "question": "Suppose 5*z - 5*j = 1965, 399 = 5*z - 4*z - 3*j. Suppose 4*y + 2*l = 520, y - 4*l - z = -2*y. What is the remainder when y is divided by 33?", "unit": "dimensionless", "value": "31", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-176"}}
{"id": "dm-numbers__div_remainder_composed-hard-176", "pool": "math", "split": "train", "question": "What is the remainder when 262 is divided by (-10)/6*2460/400*-8?", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-177"}}
{"id": "dm-numbers__div_remainder_composed-hard-177", "pool": "math", "split": "train", "question": "Let g be (1 + -3 - -4) + -26. Suppose -4*m + 4*w = -6*m + 12, 0 = -2*m + 2*w - 18. Calculate the remainder when 49 is divided by (5/m)/(6 - (-147)/g).", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-178"}}
{"id": "dm-numbers__div_remainder_composed-hard-178", "pool": "math", "split": "train", "question": "Suppose -21*j + 2746 - 499 = 0. Let n(u) = 2*u**2 + 32*u - 12. Let x = -76 + 59. What is the remainder when j is divided by n(x)?", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-179"}}
{"id": "dm-numbers__div_remainder_composed-hard-179", "pool": "math", "split": "train", "question": "Let l(o) = -42*o - 3667. Calculate the remainder when l(-94) is divided by 22.", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-180"}}
{"id": "dm-numbers__div_remainder_composed-hard-180", "pool": "math", "split": "train", "question": "Let z(k) = 10*k + 31. Suppose 62 = -31*r - 0*r. Calculate the remainder when 2/12*3*86 is divided by z(r).", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-181"}}
{"id": "dm-numbers__div_remainder_composed-hard-181", "pool": "math", "split": "train", "question": "Let s = -1050 - -1094. What is the remainder when 6643 is divided by s?", "unit": "dimensionless", "value": "43", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-182"}}
{"id": "dm-numbers__div_remainder_composed-hard-182", "pool": "math", "split": "train", "question": "Calculate the remainder when 175 is divided by (-6)/33 + (-10944)/(-176).", "unit": "dimensionless", "value": "51", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-183"}}
{"id": "dm-numbers__div_remainder_composed-hard-183", "pool": "math", "split": "train", "question": "Calculate the remainder when 442 + (-80 - 25)/7 is divided by 409.", "unit": "dimensionless", "value": "18", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-184"}}
{"id": "dm-numbers__div_remainder_composed-hard-184", "pool": "math", "split": "train", "question": "Calculate the remainder when ((-676)/6)/(-4 + 11 + 845/(-117)) is divided by 73.", "unit": "dimensionless", "value": "69", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-185"}}
{"id": "dm-numbers__div_remainder_composed-hard-185", "pool": "math", "split": "train", "question": "Suppose -4*z = -6*z + 48. Let u be (-13340)/174 - (-2)/6*-1. Let x = -43 - u. What is the remainder when x is divided by z?", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-186"}}
{"id": "dm-numbers__div_remainder_composed-hard-186", "pool": "math", "split": "train", "question": "Let w = -2265 - -2374. Suppose -15 + 1 = -y. What is the remainder when w is divided by y?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-187"}}
{"id": "dm-numbers__div_remainder_composed-hard-187", "pool": "math", "split": "train", "question": "Let o = -191 - -206. Let r = o - -16. Calculate the remainder when 59 is divided by r.", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-188"}}
{"id": "dm-numbers__div_remainder_composed-hard-188", "pool": "math", "split": "train", "question": "Suppose 0 = -6*z - 3*s + 9, 2*s - 3*s = -4*z - 3. Suppose z = -5*g - m + 19, 4*g - 6*m + m = 21. Calculate the remainder when 47 is divided by g.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-189"}}
{"id": "dm-numbers__div_remainder_composed-hard-189", "pool": "math", "split": "train", "question": "Suppose -150*x + 145*x = -10960. Calculate the remainder when x is divided by 1095.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-190"}}
{"id": "dm-numbers__div_remainder_composed-hard-190", "pool": "math", "split": "train", "question": "Calculate the remainder when 735 is divided by (-333)/72 - -5 - 669*2/(-16).", "unit": "dimensionless", "value": "63", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-191"}}
{"id": "dm-numbers__div_remainder_composed-hard-191", "pool": "math", "split": "train", "question": "Let m = -403 - -467. What is the remainder when m is divided by (-5)/(10/(-32)) - -3?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-192"}}
{"id": "dm-numbers__div_remainder_composed-hard-192", "pool": "math", "split": "train", "question": "Let v(s) = 27*s**2 - 319*s + 636. What is the remainder when 409 is divided by v(2)?", "unit": "dimensionless", "value": "91", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-193"}}
{"id": "dm-numbers__div_remainder_composed-hard-193", "pool": "math", "split": "train", "question": "Let w be (-1 - 3/2)/((-2)/4). Suppose -5*h + 25 = -0*d - d, 4*h + w*d = 49. Suppose -n = n - 2*y - 18, h = 3*y. Calculate the remainder when n is divided by 7.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-194"}}
{"id": "dm-numbers__div_remainder_composed-hard-194", "pool": "math", "split": "train", "question": "Suppose -16*l + 741 = -3*l. Let y = 895 - 755. Calculate the remainder when y is divided by l.", "unit": "dimensionless", "value": "26", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-195"}}
{"id": "dm-numbers__div_remainder_composed-hard-195", "pool": "math", "split": "train", "question": "Let z(s) = 82*s**2 + 2*s + 1. Let o be z(3). Suppose -2*r + o = -3*j, 2*j = 3*r - 472 - 633. Let m = r - 227. Calculate the remainder when m is divided by 28.", "unit": "dimensionless", "value": "26", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-196"}}
{"id": "dm-numbers__div_remainder_composed-hard-196", "pool": "math", "split": "train", "question": "Suppose 86 = 3*w - 34. Suppose 471 = 3*z + 4*v, -697*z - 1256 = -705*z - 3*v. Calculate the remainder when z is divided by w.", "unit": "dimensionless", "value": "37", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-197"}}
{"id": "dm-numbers__div_remainder_composed-hard-197", "pool": "math", "split": "train", "question": "Let c = -999 - -1015. What is the remainder when 313 is divided by c?", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-198"}}
{"id": "dm-numbers__div_remainder_composed-hard-198", "pool": "math", "split": "train", "question": "Let w be 5 + -1 + 1 + -3. Suppose 0 = -3*p - 0*p - 5*m + 69, 5*p + 5*m - 115 = 0. Calculate the remainder when 56 + (8 - 6/w) + 0 is divided by p.", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-199"}}
{"id": "dm-numbers__div_remainder_composed-hard-199", "pool": "math", "split": "train", "question": "Suppose 3*i = -3*n + 291 + 114, 0 = 6*n + 42. Calculate the remainder when 143 is divided by i.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-200"}}
{"id": "dm-numbers__div_remainder_composed-hard-200", "pool": "math", "split": "train", "question": "Let y(b) = -2*b**3 + b**2 - b + 2. Suppose k + 5*m = 15, -5*k - 730*m + 726*m + 75 = 0. What is the remainder when y(-2) is divided by k?", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-201"}}
{"id": "dm-numbers__div_remainder_composed-hard-201", "pool": "math", "split": "train", "question": "Let d = -2639 + 3288. Calculate the remainder when d is divided by 93.", "unit": "dimensionless", "value": "91", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-202"}}
{"id": "dm-numbers__div_remainder_composed-hard-202", "pool": "math", "split": "train", "question": "Let s(o) = -o**2 - 4*o + 4. Suppose -20 = m + 9*m. What is the remainder when (-99)/(-1 + m) - 0 is divided by s(-3)?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-203"}}
{"id": "dm-numbers__div_remainder_composed-hard-203", "pool": "math", "split": "train", "question": "Let c(a) = a**2 - 68*a - 227. Calculate the remainder when 1949 is divided by c(-6).", "unit": "dimensionless", "value": "213", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-204"}}
{"id": "dm-numbers__div_remainder_composed-hard-204", "pool": "math", "split": "train", "question": "Suppose 28*f + 2458 = 18950. What is the remainder when f is divided by 35?", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-205"}}
{"id": "dm-numbers__div_remainder_composed-hard-205", "pool": "math", "split": "train", "question": "Let z = 69 - 54. Suppose z*f + 13 = 2*f. Calculate the remainder when ((-885)/(6 + f))/(-3) is divided by 11.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-206"}}
{"id": "dm-numbers__div_remainder_composed-hard-206", "pool": "math", "split": "train", "question": "Calculate the remainder when 12047/4 + (-98)/(-8) + -13 is divided by 11.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-207"}}
{"id": "dm-numbers__div_remainder_composed-hard-207", "pool": "math", "split": "train", "question": "Suppose 6*k - 10 + 4 = 0. Let i(r) = 114*r**3 + 2*r**2 - 1. Calculate the remainder when i(k) is divided by 32.", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-208"}}
{"id": "dm-numbers__div_remainder_composed-hard-208", "pool": "math", "split": "train", "question": "Suppose 3*h + t = 83, 7 = 3*h - 5*t - 46. Let g be -153 + 1 + -1 + 3 + -5. Calculate the remainder when (-3 - g/10)*(7 + -1) is divided by h.", "unit": "dimensionless", "value": "23", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-209"}}
{"id": "dm-numbers__div_remainder_composed-hard-209", "pool": "math", "split": "train", "question": "Let j = -552 - -583. Let d(m) = 6*m**3 - 9*m**2 - 10*m + 2. Let i(k) = -5*k**3 + 9*k**2 + 10*k - 1. Let l(g) = -6*d(g) - 7*i(g). Calculate the remainder when j is divided by l(-8).", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-210"}}
{"id": "dm-numbers__div_remainder_composed-hard-210", "pool": "math", "split": "train", "question": "Let w(f) = f**3 - 71*f + 40. Calculate the remainder when 338 is divided by w(-8).", "unit": "dimensionless", "value": "50", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-211"}}
{"id": "dm-numbers__div_remainder_composed-hard-211", "pool": "math", "split": "train", "question": "Let r = -299 - -420. Let g(b) = b**2 + 81*b + 1659. Calculate the remainder when r is divided by g(-44).", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-212"}}
{"id": "dm-numbers__div_remainder_composed-hard-212", "pool": "math", "split": "train", "question": "Suppose -957 = c - 5*s, 20 = -5*s - 5. Let b be (-6)/(-1*42) + c/14. Calculate the remainder when 14/b + (-662)/(-10) is divided by 4.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-213"}}
{"id": "dm-numbers__div_remainder_composed-hard-213", "pool": "math", "split": "train", "question": "Suppose 5*m + 34*m - 593 = 889. Calculate the remainder when 3266 is divided by m.", "unit": "dimensionless", "value": "36", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-214"}}
{"id": "dm-numbers__div_remainder_composed-hard-214", "pool": "math", "split": "train", "question": "Suppose 5*l + 4*z - 100 = z, 3*z = 0. Suppose w - 4*w - 180 = -3*y, 3 = 3*w. Suppose y = 2*p - 55. Calculate the remainder when p is divided by l.", "unit": "dimensionless", "value": "18", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-215"}}
{"id": "dm-numbers__div_remainder_composed-hard-215", "pool": "math", "split": "train", "question": "Let k(n) = n**2 - n - 2. Let a(g) = -5*g**2 - 7*g - 32. Let o(v) = -a(v) - 4*k(v). Calculate the remainder when 40 is divided by o(-6).", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-216"}}
{"id": "dm-numbers__div_remainder_composed-hard-216", "pool": "math", "split": "train", "question": "Let p(t) = t**3 + 8*t**2 - 11*t - 15. Let b be p(-9). Suppose -b*d + 90 = -d. What is the remainder when d is divided by 6?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-217"}}
{"id": "dm-numbers__div_remainder_composed-hard-217", "pool": "math", "split": "train", "question": "Suppose 2*t = -5*x - 15, -6*t + 10 = -t + 3*x. Suppose m = 4, 4*b + t*m = 9*m - 8. Calculate the remainder when 12 + (10 + -1)/(-3) is divided by b.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-218"}}
{"id": "dm-numbers__div_remainder_composed-hard-218", "pool": "math", "split": "train", "question": "Suppose 23*n + 19*n - 756 = 0. Suppose -3*i = -n*i + 540. What is the remainder when 144 is divided by i?", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-219"}}
{"id": "dm-numbers__div_remainder_composed-hard-219", "pool": "math", "split": "train", "question": "Suppose -b - 24 = -5*l, b = 2*l - 0*b - 12. Suppose -5*p + 2*c + 312 = 0, 4*c = l*p - 100 - 152. Let i = 213 + -197. What is the remainder when p is divided by i?", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-220"}}
{"id": "dm-numbers__div_remainder_composed-hard-220", "pool": "math", "split": "train", "question": "Let b(z) = 655*z + 7901. What is the remainder when (1/(-2))/(5/(-3670)) is divided by b(-12)?", "unit": "dimensionless", "value": "39", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-221"}}
{"id": "dm-numbers__div_remainder_composed-hard-221", "pool": "math", "split": "train", "question": "Let g = -9668 + 15701. Calculate the remainder when g is divided by 71.", "unit": "dimensionless", "value": "69", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-222"}}
{"id": "dm-numbers__div_remainder_composed-hard-222", "pool": "math", "split": "train", "question": "Let n(a) = -27*a**3 + 3*a**2 + 4*a + 4. Let p be n(-2). Let k = p - 207. What is the remainder when 456 is divided by k?", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-223"}}
{"id": "dm-numbers__div_remainder_composed-hard-223", "pool": "math", "split": "train", "question": "Calculate the remainder when (-31)/(-1209) + (-49956)/(-117) is divided by 130.", "unit": "dimensionless", "value": "37", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-224"}}
{"id": "dm-numbers__div_remainder_composed-hard-224", "pool": "math", "split": "train", "question": "Let b(l) = -10*l - 48. Let y be b(-5). Suppose -5 = y*o - 3*o. What is the remainder when 5 is divided by o?", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-225"}}
{"id": "dm-numbers__div_remainder_composed-hard-225", "pool": "math", "split": "train", "question": "Suppose -25*y + 1365 = 10*y. Let u(q) = -q**2 + 23*q + 9. What is the remainder when y is divided by u(23)?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-226"}}
{"id": "dm-numbers__div_remainder_composed-hard-226", "pool": "math", "split": "train", "question": "Suppose 2*b + 101 = -117. Let d = 94 + b. Calculate the remainder when (32/(-6))/(5/d) is divided by 11.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-227"}}
{"id": "dm-numbers__div_remainder_composed-hard-227", "pool": "math", "split": "train", "question": "What is the remainder when 42115/30 + 2/(-15) + 3/10 is divided by 10?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-228"}}
{"id": "dm-numbers__div_remainder_composed-hard-228", "pool": "math", "split": "train", "question": "Suppose 5*v - k - 9 = 2*v, 3*v - 3*k - 9 = 0. Suppose 2 + 12 = 3*b - i, 2*b = -v*i + 13. Calculate the remainder when b/10 - (-261)/6 is divided by 12.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-229"}}
{"id": "dm-numbers__div_remainder_composed-hard-229", "pool": "math", "split": "train", "question": "Suppose -4*y - y + 350 = 3*j, 233 = 2*j + 3*y. What is the remainder when 796 is divided by j?", "unit": "dimensionless", "value": "106", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-230"}}
{"id": "dm-numbers__div_remainder_composed-hard-230", "pool": "math", "split": "train", "question": "Let i = 2863 - 2286. What is the remainder when 2311 is divided by i?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-231"}}
{"id": "dm-numbers__div_remainder_composed-hard-231", "pool": "math", "split": "train", "question": "Suppose -13*i - 111 = -5*f - 11*i, 2*i = 2*f - 48. Let u be ((-30)/(-8))/((-3)/(-248)). Suppose 0 = -d - 3*h + 97, -3*d + 5 = -3*h - u. What is the remainder when d is divided by f?", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-232"}}
{"id": "dm-numbers__div_remainder_composed-hard-232", "pool": "math", "split": "train", "question": "Let s(y) = 3*y + 23. Let j be s(-5). Let f be -6*1/j - 30/(-8). Suppose -2*b + 165 = 5*g, f*b = 4*g - 2*b - 165. Calculate the remainder when 135 is divided by g.", "unit": "dimensionless", "value": "30", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-233"}}
{"id": "dm-numbers__div_remainder_composed-hard-233", "pool": "math", "split": "train", "question": "Suppose -1472*o + 154 - 442 = -1484*o. Let l be 1/1 + 27/9. Suppose 0*s - l*s + 130 = 3*n, n = 4*s + 54. What is the remainder when n is divided by o?", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-234"}}
{"id": "dm-numbers__div_remainder_composed-hard-234", "pool": "math", "split": "train", "question": "Suppose -4*s + k + 118 = 0, -s = -6*s - 4*k + 116. Calculate the remainder when 489 is divided by s.", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-235"}}
{"id": "dm-numbers__div_remainder_composed-hard-235", "pool": "math", "split": "train", "question": "Suppose -2 = 4*k - 3*n - 54, 2*n + 28 = 2*k. What is the remainder when 211 is divided by k?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-236"}}
{"id": "dm-numbers__div_remainder_composed-hard-236", "pool": "math", "split": "train", "question": "Let u = 13126 + -7926. What is the remainder when u is divided by 17?", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-237"}}
{"id": "dm-numbers__div_remainder_composed-hard-237", "pool": "math", "split": "train", "question": "Suppose 3*q = 93 + 96. Let v = q + -33. Let h = 34 - v. What is the remainder when 6 is divided by h?", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-238"}}
{"id": "dm-numbers__div_remainder_composed-hard-238", "pool": "math", "split": "train", "question": "Let n = 11161 + -10959. Calculate the remainder when 741 is divided by n.", "unit": "dimensionless", "value": "135", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-239"}}
{"id": "dm-numbers__div_remainder_composed-hard-239", "pool": "math", "split": "train", "question": "Let w be 10/25*(-105)/3. Let d be (-1269)/(-189) + (-4)/w. Suppose -d*f - f = -1064. What is the remainder when f is divided by 34?", "unit": "dimensionless", "value": "31", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-240"}}
{"id": "dm-numbers__div_remainder_composed-hard-240", "pool": "math", "split": "train", "question": "Suppose 3*x - 12 = 0, 6*k = k - 4*x + 41. Suppose 4*h = 3*v + 84, -93 = -k*h + 2*v + 5. Suppose -a = -3*f + 4*a + 58, -35 = -5*f - 4*a. Calculate the remainder when h is divided by f.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-241"}}
{"id": "dm-numbers__div_remainder_composed-hard-241", "pool": "math", "split": "train", "question": "Let u(p) = 1710 - 80*p. Calculate the remainder when 11635 is divided by u(21).", "unit": "dimensionless", "value": "25", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-242"}}
{"id": "dm-numbers__div_remainder_composed-hard-242", "pool": "math", "split": "train", "question": "Suppose 149*k - 125 = 620. What is the remainder when 12109 is divided by k?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-243"}}
{"id": "dm-numbers__div_remainder_composed-hard-243", "pool": "math", "split": "train", "question": "Let t be 4 - 1 - -2*(-28 - -1). Let b = 46 + t. What is the remainder when 74 is divided by 4*(4 + b/(-2))?", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-244"}}
{"id": "dm-numbers__div_remainder_composed-hard-244", "pool": "math", "split": "train", "question": "Let p(w) = -w**2 + 5*w - 2. Let x be p(3). Suppose -3*a = x*h - 36, -6*h = -2*h - a - 36. Let k(n) = -3*n**2 - 39*n + 629. What is the remainder when k(-22) is divided by h?", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-245"}}
{"id": "dm-numbers__div_remainder_composed-hard-245", "pool": "math", "split": "train", "question": "Let i(j) = 8*j**2 + 14. Let t be i(-7). Let q be (7 - 3)*(-2 + 1) + t. Suppose 3*r = q - 63. What is the remainder when r is divided by 34?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-246"}}
{"id": "dm-numbers__div_remainder_composed-hard-246", "pool": "math", "split": "train", "question": "What is the remainder when -6 + -9 - (-21832)/8 is divided by 19?", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-247"}}
{"id": "dm-numbers__div_remainder_composed-hard-247", "pool": "math", "split": "train", "question": "Suppose -28*n + 480 = -20*n. Calculate the remainder when 167 is divided by n.", "unit": "dimensionless", "value": "47", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-248"}}
{"id": "dm-numbers__div_remainder_composed-hard-248", "pool": "math", "split": "train", "question": "Let z(q) = -q**2 - 12*q + 1. Let m = -64 + 56. Calculate the remainder when 159 is divided by z(m).", "unit": "dimensionless", "value": "27", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-249"}}
{"id": "dm-numbers__div_remainder_composed-hard-249", "pool": "math", "split": "train", "question": "Let o(f) = 5*f**2 + 27*f - 17. Calculate the remainder when o(6) is divided by 15.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-250"}}
{"id": "dm-numbers__div_remainder_composed-hard-250", "pool": "math", "split": "train", "question": "Suppose -4*n + 184 = 4*g, -2*g + 168 = 5*n - 50. Suppose -n*d - 148 = -46*d. Calculate the remainder when d is divided by 21.", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-251"}}
{"id": "dm-numbers__div_remainder_composed-hard-251", "pool": "math", "split": "train", "question": "Suppose -4*n + 11927 = 11467. Calculate the remainder when n is divided by 21.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-252"}}
{"id": "dm-numbers__div_remainder_composed-hard-252", "pool": "math", "split": "train", "question": "Let c(v) be the first derivative of -v**3/3 - 15*v**2/2 - 29*v - 10. Let o be c(-12). Suppose -3*q = 3*y - o - 8, -3*q = 5*y - 23. What is the remainder when y is divided by 3?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-253"}}
{"id": "dm-numbers__div_remainder_composed-hard-253", "pool": "math", "split": "train", "question": "Let p = 31 + -8. Let o = -179 - -347. Suppose 5*b = -19*b + o. Calculate the remainder when p is divided by b.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-254"}}
{"id": "dm-numbers__div_remainder_composed-hard-254", "pool": "math", "split": "train", "question": "Let y(t) = -15*t + 138 + 47 - 42. Calculate the remainder when 90 is divided by y(8).", "unit": "dimensionless", "value": "21", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-255"}}
{"id": "dm-numbers__div_remainder_composed-hard-255", "pool": "math", "split": "train", "question": "Suppose 0 = -5*o - h + 1420, 2*o - 5*h - 227 - 341 = 0. Suppose 0 = 18*l - o - 1318. Calculate the remainder when l is divided by 32.", "unit": "dimensionless", "value": "25", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-256"}}
{"id": "dm-numbers__div_remainder_composed-hard-256", "pool": "math", "split": "train", "question": "Let w(z) = -5*z**2 - 2*z + 2. Let y be w(-3). Let x = 12 - y. Let r(m) = -9*m - 332. What is the remainder when x is divided by r(-39)?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-257"}}
{"id": "dm-numbers__div_remainder_composed-hard-257", "pool": "math", "split": "train", "question": "Let c(b) = -31*b - 538. Calculate the remainder when c(-19) is divided by 6.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-258"}}
{"id": "dm-numbers__div_remainder_composed-hard-258", "pool": "math", "split": "train", "question": "Suppose 2*o + 203 = -5*o. Let l = 11 - o. What is the remainder when 238 is divided by l?", "unit": "dimensionless", "value": "38", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-259"}}
{"id": "dm-numbers__div_remainder_composed-hard-259", "pool": "math", "split": "train", "question": "Let u(d) = -d**3 + 10*d**2 - 15*d + 16. Let c be u(9). Let a = 41 + c. Suppose 11*l = 25 - a. What is the remainder when l is divided by 1?", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-260"}}
{"id": "dm-numbers__div_remainder_composed-hard-260", "pool": "math", "split": "train", "question": "Suppose 0 = -22*l + 37 + 117. Suppose l*u - 9*u - 4*n = -174, -87 = -u + 3*n. What is the remainder when u is divided by 36?", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-261"}}
{"id": "dm-numbers__div_remainder_composed-hard-261", "pool": "math", "split": "train", "question": "Let s = -49 - -12. Let q = s - -130. Suppose -19*h + 120 = -14*h. What is the remainder when q is divided by h?", "unit": "dimensionless", "value": "21", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-262"}}
{"id": "dm-numbers__div_remainder_composed-hard-262", "pool": "math", "split": "train", "question": "Let v(u) = 144*u + 287. Let w be v(-2). Calculate the remainder when -18*(1 + 5/(-3)) is divided by (4 + -7)/(-3)*(-3)/w.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-263"}}
{"id": "dm-numbers__div_remainder_composed-hard-263", "pool": "math", "split": "train", "question": "Let a be 1 + 0 - 415/20*4. Let f = a - -137. Calculate the remainder when f is divided by ((-14)/1)/(-2 + 1).", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-264"}}
{"id": "dm-numbers__div_remainder_composed-hard-264", "pool": "math", "split": "train", "question": "Let v(k) = 102*k - 317. Let t(q) = 7 - 2*q. Let l be t(7). Let g(h) = 2*h**2 + 11*h + 10. Calculate the remainder when v(4) is divided by g(l).", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-265"}}
{"id": "dm-numbers__div_remainder_composed-hard-265", "pool": "math", "split": "train", "question": "Let x = 154 + -73. Suppose x*f + 638 = 103*f. Calculate the remainder when 86 is divided by f.", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-266"}}
{"id": "dm-numbers__div_remainder_composed-hard-266", "pool": "math", "split": "train", "question": "Let i = -134 + 164. Calculate the remainder when 893 is divided by i.", "unit": "dimensionless", "value": "23", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-267"}}
{"id": "dm-numbers__div_remainder_composed-hard-267", "pool": "math", "split": "train", "question": "Calculate the remainder when 2443 is divided by (-4200)/(-260) - 16/104.", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-268"}}
{"id": "dm-numbers__div_remainder_composed-hard-268", "pool": "math", "split": "train", "question": "Let b be 36*3/(12/19). Suppose 0*s + 4*s + 67 = c, -3*c + b = -2*s. Let w(h) = -6*h - 8. Calculate the remainder when c is divided by w(-6).", "unit": "dimensionless", "value": "27", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-269"}}
{"id": "dm-numbers__div_remainder_composed-hard-269", "pool": "math", "split": "train", "question": "Suppose u - 2*h = 38, 3*h = 195*u - 196*u + 18. Suppose 4*a + 223 = 3*o - 2*o, 2*a = -4*o - 134. Let p = 116 + a. What is the remainder when p is divided by u?", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-270"}}
{"id": "dm-numbers__div_remainder_composed-hard-270", "pool": "math", "split": "train", "question": "Suppose 0 = -58*n + 62*n - 152. Let k = 67 - n. Let o = 34 - k. Calculate the remainder when 12 is divided by o.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-271"}}
{"id": "dm-numbers__div_remainder_composed-hard-271", "pool": "math", "split": "train", "question": "Let m = -6189 + 6260. Suppose 0 = 4*u - 217 + 65. Calculate the remainder when m is divided by u.", "unit": "dimensionless", "value": "33", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-272"}}
{"id": "dm-numbers__div_remainder_composed-hard-272", "pool": "math", "split": "train", "question": "Let w be (12/16)/(6/216). Suppose w*p - 19*p = 192. Calculate the remainder when 116 is divided by p.", "unit": "dimensionless", "value": "20", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-273"}}
{"id": "dm-numbers__div_remainder_composed-hard-273", "pool": "math", "split": "train", "question": "Let o(b) = -b**3 + 5*b**2 - 4*b - 3. Let f be o(2). Let q(m) = 39*m**2 - 8*m + 9. Calculate the remainder when 113 is divided by q(f).", "unit": "dimensionless", "value": "33", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-274"}}
{"id": "dm-numbers__div_remainder_composed-hard-274", "pool": "math", "split": "train", "question": "Let r(u) be the second derivative of -u**3/3 + 32*u**2 - 64*u. What is the remainder when 189 is divided by r(16)?", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-275"}}
{"id": "dm-numbers__div_remainder_composed-hard-275", "pool": "math", "split": "train", "question": "Suppose 5 = 3*m - 3*d - 28, -17 = -m - 5*d. Calculate the remainder when 682 is divided by m.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-276"}}
{"id": "dm-numbers__div_remainder_composed-hard-276", "pool": "math", "split": "train", "question": "Suppose m = -4*k + 883, 5*k + 349 = -2*m + 1452. Calculate the remainder when 934 is divided by k.", "unit": "dimensionless", "value": "50", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-277"}}
{"id": "dm-numbers__div_remainder_composed-hard-277", "pool": "math", "split": "train", "question": "Let d(s) = -5*s**3 + 13*s - 34*s**2 + 21*s**2 - 8 + 16*s**2. Let t(j) = 14*j**3 - 9*j**2 - 38*j + 23. Let w(z) = 8*d(z) + 3*t(z). Calculate the remainder when w(4) is divided by 6.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-278"}}
{"id": "dm-numbers__div_remainder_composed-hard-278", "pool": "math", "split": "train", "question": "Suppose -4*a + u = -3*u - 132, a - 48 = 4*u. Suppose 30*f - 648 = 22*f. Calculate the remainder when f is divided by a.", "unit": "dimensionless", "value": "25", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-279"}}
{"id": "dm-numbers__div_remainder_composed-hard-279", "pool": "math", "split": "train", "question": "Let v(t) = 73*t + 132. Let u be v(-8). Let p = 472 + u. Calculate the remainder when 52 is divided by p.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-280"}}
{"id": "dm-numbers__div_remainder_composed-hard-280", "pool": "math", "split": "train", "question": "Let a = 5632 + -2724. What is the remainder when a is divided by 15?", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-281"}}
{"id": "dm-numbers__div_remainder_composed-hard-281", "pool": "math", "split": "train", "question": "Calculate the remainder when ((-8)/80*12)/(2511/840 - 3) is divided by 32.", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-282"}}
{"id": "dm-numbers__div_remainder_composed-hard-282", "pool": "math", "split": "train", "question": "Let h = 265 + -184. Let z = -6890 + 6897. What is the remainder when h is divided by z?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-283"}}
{"id": "dm-numbers__div_remainder_composed-hard-283", "pool": "math", "split": "train", "question": "Suppose -17901 = 4*w - 81*w + 26*w. Calculate the remainder when w is divided by 36.", "unit": "dimensionless", "value": "27", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-284"}}
{"id": "dm-numbers__div_remainder_composed-hard-284", "pool": "math", "split": "train", "question": "Suppose -26 = f - 2*h, -116 = 2*f + 2*h - 76. Suppose 0 = -3*i - 2*i + 255. Let t = f + i. What is the remainder when t is divided by 11?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-285"}}
{"id": "dm-numbers__div_remainder_composed-hard-285", "pool": "math", "split": "train", "question": "What is the remainder when (-20334)/(-13) + 66/(-429) is divided by 87?", "unit": "dimensionless", "value": "85", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-286"}}
{"id": "dm-numbers__div_remainder_composed-hard-286", "pool": "math", "split": "train", "question": "Let c = 3818 - 3775. Calculate the remainder when 1976 is divided by c.", "unit": "dimensionless", "value": "41", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-287"}}
{"id": "dm-numbers__div_remainder_composed-hard-287", "pool": "math", "split": "train", "question": "Let t(g) = -g**3 + 6*g**2 + 24*g + 52. What is the remainder when 1349 is divided by t(9)?", "unit": "dimensionless", "value": "24", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-288"}}
{"id": "dm-numbers__div_remainder_composed-hard-288", "pool": "math", "split": "train", "question": "Suppose -k = 3*s - 220, k + 75 = 82. Calculate the remainder when s is divided by 32.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-289"}}
{"id": "dm-numbers__div_remainder_composed-hard-289", "pool": "math", "split": "train", "question": "Suppose -11*k + 398 + 72 + 14 = 0. What is the remainder when 3783 is divided by k?", "unit": "dimensionless", "value": "43", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-290"}}
{"id": "dm-numbers__div_remainder_composed-hard-290", "pool": "math", "split": "train", "question": "Suppose -y - 114 = -j, -378*y + 375*y = j - 90. What is the remainder when j is divided by 17?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-291"}}
{"id": "dm-numbers__div_remainder_composed-hard-291", "pool": "math", "split": "train", "question": "What is the remainder when 595 is divided by (-1 - 15/(-4)) + (-212)/(-848) - -1?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-292"}}
{"id": "dm-numbers__div_remainder_composed-hard-292", "pool": "math", "split": "train", "question": "Let o = -355 - -608. Calculate the remainder when 759 is divided by o.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-293"}}
{"id": "dm-numbers__div_remainder_composed-hard-293", "pool": "math", "split": "train", "question": "Calculate the remainder when 17181 is divided by ((-4)/2 + 286)*(-4 - (-81)/18).", "unit": "dimensionless", "value": "141", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-294"}}
{"id": "dm-numbers__div_remainder_composed-hard-294", "pool": "math", "split": "train", "question": "Let u = 128 - 129. Calculate the remainder when 608 is divided by -1 + (5 - u) - (-28 + 4).", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-295"}}
{"id": "dm-numbers__div_remainder_composed-hard-295", "pool": "math", "split": "train", "question": "Suppose 0 = 4*o - 4*d - 12, -5*d + 21 = -o + 5*o. Suppose j = -2*h + 5*h - 84, o*h + j - 105 = 0. Calculate the remainder when h is divided by 22.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-296"}}
{"id": "dm-numbers__div_remainder_composed-hard-296", "pool": "math", "split": "train", "question": "Suppose x - 5*v - 189 = 0, 66 = x + 3*v - 123. Let r = 260 - x. What is the remainder when 278 is divided by r?", "unit": "dimensionless", "value": "65", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-297"}}
{"id": "dm-numbers__div_remainder_composed-hard-297", "pool": "math", "split": "train", "question": "Let k be (-10)/(-6)*(-52038)/(-295). Suppose k = 40*o - 33*o. Calculate the remainder when 155 is divided by o.", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-298"}}
{"id": "dm-numbers__div_remainder_composed-hard-298", "pool": "math", "split": "train", "question": "What is the remainder when (185 - 17) + (-154)/11 is divided by 45?", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-299"}}
{"id": "dm-numbers__div_remainder_composed-hard-299", "pool": "math", "split": "train", "question": "Suppose -29*a + 20*a = -63. Suppose 18*b = -a*b + 2200. Calculate the remainder when b is divided by 16.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-300"}}
{"id": "dm-numbers__div_remainder_composed-hard-300", "pool": "math", "split": "train", "question": "Suppose 2*s = d + 62, -166 = s - 6*s - 3*d. Suppose -5*m = -13*m + s. Suppose -3*k - f = -26, 3*k - 66 = -2*k + m*f. What is the remainder when 199 is divided by k?", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-301"}}
{"id": "dm-numbers__div_remainder_composed-hard-301", "pool": "math", "split": "train", "question": "Let q(t) = -41*t - 20. Let h(x) = -x**3 - 34*x**2 + 35*x - 2. Let p be h(-35). Calculate the remainder when q(p) is divided by 27.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-302"}}
{"id": "dm-numbers__div_remainder_composed-hard-302", "pool": "math", "split": "train", "question": "Let f(y) = 5*y**2 + 8*y + 70. Let i(u) = -9*u**2 - 15*u - 138. Let t(c) = -11*f(c) - 6*i(c). What is the remainder when 397 is divided by t(8)?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-303"}}
{"id": "dm-numbers__div_remainder_composed-hard-303", "pool": "math", "split": "train", "question": "Let r = 16459 + -16448. Calculate the remainder when 258 is divided by r.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-304"}}
{"id": "dm-numbers__div_remainder_composed-hard-304", "pool": "math", "split": "train", "question": "Suppose 0 = -57*y + 19*y + 118180. What is the remainder when y is divided by 17?", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-305"}}
{"id": "dm-numbers__div_remainder_composed-hard-305", "pool": "math", "split": "train", "question": "Suppose -k + 32 = -64 - 52. What is the remainder when 1032 is divided by k?", "unit": "dimensionless", "value": "144", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-306"}}
{"id": "dm-numbers__div_remainder_composed-hard-306", "pool": "math", "split": "train", "question": "Let j be (-54)/(-135) - (-23)/5. Suppose 0 = -6*n + j*n - 4*b + 15, 3*n = -b + 67. Calculate the remainder when 160 is divided by n.", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-307"}}
{"id": "dm-numbers__div_remainder_composed-hard-307", "pool": "math", "split": "train", "question": "Let i(p) = -6*p**3 + 29*p**2 + 14*p + 98. Calculate the remainder when i(-7) is divided by 43.", "unit": "dimensionless", "value": "39", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-308"}}
{"id": "dm-numbers__div_remainder_composed-hard-308", "pool": "math", "split": "train", "question": "Let z = -15140 + 15356. Calculate the remainder when 410 is divided by z.", "unit": "dimensionless", "value": "194", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-309"}}
{"id": "dm-numbers__div_remainder_composed-hard-309", "pool": "math", "split": "train", "question": "Let d = -3214 + 3539. Calculate the remainder when d is divided by 51.", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-310"}}
{"id": "dm-numbers__div_remainder_composed-hard-310", "pool": "math", "split": "train", "question": "Calculate the remainder when (((-21)/7)/15 + 0)/(2/(-3970)) is divided by 158.", "unit": "dimensionless", "value": "81", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-311"}}
{"id": "dm-numbers__div_remainder_composed-hard-311", "pool": "math", "split": "train", "question": "Suppose -2*f = 3*f - 2*m - 39, 6 = f - m. Suppose u = 20 + f. Suppose -451 + 1530 = 13*b. Calculate the remainder when b is divided by u.", "unit": "dimensionless", "value": "25", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-312"}}
{"id": "dm-numbers__div_remainder_composed-hard-312", "pool": "math", "split": "train", "question": "Suppose 0 = n + 2*w, 4*n + 27 = n + 3*w. Let q(y) be the second derivative of -5*y**3/6 - 11*y**2/2 + y. What is the remainder when 75 is divided by q(n)?", "unit": "dimensionless", "value": "18", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-313"}}
{"id": "dm-numbers__div_remainder_composed-hard-313", "pool": "math", "split": "train", "question": "Let h(r) = r**3 - 8*r**2 - 16*r + 7. Let s be h(10). Let w = s + -51. What is the remainder when (w + -2)/(4*4/(-184)) is divided by 24?", "unit": "dimensionless", "value": "21", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-314"}}
{"id": "dm-numbers__div_remainder_composed-hard-314", "pool": "math", "split": "train", "question": "Let i be (9 + -13)*(-3)/6. Suppose -2*k = -6*k + u + 35, 20 = 2*k + i*u. What is the remainder when 192 is divided by k?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-315"}}
{"id": "dm-numbers__div_remainder_composed-hard-315", "pool": "math", "split": "train", "question": "Let u = 4 - 4. Suppose -s + 29 + 88 = u. Suppose -r - 4 = 4*b - 124, -5*r = 0. What is the remainder when s is divided by b?", "unit": "dimensionless", "value": "27", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-316"}}
{"id": "dm-numbers__div_remainder_composed-hard-316", "pool": "math", "split": "train", "question": "Suppose 11*h - 606 = 5*h. Let m = -67 + h. Suppose 3*y = 4*o - 44, -m = -5*o + 4*y + 21. Calculate the remainder when 62 is divided by o.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-317"}}
{"id": "dm-numbers__div_remainder_composed-hard-317", "pool": "math", "split": "train", "question": "Let a be ((-3)/(-5))/(4 - (-351)/(-90)). What is the remainder when 17 - 3 - (7 - 12/a) is divided by 5?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-318"}}
{"id": "dm-numbers__div_remainder_composed-hard-318", "pool": "math", "split": "train", "question": "Suppose 2*a = 273 + 73. Suppose 4*k + 9 = a. Suppose -2*g + 67 = k. Calculate the remainder when 25 is divided by g.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-319"}}
{"id": "dm-numbers__div_remainder_composed-hard-319", "pool": "math", "split": "train", "question": "Suppose 0 = -51*s - 49*s - 60*s + 4283680. Calculate the remainder when s is divided by 63.", "unit": "dimensionless", "value": "61", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-320"}}
{"id": "dm-numbers__div_remainder_composed-hard-320", "pool": "math", "split": "train", "question": "Let g(o) = -o**2 - 9*o + 31. Suppose 3974 = 51*s - 19639. Calculate the remainder when s is divided by g(-9).", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-321"}}
{"id": "dm-numbers__div_remainder_composed-hard-321", "pool": "math", "split": "train", "question": "Let w = -44765 + 45446. Calculate the remainder when w is divided by 38.", "unit": "dimensionless", "value": "35", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-322"}}
{"id": "dm-numbers__div_remainder_composed-hard-322", "pool": "math", "split": "train", "question": "Suppose -254*c + 87*c = -96165 - 130621. What is the remainder when c is divided by 154?", "unit": "dimensionless", "value": "126", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-323"}}
{"id": "dm-numbers__div_remainder_composed-hard-323", "pool": "math", "split": "train", "question": "Suppose -2*l + 7 = 3*h, -3*l + 1 = -3*h - 2. Calculate the remainder when (22 - 8)*21/l is divided by 19.", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-324"}}
{"id": "dm-numbers__div_remainder_composed-hard-324", "pool": "math", "split": "train", "question": "Suppose -5*m = -8 - 62. Suppose 1024 = m*g - 558. Calculate the remainder when g is divided by 32.", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-325"}}
{"id": "dm-numbers__div_remainder_composed-hard-325", "pool": "math", "split": "train", "question": "Suppose -41 - 1099 = -3*s. Let x = s - 368. Let g(q) = 32*q**2 + 2*q - 2. Calculate the remainder when g(2) is divided by x.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-326"}}
{"id": "dm-numbers__div_remainder_composed-hard-326", "pool": "math", "split": "train", "question": "Suppose -4*f + 53 + 6 = m, f + 216 = 3*m. What is the remainder when m is divided by 12?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-327"}}
{"id": "dm-numbers__div_remainder_composed-hard-327", "pool": "math", "split": "train", "question": "Suppose 126*w - 20 = 121*w. Let g(n) be the third derivative of 7*n**5/60 - n**4/4 + n**3/2 - 3*n**2. Calculate the remainder when g(w) is divided by 23.", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-328"}}
{"id": "dm-numbers__div_remainder_composed-hard-328", "pool": "math", "split": "train", "question": "Let l(m) be the second derivative of m**4/12 + 4*m**3/3 + 9*m**2/2 + 14*m. Let p be l(-10). Suppose 4*y + p = 125. What is the remainder when y is divided by 5?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-329"}}
{"id": "dm-numbers__div_remainder_composed-hard-329", "pool": "math", "split": "train", "question": "Let u = 175 + -97. Calculate the remainder when 269 is divided by (-13)/(u/20)*27/(-6).", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-330"}}
{"id": "dm-numbers__div_remainder_composed-hard-330", "pool": "math", "split": "train", "question": "Let z = -3802 + 3827. What is the remainder when 67 is divided by z?", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-331"}}
{"id": "dm-numbers__div_remainder_composed-hard-331", "pool": "math", "split": "train", "question": "Let b(q) = -2*q**3 + 40*q**2 - 24*q - 18. What is the remainder when b(5) is divided by 584?", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-332"}}
{"id": "dm-numbers__div_remainder_composed-hard-332", "pool": "math", "split": "train", "question": "Let j(h) = -h**3 - 4*h**2 + 2*h - 2. Suppose u + 5*u - 456 = 0. Suppose u = -8*m + 10*m. Calculate the remainder when m is divided by j(-5).", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-333"}}
{"id": "dm-numbers__div_remainder_composed-hard-333", "pool": "math", "split": "train", "question": "Suppose -22 = 5*j + 3, 3*f - 4*j + 34 = 0. Let c = 41 + f. Suppose -2*l + i + 11 = 0, -2*l + c = -0*l - 5*i. What is the remainder when 8 is divided by l?", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-334"}}
{"id": "dm-numbers__div_remainder_composed-hard-334", "pool": "math", "split": "train", "question": "Let g = -1 + 5. Let k(v) = v**3 - 10*v**2 + 17*v - 12. Let w be k(8). What is the remainder when (w - (-144)/42)*-28 is divided by g?", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-335"}}
{"id": "dm-numbers__div_remainder_composed-hard-335", "pool": "math", "split": "train", "question": "Let v(w) = -5*w**2 - 89*w - 262. What is the remainder when 63 is divided by v(-13)?", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-336"}}
{"id": "dm-numbers__div_remainder_composed-hard-336", "pool": "math", "split": "train", "question": "Let f(u) = 17*u**3 - 2. Let i(w) = -w**2 - 2*w + 4. Let q be i(-3). Calculate the remainder when 55 is divided by f(q).", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-337"}}
{"id": "dm-numbers__div_remainder_composed-hard-337", "pool": "math", "split": "train", "question": "Let t(c) = 3*c - 11. Let s(r) = 22 - 6*r. Let b(h) = 2*s(h) + 5*t(h). Let w be b(5). What is the remainder when 92 is divided by w/8*63 + (-2)/4?", "unit": "dimensionless", "value": "30", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-338"}}
{"id": "dm-numbers__div_remainder_composed-hard-338", "pool": "math", "split": "train", "question": "Let f(c) = 10*c**2 - 26*c - 70. Calculate the remainder when f(-3) is divided by 35.", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-339"}}
{"id": "dm-numbers__div_remainder_composed-hard-339", "pool": "math", "split": "train", "question": "Suppose -98 = -4*s + 2*i, -4*s - 4*i + 58 = -70. Suppose 4*c - 29 + 9 = -4*n, 0 = 4*c - 3*n - s. Calculate the remainder when 34 is divided by c.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-340"}}
{"id": "dm-numbers__div_remainder_composed-hard-340", "pool": "math", "split": "train", "question": "Suppose -3*t + 7 + 14 = 0. Suppose 9*y = t*y + 24. Calculate the remainder when 49 is divided by y - (-2 - (4 + -7)).", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-341"}}
{"id": "dm-numbers__div_remainder_composed-hard-341", "pool": "math", "split": "train", "question": "Suppose 2*l - 3*a - 343 = 0, -2*l + 263 = 3*a - 110. Calculate the remainder when 360 is divided by l.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-342"}}
{"id": "dm-numbers__div_remainder_composed-hard-342", "pool": "math", "split": "train", "question": "Suppose -4*r = -13 - 7, u - 2*r = 1094. Let l(o) = 9 - o. Calculate the remainder when (u/60 + -8)/((-4)/(-10)) is divided by l(-6).", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-343"}}
{"id": "dm-numbers__div_remainder_composed-hard-343", "pool": "math", "split": "train", "question": "Let y = 94 - 14. Let b(x) = 2*x**3 - 6*x**2 + 9*x. Let f be -1 - 0 - (-5)/5*4. What is the remainder when y is divided by b(f)?", "unit": "dimensionless", "value": "26", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-344"}}
{"id": "dm-numbers__div_remainder_composed-hard-344", "pool": "math", "split": "train", "question": "Suppose 22*k + 162 = 24*k. Suppose -3*r + 32 = -4*y, -2*r + 3*r - 3*y = 19. Suppose 3*u = 5*a - 104, 0*u = a + r*u - 30. Calculate the remainder when k is divided by a.", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-345"}}
{"id": "dm-numbers__div_remainder_composed-hard-345", "pool": "math", "split": "train", "question": "Suppose 0 = 16*z - 21*z - 20, 2*z - 36 = -4*c. What is the remainder when -1 + 39 + 15/3 is divided by c?", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-346"}}
{"id": "dm-numbers__div_remainder_composed-hard-346", "pool": "math", "split": "train", "question": "Let w(l) = -l**2 + 8 - 3 + 97*l**3 + 2*l + 2 - 98*l**3. Let p(q) = 6*q. What is the remainder when p(4) is divided by w(0)?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-347"}}
{"id": "dm-numbers__div_remainder_composed-hard-347", "pool": "math", "split": "train", "question": "Suppose -2 = 3*x - 8. Suppose -3*p - 71 = -5*g - p, -x*p = -3*g + 45. Calculate the remainder when (1 - 2) + 33 - (52 + -56) is divided by g.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-348"}}
{"id": "dm-numbers__div_remainder_composed-hard-348", "pool": "math", "split": "train", "question": "Suppose 53 - 293 = -8*j. What is the remainder when 142 is divided by 4/j - (-4 - 298/15)?", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-349"}}
{"id": "dm-numbers__div_remainder_composed-hard-349", "pool": "math", "split": "train", "question": "Suppose 0 = -4508*m + 4506*m + 194. Calculate the remainder when 678 is divided by m.", "unit": "dimensionless", "value": "96", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-350"}}
{"id": "dm-numbers__div_remainder_composed-hard-350", "pool": "math", "split": "train", "question": "Suppose -5*y = -5*b + 2290, 5*b + y - 2284 = 4*y. Suppose 164*m + b = 177*m. What is the remainder when m is divided by 9?", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-351"}}
{"id": "dm-numbers__div_remainder_composed-hard-351", "pool": "math", "split": "train", "question": "Suppose -3*p = -4*t + 133 - 322, -50 = t + 2*p. Suppose 73 = -5*o - 52. Calculate the remainder when -3 + (t/(-20))/((-1)/o) is divided by 10.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-352"}}
{"id": "dm-numbers__div_remainder_composed-hard-352", "pool": "math", "split": "train", "question": "Let h(i) = i**2 + 14*i + 5. Let v be h(-14). Suppose v*c - 3*r = -r + 26, -4*r = -4*c + 16. Suppose c*f + 5 = 59. What is the remainder when 52 is divided by f?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-353"}}
{"id": "dm-numbers__div_remainder_composed-hard-353", "pool": "math", "split": "train", "question": "Suppose 4*o - 520 = 5*p - 83, 5*o - 4*p - 535 = 0. What is the remainder when 453 is divided by o?", "unit": "dimensionless", "value": "41", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-354"}}
{"id": "dm-numbers__div_remainder_composed-hard-354", "pool": "math", "split": "train", "question": "Let i(t) = -t**2 - 10*t + 679. Suppose 2*p + 3*h - 12 = 0, 30*p + h - 4 = 33*p. What is the remainder when i(p) is divided by 8?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-355"}}
{"id": "dm-numbers__div_remainder_composed-hard-355", "pool": "math", "split": "train", "question": "What is the remainder when 142 is divided by (765/18 - 20)/(2/4)?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-356"}}
{"id": "dm-numbers__div_remainder_composed-hard-356", "pool": "math", "split": "train", "question": "Suppose 263 = 2*f + 5*l + 18, -254 = -2*f + 4*l. Suppose -3*r = -z - 20, -36 = 4*r - 9*r - z. What is the remainder when f is divided by r?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-357"}}
{"id": "dm-numbers__div_remainder_composed-hard-357", "pool": "math", "split": "train", "question": "Let s(m) = -35*m**3 + 3*m**2 - 6*m - 7. Let t = -164 - -163. What is the remainder when 143 is divided by s(t)?", "unit": "dimensionless", "value": "32", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-358"}}
{"id": "dm-numbers__div_remainder_composed-hard-358", "pool": "math", "split": "train", "question": "What is the remainder when 858 is divided by -53*((2 - 5 - 2) + 3)?", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-359"}}
{"id": "dm-numbers__div_remainder_composed-hard-359", "pool": "math", "split": "train", "question": "Suppose 0 = 11*z - 75 - 82 - 569. Let u(w) = -w**3 - 3*w**2. Let v be u(-5). Let b = z - v. What is the remainder when b is divided by 3?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-360"}}
{"id": "dm-numbers__div_remainder_composed-hard-360", "pool": "math", "split": "train", "question": "Let f(c) = 763 - 14*c. What is the remainder when 8305 is divided by f(54)?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-361"}}
{"id": "dm-numbers__div_remainder_composed-hard-361", "pool": "math", "split": "train", "question": "Let r(q) = -q**3 - 19*q**2 + 33*q - 76. What is the remainder when 343 is divided by r(-21)?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-362"}}
{"id": "dm-numbers__div_remainder_composed-hard-362", "pool": "math", "split": "train", "question": "Suppose 2*v - 4*b = 532 - 1902, 2*b - 2722 = 4*v. Suppose -u + 60 = 4*u. What is the remainder when v/(-42) - ((-22)/u - -2) is divided by 5?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-363"}}
{"id": "dm-numbers__div_remainder_composed-hard-363", "pool": "math", "split": "train", "question": "Let m be 1 - 3 - (72 - 59). Let l(f) = -f**2 - 6. Let u be l(0). Calculate the remainder when 3*22*(m/u + -1) is divided by 34.", "unit": "dimensionless", "value": "31", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-364"}}
{"id": "dm-numbers__div_remainder_composed-hard-364", "pool": "math", "split": "train", "question": "Let g(h) = h**3 - 4*h**2 + 7*h - 2. Let x be g(3). Suppose -2*u - v = -0*u - 10, -2*u + 4*v + x = 0. What is the remainder when 95 is divided by (-1)/(-1*u/160)?", "unit": "dimensionless", "value": "31", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-365"}}
{"id": "dm-numbers__div_remainder_composed-hard-365", "pool": "math", "split": "train", "question": "Let u be -6 + (-422)/(-8) + 1/4. Suppose 7*z = -128 - u. What is the remainder when 3*(4 + z/15) is divided by 2?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-366"}}
{"id": "dm-numbers__div_remainder_composed-hard-366", "pool": "math", "split": "train", "question": "Let j = -6923 - -6979. Let p = 273 + -68. What is the remainder when p is divided by j?", "unit": "dimensionless", "value": "37", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-367"}}
{"id": "dm-numbers__div_remainder_composed-hard-367", "pool": "math", "split": "train", "question": "Let h(y) = 103*y - 1687. What is the remainder when 1137 is divided by h(17)?", "unit": "dimensionless", "value": "49", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-368"}}
{"id": "dm-numbers__div_remainder_composed-hard-368", "pool": "math", "split": "train", "question": "Suppose -5*c = 18 - 8. Let d(m) = 2*m + 12. Let a be d(6). What is the remainder when (-180)/a*((-44)/10 + c) is divided by 10?", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-369"}}
{"id": "dm-numbers__div_remainder_composed-hard-369", "pool": "math", "split": "train", "question": "Let r = -5837 - -5839. Calculate the remainder when 802 is divided by r.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-370"}}
{"id": "dm-numbers__div_remainder_composed-hard-370", "pool": "math", "split": "train", "question": "Suppose 10*u = 6*u + 8. Let n = u + 13. Suppose -4*m + 5*h + 137 = 0, 0 = 5*h - 3*h - 6. Calculate the remainder when m is divided by n.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-371"}}
{"id": "dm-numbers__div_remainder_composed-hard-371", "pool": "math", "split": "train", "question": "Let v = -271 + 269. Let f(j) = -61*j - 33. Calculate the remainder when f(v) is divided by 18.", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-372"}}
{"id": "dm-numbers__div_remainder_composed-hard-372", "pool": "math", "split": "train", "question": "Suppose 72*h = -99*h + 27531. Calculate the remainder when h is divided by 14.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-373"}}
{"id": "dm-numbers__div_remainder_composed-hard-373", "pool": "math", "split": "train", "question": "Suppose g + g = -4. Suppose -31*b = -35*b + 60. Calculate the remainder when 9 is divided by g/(-4) - b/(-6).", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-374"}}
{"id": "dm-numbers__div_remainder_composed-hard-374", "pool": "math", "split": "train", "question": "Suppose 5*k - 3*q = 1903 - 505, 4*q = -2*k + 554. Let j = 409 - k. What is the remainder when j is divided by 67?", "unit": "dimensionless", "value": "63", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-375"}}
{"id": "dm-numbers__div_remainder_composed-hard-375", "pool": "math", "split": "train", "question": "Suppose -2*s = 2*s - 5*o - 52, -65 = -5*s + 5*o. Suppose 8 - 3 = u, 915 = 2*m - u. Let r = -398 + m. What is the remainder when r is divided by s?", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-376"}}
{"id": "dm-numbers__div_remainder_composed-hard-376", "pool": "math", "split": "train", "question": "Let a(c) = -c**3 + 9*c**2 + 23*c - 11. Let p be a(11). Calculate the remainder when 23/((-759)/22)*(p - 372) is divided by 36.", "unit": "dimensionless", "value": "32", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-377"}}
{"id": "dm-numbers__div_remainder_composed-hard-377", "pool": "math", "split": "train", "question": "Let c(p) = -20 - 40*p - 12 - 4 + 62 - 7*p**2. Calculate the remainder when 54 is divided by c(-6).", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-378"}}
{"id": "dm-numbers__div_remainder_composed-hard-378", "pool": "math", "split": "train", "question": "Let u = -59 - -250. Let p = u - -3. What is the remainder when p is divided by 28?", "unit": "dimensionless", "value": "26", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-379"}}
{"id": "dm-numbers__div_remainder_composed-hard-379", "pool": "math", "split": "train", "question": "Let g = -5056 - -5125. What is the remainder when 965 is divided by g?", "unit": "dimensionless", "value": "68", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-380"}}
{"id": "dm-numbers__div_remainder_composed-hard-380", "pool": "math", "split": "train", "question": "Let s = -20910 + 21074. Calculate the remainder when 2267 is divided by s.", "unit": "dimensionless", "value": "135", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-381"}}
{"id": "dm-numbers__div_remainder_composed-hard-381", "pool": "math", "split": "train", "question": "Let s(q) = 6*q**2 - 17*q - 2. Suppose -15*i = -16*i + 6. What is the remainder when s(i) is divided by 38?", "unit": "dimensionless", "value": "36", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-382"}}
{"id": "dm-numbers__div_remainder_composed-hard-382", "pool": "math", "split": "train", "question": "Suppose 0 = -6*r - 44*s + 39*s + 638, -5*s = -2*r + 226. What is the remainder when 765 is divided by r?", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-383"}}
{"id": "dm-numbers__div_remainder_composed-hard-383", "pool": "math", "split": "train", "question": "Let x(r) be the first derivative of r**4/4 + 8*r**3/3 - r**2/2 - 6*r + 17. Let k be x(-8). Suppose k*u = -p + 13, -2*u + 7 + 16 = 3*p. Calculate the remainder when 18 is divided by p.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-384"}}
{"id": "dm-numbers__div_remainder_composed-hard-384", "pool": "math", "split": "train", "question": "Suppose 3*n - 30 + 6 = 0. Suppose n*u - 21 - 27 = 0. Calculate the remainder when 4 - ((u - 5) + -29) is divided by 7.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-385"}}
{"id": "dm-numbers__div_remainder_composed-hard-385", "pool": "math", "split": "train", "question": "Let f = 1998 + -1971. What is the remainder when 3400 is divided by f?", "unit": "dimensionless", "value": "25", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-386"}}
{"id": "dm-numbers__div_remainder_composed-hard-386", "pool": "math", "split": "train", "question": "Calculate the remainder when 314 is divided by (3/30)/((-2)/(-8))*176400/504.", "unit": "dimensionless", "value": "34", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-387"}}
{"id": "dm-numbers__div_remainder_composed-hard-387", "pool": "math", "split": "train", "question": "Let w be 35/15 + 1/(-3). Suppose -w*p + 5*p - 375 = 0. Suppose 0 = -7*q + 57 + 167. What is the remainder when p is divided by q?", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-388"}}
{"id": "dm-numbers__div_remainder_composed-hard-388", "pool": "math", "split": "train", "question": "Suppose 4*f - 355 = 5*o, -229*f + 230*f - 75 = 4*o. Calculate the remainder when f is divided by 33.", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-389"}}
{"id": "dm-numbers__div_remainder_composed-hard-389", "pool": "math", "split": "train", "question": "Suppose -4*s - q = -7, -q - 13 = -2*s - 2. Let n = -76 + 48. Calculate the remainder when n*(3 - -1)/(-4) is divided by s.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-390"}}
{"id": "dm-numbers__div_remainder_composed-hard-390", "pool": "math", "split": "train", "question": "Let n(x) = 5*x**2 + 32*x - 16. Calculate the remainder when 660 is divided by n(-7).", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-391"}}
{"id": "dm-numbers__div_remainder_composed-hard-391", "pool": "math", "split": "train", "question": "Let s(q) = 3*q**2 + 7*q - 10. Let j(b) = -19*b - 1987. What is the remainder when s(-8) is divided by j(-108)?", "unit": "dimensionless", "value": "61", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-392"}}
{"id": "dm-numbers__div_remainder_composed-hard-392", "pool": "math", "split": "train", "question": "Let l(n) = -n**3 - 14*n**2 - 7*n + 313. Suppose 4*s - 5*r = 43, -6*s - 3*r + 51 = -2*s. What is the remainder when l(-11) is divided by s?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-393"}}
{"id": "dm-numbers__div_remainder_composed-hard-393", "pool": "math", "split": "train", "question": "Suppose 5*k = 7*k - 3*w + 79, 2*k + w = -67. Let m = k - -49. What is the remainder when 76 is divided by m?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-394"}}
{"id": "dm-numbers__div_remainder_composed-hard-394", "pool": "math", "split": "train", "question": "Let h = 6717 + -6666. What is the remainder when h is divided by 40?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-395"}}
{"id": "dm-numbers__div_remainder_composed-hard-395", "pool": "math", "split": "train", "question": "Let z = -5590 - -5619. Calculate the remainder when 1473 is divided by z.", "unit": "dimensionless", "value": "23", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-396"}}
{"id": "dm-numbers__div_remainder_composed-hard-396", "pool": "math", "split": "train", "question": "What is the remainder when (-2)/(10/(-16485)) - (9/(-3) + 7) is divided by 32?", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-397"}}
{"id": "dm-numbers__div_remainder_composed-hard-397", "pool": "math", "split": "train", "question": "Let b(f) = -6*f - 99. Suppose 3*s = 10*j - 9*j + 25, 4*s - 8 = 0. Suppose 3*k + 0 = 21. What is the remainder when b(j) is divided by k?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-398"}}
{"id": "dm-numbers__div_remainder_composed-hard-398", "pool": "math", "split": "train", "question": "Suppose 0 = -12*p + 27*p - 255. Let z(x) = 6*x**2 - 4*x + 3. Let r be z(2). Suppose -4*b + r = -113. Calculate the remainder when b is divided by p.", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-399"}}
{"id": "dm-numbers__div_remainder_composed-hard-399", "pool": "math", "split": "train", "question": "Suppose -3*t - 4563 - 4986 = -2*a, -3*a - 5*t = -14371. What is the remainder when a is divided by 26?", "unit": "dimensionless", "value": "24", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-400"}}
{"id": "dm-numbers__div_remainder_composed-hard-400", "pool": "math", "split": "train", "question": "Let n(d) = 152*d - 190. Calculate the remainder when n(4) is divided by 29.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-401"}}
{"id": "dm-numbers__div_remainder_composed-hard-401", "pool": "math", "split": "train", "question": "Let z(u) = -4*u - 45. Let t be z(-14). Suppose -16 = -15*h + t*h. Suppose 0 = -2*q - 3*q - h*w + 62, -w - 72 = -5*q. Calculate the remainder when 49 is divided by q.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-402"}}
{"id": "dm-numbers__div_remainder_composed-hard-402", "pool": "math", "split": "train", "question": "Suppose -o = -117*o + 1160. What is the remainder when 1708 is divided by o?", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-403"}}
{"id": "dm-numbers__div_remainder_composed-hard-403", "pool": "math", "split": "train", "question": "Let x be (-6)/(-4)*(-12)/144*-16. Suppose 1 = -3*g - 4*z + 2, 3*z + 6 = 0. Suppose -x*v - 6 = -3*v - 5*j, 0 = -g*v + 4*j + 37. Calculate the remainder when 74 is divided by v.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-404"}}
{"id": "dm-numbers__div_remainder_composed-hard-404", "pool": "math", "split": "train", "question": "Let n(o) = -o**2 + 139*o - 1459. What is the remainder when n(12) is divided by 48?", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-405"}}
{"id": "dm-numbers__div_remainder_composed-hard-405", "pool": "math", "split": "train", "question": "Suppose -57*k = -2094 - 7083. Calculate the remainder when 732 is divided by k.", "unit": "dimensionless", "value": "88", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-406"}}
{"id": "dm-numbers__div_remainder_composed-hard-406", "pool": "math", "split": "train", "question": "Let r(d) = -3*d**3 + 74*d**2 + 107*d - 9. Calculate the remainder when 84 is divided by r(26).", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-407"}}
{"id": "dm-numbers__div_remainder_composed-hard-407", "pool": "math", "split": "train", "question": "Suppose -13*s - 6 = -8*s + 2*h, 3*h = -3*s - 9. Suppose s = k + 33*n - 35*n - 275, 0 = -k + n + 276. Calculate the remainder when k is divided by 72.", "unit": "dimensionless", "value": "61", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-408"}}
{"id": "dm-numbers__div_remainder_composed-hard-408", "pool": "math", "split": "train", "question": "What is the remainder when 334 is divided by (-50 + -11)*(-3 + (-4)/(-4))?", "unit": "dimensionless", "value": "90", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-409"}}
{"id": "dm-numbers__div_remainder_composed-hard-409", "pool": "math", "split": "train", "question": "Suppose 0 = a + 3*a - u - 266, -2*u + 62 = a. Let b = -689 - -706. Calculate the remainder when a is divided by b.", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__div_remainder_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__div_remainder_composed", "level": "hard", "seed": "numbers__div_remainder_composed-hard-410"}}
{"id": "dm-numbers__gcd_composed-hard-0", "pool": "math", "split": "train", "question": "Suppose 0 = -4*g + 2*g - h - 601, 2*g + 2*h + 602 = 0. Let b = -60 - g. Calculate the highest common divisor of b and 48.", "unit": "dimensionless", "value": "48", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-1"}}
{"id": "dm-numbers__gcd_composed-hard-1", "pool": "math", "split": "train", "question": "Let t be ((-5)/(-10))/((-3)/(-30)). Let p = -177 - -123. Let z = 74 + p. What is the greatest common divisor of z and t?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-2"}}
{"id": "dm-numbers__gcd_composed-hard-2", "pool": "math", "split": "train", "question": "Let g(j) = 2 - 108*j. Let m be g(-1). Suppose -3*x - 80 = -11*x. Calculate the highest common divisor of x and m.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-3"}}
{"id": "dm-numbers__gcd_composed-hard-3", "pool": "math", "split": "train", "question": "Suppose -3 = 4*d + j, -2*d + j = 2*j + 1. Let b(o) = 18*o - 46*o - 3*o - 50*o - 1. Let z be b(d). Calculate the highest common divisor of 5 and z.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-4"}}
{"id": "dm-numbers__gcd_composed-hard-4", "pool": "math", "split": "train", "question": "Let g(d) = 19*d**2 + 35*d + 306. Let m be g(-7). What is the highest common factor of 96 and m?", "unit": "dimensionless", "value": "32", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-5"}}
{"id": "dm-numbers__gcd_composed-hard-5", "pool": "math", "split": "train", "question": "Let g(w) be the third derivative of w**5/12 - w**4/4 - 5*w**3/6 - 12*w**2. Let z be g(5). Suppose 5*n + 76 = 3*j, -4*j - 2*n + z = -3*n. Calculate the highest common factor of 33 and j.", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-6"}}
{"id": "dm-numbers__gcd_composed-hard-6", "pool": "math", "split": "train", "question": "Suppose 440*h + 2 = 439*h, 3*j + 1 = -2*h. Calculate the greatest common factor of 131 and j.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-7"}}
{"id": "dm-numbers__gcd_composed-hard-7", "pool": "math", "split": "train", "question": "Let r(p) = 2*p + 1007. Let u be r(4). Calculate the highest common factor of 203 and u.", "unit": "dimensionless", "value": "203", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-8"}}
{"id": "dm-numbers__gcd_composed-hard-8", "pool": "math", "split": "train", "question": "Suppose -v - 3*h + 7 = 0, -11 = -4*v - 0*h + 5*h. Suppose j = v, 0*r + j = 4*r - 880. Suppose o - 5*b + r = 3*o, -b = 4*o - 433. Calculate the greatest common divisor of 18 and o.", "unit": "dimensionless", "value": "18", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-9"}}
{"id": "dm-numbers__gcd_composed-hard-9", "pool": "math", "split": "train", "question": "Suppose 26 - 6 = 5*y, -3*k - 4*y = -289. Suppose 0 = -c - 29*c + 170 + 40. Calculate the highest common divisor of k and c.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-10"}}
{"id": "dm-numbers__gcd_composed-hard-10", "pool": "math", "split": "train", "question": "Let j(i) = 2260 - 88*i. Let f be j(22). What is the highest common divisor of f and 588?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-11"}}
{"id": "dm-numbers__gcd_composed-hard-11", "pool": "math", "split": "train", "question": "Suppose 3*f - 5344 = q, 144*q = 2*f + 146*q - 3552. What is the highest common factor of 1 and f?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-12"}}
{"id": "dm-numbers__gcd_composed-hard-12", "pool": "math", "split": "train", "question": "Let b = -1410 + 1608. Let w be 261/6 + 1/2. Calculate the greatest common factor of b and w.", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-13"}}
{"id": "dm-numbers__gcd_composed-hard-13", "pool": "math", "split": "train", "question": "Let v(s) = -s**3 - 10*s**2 - 3*s - 28. Let m be v(-10). Suppose -2*w - m*w + f - 127 = 0, -f = -3*w - 95. Let z be w/24*(1 + -121). What is the greatest common divisor of z and 40?", "unit": "dimensionless", "value": "40", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-14"}}
{"id": "dm-numbers__gcd_composed-hard-14", "pool": "math", "split": "train", "question": "Let j = -22881 + 23247. Calculate the highest common divisor of 14762 and j.", "unit": "dimensionless", "value": "122", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-15"}}
{"id": "dm-numbers__gcd_composed-hard-15", "pool": "math", "split": "train", "question": "Let m(k) = -k**2 + 16*k + 20. Let f be m(18). Let u be 69/15 - f/40. Suppose -z = 2*p + 98 - 295, -3*p + 313 = u*z. Calculate the greatest common divisor of p and 24.", "unit": "dimensionless", "value": "24", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-16"}}
{"id": "dm-numbers__gcd_composed-hard-16", "pool": "math", "split": "train", "question": "Let q be (-16)/(-1*(0 + 1)). Let o be (-945)/70*(-16)/6. What is the greatest common factor of o and q?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-17"}}
{"id": "dm-numbers__gcd_composed-hard-17", "pool": "math", "split": "train", "question": "Let y be (-2)/6 + (-946)/(-3). Let s = 27993 + -27963. Calculate the highest common factor of y and s.", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-18"}}
{"id": "dm-numbers__gcd_composed-hard-18", "pool": "math", "split": "train", "question": "Suppose 260 = 3*m + 2*p + 2*p, m - 5*p - 55 = 0. Let n be (-1 + -11)/((-27)/(-18)). Let r be (20/n)/(4/(-8)). Calculate the greatest common divisor of m and r.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-19"}}
{"id": "dm-numbers__gcd_composed-hard-19", "pool": "math", "split": "train", "question": "Let i = 195 + 377. Let o(d) = -d**2 - 9*d + 24. Let z be o(-4). What is the highest common divisor of z and i?", "unit": "dimensionless", "value": "44", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-20"}}
{"id": "dm-numbers__gcd_composed-hard-20", "pool": "math", "split": "train", "question": "Let n be (-13)/((-52)/(-60))*(-4)/10. Let i be n/1 - 3 - -4. Suppose -553 = -i*w + 518. What is the greatest common divisor of 17 and w?", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-21"}}
{"id": "dm-numbers__gcd_composed-hard-21", "pool": "math", "split": "train", "question": "Suppose -121 = -2*j + 25. Let q = 298 - j. What is the highest common divisor of 25 and q?", "unit": "dimensionless", "value": "25", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-22"}}
{"id": "dm-numbers__gcd_composed-hard-22", "pool": "math", "split": "train", "question": "Suppose -31*x + 34 = -29*x. Suppose -4*q = 4*y + 4, -3*y = -q + 2*y + x. Suppose 33 = q*i - 33. Calculate the highest common divisor of i and 3.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-23"}}
{"id": "dm-numbers__gcd_composed-hard-23", "pool": "math", "split": "train", "question": "Let h = -3229 + 3325. What is the greatest common divisor of h and 72?", "unit": "dimensionless", "value": "24", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-24"}}
{"id": "dm-numbers__gcd_composed-hard-24", "pool": "math", "split": "train", "question": "Suppose -155 + 955 = -m. Let y = -792 - m. Calculate the greatest common factor of y and 12.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-25"}}
{"id": "dm-numbers__gcd_composed-hard-25", "pool": "math", "split": "train", "question": "Let m(j) = j**3 + 22*j**2 - 20*j + 101. Let d be m(-23). What is the greatest common factor of 1584 and d?", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-26"}}
{"id": "dm-numbers__gcd_composed-hard-26", "pool": "math", "split": "train", "question": "Let i(f) = -2*f - 21. Let n = 34 + -29. Suppose k - 3*k + 4*s = 66, 3*s = n*k + 151. Let q be i(k). Calculate the greatest common factor of q and 333.", "unit": "dimensionless", "value": "37", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-27"}}
{"id": "dm-numbers__gcd_composed-hard-27", "pool": "math", "split": "train", "question": "Suppose 0*m + 3*m + 3*v - 837 = 0, -1092 = -4*m - v. Calculate the greatest common factor of 271 and m.", "unit": "dimensionless", "value": "271", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-28"}}
{"id": "dm-numbers__gcd_composed-hard-28", "pool": "math", "split": "train", "question": "Suppose 36 - 14 = l. Let c be 40/l - 4/(-22). Suppose 4*j + 5*a + 31 = 159, -24 = -3*a. What is the greatest common divisor of j and c?", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-29"}}
{"id": "dm-numbers__gcd_composed-hard-29", "pool": "math", "split": "train", "question": "Let i(h) = -h**3 + 21*h**2 + 23*h - 20. Let p be i(22). Suppose p*z + 5*j - 49 - 4 = 0, -j = 1. Calculate the highest common factor of 232 and z.", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-30"}}
{"id": "dm-numbers__gcd_composed-hard-30", "pool": "math", "split": "train", "question": "Suppose -r + 35 = 12. Let k be 204 - (3 + 1 + -7). Calculate the highest common factor of r and k.", "unit": "dimensionless", "value": "23", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-31"}}
{"id": "dm-numbers__gcd_composed-hard-31", "pool": "math", "split": "train", "question": "Let n be 6*2*22/66. Let g be 10/n*(-102)/(-17)*-13. Let h be 0 + ((-1444)/(-30) - (-26)/g). What is the greatest common divisor of h and 16?", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-32"}}
{"id": "dm-numbers__gcd_composed-hard-32", "pool": "math", "split": "train", "question": "Suppose 5*c - 72 = -5*q + 53, -2*c = 4*q - 98. Suppose -3*j + 0*j = -4*m + 1647, 4*m - 1612 = -4*j. What is the greatest common divisor of q and m?", "unit": "dimensionless", "value": "24", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-33"}}
{"id": "dm-numbers__gcd_composed-hard-33", "pool": "math", "split": "train", "question": "Let n be -2*(-1 - 0) + 102/34. Suppose 30 = n*c - 115. What is the highest common divisor of 1 and c?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-34"}}
{"id": "dm-numbers__gcd_composed-hard-34", "pool": "math", "split": "train", "question": "Let b = -1927 - -1956. Calculate the highest common divisor of b and 1421.", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-35"}}
{"id": "dm-numbers__gcd_composed-hard-35", "pool": "math", "split": "train", "question": "Let x(p) = 60*p - 169. Let d be x(3). Suppose -66*v + 4840 = -d*v. Calculate the greatest common divisor of 121 and v.", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-36"}}
{"id": "dm-numbers__gcd_composed-hard-36", "pool": "math", "split": "train", "question": "Let a be 4/(-1) + 1 - -23. Suppose 4*s - 5*c + 13 = 0, 5*s - 5*c = -9*c - 47. Let z be 56 - (s + 9 + -6). Calculate the greatest common divisor of a and z.", "unit": "dimensionless", "value": "20", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-37"}}
{"id": "dm-numbers__gcd_composed-hard-37", "pool": "math", "split": "train", "question": "Let o be (27/6)/((-1)/2). Let u(i) = 42 - 5*i. Let d be u(6). Let k be d/o - (-488)/24. What is the greatest common factor of 133 and k?", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-38"}}
{"id": "dm-numbers__gcd_composed-hard-38", "pool": "math", "split": "train", "question": "Let l(g) = -g**2 + 67*g + 3247. Let k be l(-31). What is the greatest common factor of k and 242?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-39"}}
{"id": "dm-numbers__gcd_composed-hard-39", "pool": "math", "split": "train", "question": "Suppose 4*a - r - 70 = 0, 0 = -3*a - 3*r + 4*r + 52. Let q(o) = o**3 - 36*o**2 + 51*o - 146. Let b be q(35). What is the greatest common factor of a and b?", "unit": "dimensionless", "value": "18", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-40"}}
{"id": "dm-numbers__gcd_composed-hard-40", "pool": "math", "split": "train", "question": "Suppose -4*d + 252 = 236. Suppose -12 = -d*f + v, -2*v + 6*v - 6 = -2*f. What is the greatest common divisor of f and 54?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-41"}}
{"id": "dm-numbers__gcd_composed-hard-41", "pool": "math", "split": "train", "question": "Let n = -182 + 185. Suppose n*k = 4*d + 384, -9*k + d + 256 = -7*k. Calculate the highest common factor of k and 64.", "unit": "dimensionless", "value": "64", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-42"}}
{"id": "dm-numbers__gcd_composed-hard-42", "pool": "math", "split": "train", "question": "Suppose -3*r + 135 = 6*r. Suppose 0 = g - 2*o - 50 + r, -100 = -3*g + o. Suppose 0 = 5*j + 5*y - 1465, y + 845 = 5*j - 644. Calculate the greatest common divisor of j and g.", "unit": "dimensionless", "value": "33", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-43"}}
{"id": "dm-numbers__gcd_composed-hard-43", "pool": "math", "split": "train", "question": "Suppose 0 = 55*j - 48*j - 1512. Let h = j - -83. Calculate the greatest common divisor of 23 and h.", "unit": "dimensionless", "value": "23", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-44"}}
{"id": "dm-numbers__gcd_composed-hard-44", "pool": "math", "split": "train", "question": "Let k(b) = -b**3 - 7*b**2 - 13*b - 4. Let w be k(-3). Let a be -1*(-4)/w - -18. Suppose 2*x - 16 = 6*x, -3*l - 2 = 2*x. What is the highest common divisor of a and l?", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-45"}}
{"id": "dm-numbers__gcd_composed-hard-45", "pool": "math", "split": "train", "question": "Suppose 169 = n - h - 17, 510 = 3*n + 5*h. Calculate the greatest common factor of 44 and n.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-46"}}
{"id": "dm-numbers__gcd_composed-hard-46", "pool": "math", "split": "train", "question": "Let b = 3627 + -3612. What is the greatest common factor of 435 and b?", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-47"}}
{"id": "dm-numbers__gcd_composed-hard-47", "pool": "math", "split": "train", "question": "Let o be 0/((-6)/(-3)) - -36. Suppose 7*f = 11*f + 2*m - 426, m = 4*f - 435. Suppose 92*p - 93*p - 3*t = -36, 3*t + f = 2*p. What is the highest common divisor of o and p?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-48"}}
{"id": "dm-numbers__gcd_composed-hard-48", "pool": "math", "split": "train", "question": "Let o(f) = 101 - 29*f. Suppose -14*w + 9*w = -15. Let c be o(w). Let u = -14 - -28. What is the greatest common factor of c and u?", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-49"}}
{"id": "dm-numbers__gcd_composed-hard-49", "pool": "math", "split": "train", "question": "Suppose 274*k + 2431 - 5719 = 0. Suppose 3*u - u + 3*f - 771 = 0, 5*u - 3*f - 1917 = 0. Calculate the highest common divisor of k and u.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-50"}}
{"id": "dm-numbers__gcd_composed-hard-50", "pool": "math", "split": "train", "question": "Let i(d) = 9*d + 11 + d**2 + 2*d**2 - 4*d**2. Let h be i(7). Suppose -5*m + 4*t = -3 - 30, -3*t - 26 = -4*m. Calculate the greatest common factor of h and m.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-51"}}
{"id": "dm-numbers__gcd_composed-hard-51", "pool": "math", "split": "train", "question": "Suppose w - 11 = 5*y, -3*y - 7*w + 11*w = 10. Let m be (-5 - (2 - (2 - y))) + 25. Calculate the greatest common divisor of 154 and m.", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-52"}}
{"id": "dm-numbers__gcd_composed-hard-52", "pool": "math", "split": "train", "question": "Suppose 1882 - 676 = 4*f - 5*a, a + 1230 = 4*f. What is the highest common divisor of 6 and f?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-53"}}
{"id": "dm-numbers__gcd_composed-hard-53", "pool": "math", "split": "train", "question": "Suppose 133 + 35 = -6*w. Let n = -16 - w. Let z be n/4 - -1 - 0. What is the greatest common divisor of 44 and z?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-54"}}
{"id": "dm-numbers__gcd_composed-hard-54", "pool": "math", "split": "train", "question": "Let s(t) = t**2 + 3*t - 2. Let m be s(-4). Let z(i) = -2*i - 2 - 2*i**2 - 1 + m + 23*i**3 - 26*i**3. Let x be z(-1). What is the greatest common factor of 1 and x?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-55"}}
{"id": "dm-numbers__gcd_composed-hard-55", "pool": "math", "split": "train", "question": "Let d(h) = 8*h - 93. Let o(y) = 4*y - 45. Let b(s) = -4*d(s) + 9*o(s). Let m be b(15). What is the greatest common factor of 12 and m?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-56"}}
{"id": "dm-numbers__gcd_composed-hard-56", "pool": "math", "split": "train", "question": "Let u(d) = -d**3 + 5*d**2 - 9*d + 2. Let s be u(3). Let n be 111 - (56/(-7) - s). Calculate the greatest common divisor of 28 and n.", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-57"}}
{"id": "dm-numbers__gcd_composed-hard-57", "pool": "math", "split": "train", "question": "Suppose -12 = -7*b + 2. Let n(l) be the third derivative of l**6/30 - l**5/30 - l**3/6 - l**2. Let v be n(b). Calculate the highest common divisor of v and 207.", "unit": "dimensionless", "value": "23", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-58"}}
{"id": "dm-numbers__gcd_composed-hard-58", "pool": "math", "split": "train", "question": "Let w(l) = -4*l**3 - 12. Let p be w(-3). Suppose 2 = -7*u - 5. Let c = 11 - u. Calculate the highest common divisor of c and p.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-59"}}
{"id": "dm-numbers__gcd_composed-hard-59", "pool": "math", "split": "train", "question": "Suppose -13*b = -7550 - 1693. Suppose n - 802 = -b. What is the greatest common divisor of n and 7?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-60"}}
{"id": "dm-numbers__gcd_composed-hard-60", "pool": "math", "split": "train", "question": "Suppose -9*l = -l. Suppose l = s - 5*v - 15, 10 = 4*s + 3*v + 2*v. Let c(d) = 6*d + 10. Let f be c(s). What is the greatest common divisor of 16 and f?", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-61"}}
{"id": "dm-numbers__gcd_composed-hard-61", "pool": "math", "split": "train", "question": "Suppose 323 = 2*t - 5*l + 103, -110 = -t + 2*l. Let s be -4 - ((-12)/(-16))/((-3)/156). Let k = s + -25. What is the greatest common divisor of t and k?", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-62"}}
{"id": "dm-numbers__gcd_composed-hard-62", "pool": "math", "split": "train", "question": "Suppose 161*j - 292*j = -149*j + 18360. Suppose 2*w + 60 = 5*w. Calculate the greatest common divisor of w and j.", "unit": "dimensionless", "value": "20", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-63"}}
{"id": "dm-numbers__gcd_composed-hard-63", "pool": "math", "split": "train", "question": "Let n(a) be the second derivative of -a**4/12 - 5*a**3/2 + 35*a**2/2 + 4*a. Let d be n(-13). Suppose -t - 3*r + 8 = -2, -d = -4*t - 5*r. Calculate the highest common divisor of 57 and t.", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-64"}}
{"id": "dm-numbers__gcd_composed-hard-64", "pool": "math", "split": "train", "question": "Suppose 6857 = 5*x + 5027. Calculate the highest common divisor of x and 3050.", "unit": "dimensionless", "value": "122", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-65"}}
{"id": "dm-numbers__gcd_composed-hard-65", "pool": "math", "split": "train", "question": "Suppose -1722 = -7*o + 2590. Suppose 92 = -3*b - q - 528, 0 = 3*b + 2*q + o. Let s = 433 + b. Calculate the highest common divisor of 25 and s.", "unit": "dimensionless", "value": "25", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-66"}}
{"id": "dm-numbers__gcd_composed-hard-66", "pool": "math", "split": "train", "question": "Let h(v) be the second derivative of 7*v**3/2 + 2*v. Let n be h(2). Let z be (-8)/(-20) - 28/(-5). Calculate the greatest common divisor of n and z.", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-67"}}
{"id": "dm-numbers__gcd_composed-hard-67", "pool": "math", "split": "train", "question": "Let j be (-2)/4 - (-90)/12. Let g be 7*(-180)/(-378) + (-4)/3. Calculate the highest common divisor of g and j.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-68"}}
{"id": "dm-numbers__gcd_composed-hard-68", "pool": "math", "split": "train", "question": "Suppose 0 = 4*j - j - 1110. Let u = -206176 + 206472. What is the greatest common factor of j and u?", "unit": "dimensionless", "value": "74", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-69"}}
{"id": "dm-numbers__gcd_composed-hard-69", "pool": "math", "split": "train", "question": "Let r = 34 + -13. Let d(w) = 42 - 2*w. Let m be d(r). Suppose 0 = -m*a + a - 22. What is the greatest common factor of 33 and a?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-70"}}
{"id": "dm-numbers__gcd_composed-hard-70", "pool": "math", "split": "train", "question": "Let k(b) be the second derivative of -b**3/6 + 51*b**2/2 - 9*b - 5. Let w be k(-9). What is the greatest common factor of 240 and w?", "unit": "dimensionless", "value": "60", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-71"}}
{"id": "dm-numbers__gcd_composed-hard-71", "pool": "math", "split": "train", "question": "Suppose 2*j + w = 2, w = 4*j + j - 12. Let l = -76 + 36. Let g be (-3)/(-6*(-2)/l). What is the greatest common divisor of g and j?", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-72"}}
{"id": "dm-numbers__gcd_composed-hard-72", "pool": "math", "split": "train", "question": "Let b = 255 - 90. Let q(z) = -2*z**3 + 19*z**2 - 7*z - 9. Let h be q(9). Let r(g) = -g**2 + 10*g + 6. Let m be r(h). What is the greatest common factor of b and m?", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-73"}}
{"id": "dm-numbers__gcd_composed-hard-73", "pool": "math", "split": "train", "question": "Suppose -3*j + 1630 = -5*p, -133*j + 128*j + 2723 = -2*p. What is the greatest common factor of j and 218?", "unit": "dimensionless", "value": "109", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-74"}}
{"id": "dm-numbers__gcd_composed-hard-74", "pool": "math", "split": "train", "question": "Let b(x) = x**3 + 10*x**2 - 34*x + 4. Let l = 1191 - 1188. Let r be b(l). Let s be -1*1 + 97 + -1. Calculate the highest common divisor of r and s.", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-75"}}
{"id": "dm-numbers__gcd_composed-hard-75", "pool": "math", "split": "train", "question": "Let l = 323 + -190. What is the greatest common divisor of 259 and l?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-76"}}
{"id": "dm-numbers__gcd_composed-hard-76", "pool": "math", "split": "train", "question": "Let a = -2353 + 2357. What is the highest common factor of 122 and a?", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-77"}}
{"id": "dm-numbers__gcd_composed-hard-77", "pool": "math", "split": "train", "question": "Let z = -7323 + 11256. Calculate the highest common divisor of z and 1026.", "unit": "dimensionless", "value": "171", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-78"}}
{"id": "dm-numbers__gcd_composed-hard-78", "pool": "math", "split": "train", "question": "Suppose 55*d - 86*d = -1240. What is the greatest common factor of d and 64?", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-79"}}
{"id": "dm-numbers__gcd_composed-hard-79", "pool": "math", "split": "train", "question": "Suppose -6999 = -2*b - 5613. Suppose 5*o - 255 = -4*t + 2*o, 3*t = 3*o + 186. Calculate the greatest common divisor of t and b.", "unit": "dimensionless", "value": "63", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-80"}}
{"id": "dm-numbers__gcd_composed-hard-80", "pool": "math", "split": "train", "question": "Let m = -50 + 55. Let u = m - 0. Suppose -u*v + 739 = -241. Calculate the greatest common factor of v and 28.", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-81"}}
{"id": "dm-numbers__gcd_composed-hard-81", "pool": "math", "split": "train", "question": "Let x(n) = -4*n**2 - 62*n - 105. Let b be x(-5). Let f = 63 - 42. Calculate the greatest common divisor of b and f.", "unit": "dimensionless", "value": "21", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-82"}}
{"id": "dm-numbers__gcd_composed-hard-82", "pool": "math", "split": "train", "question": "Suppose 10 = -5*n + 5*s, 2*n - 19*s + 22*s - 21 = 0. Suppose n*y - y - 42 = 0. Calculate the highest common factor of 18 and y.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-83"}}
{"id": "dm-numbers__gcd_composed-hard-83", "pool": "math", "split": "train", "question": "Suppose -206*k - 32*k = 1177 - 8555. Let w = 146 + 9. Calculate the greatest common factor of k and w.", "unit": "dimensionless", "value": "31", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-84"}}
{"id": "dm-numbers__gcd_composed-hard-84", "pool": "math", "split": "train", "question": "Let u be 3 - -79 - 2/(-1). Let z = 146878 + -146766. What is the greatest common factor of z and u?", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-85"}}
{"id": "dm-numbers__gcd_composed-hard-85", "pool": "math", "split": "train", "question": "Let d be 0/(((-15)/3)/5). Suppose -3*n + 41 + 34 = d. What is the greatest common divisor of 2 and n?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-86"}}
{"id": "dm-numbers__gcd_composed-hard-86", "pool": "math", "split": "train", "question": "Suppose 11*x - 403 = 939. What is the greatest common divisor of 1403 and x?", "unit": "dimensionless", "value": "61", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-87"}}
{"id": "dm-numbers__gcd_composed-hard-87", "pool": "math", "split": "train", "question": "Suppose -4*n = 5*w - 51, 8*n - 58 = 4*n + 2*w. Let v be (-1 - 16/(-14)) + 3161/(-763). Let o = n + v. What is the greatest common divisor of 2 and o?", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-88"}}
{"id": "dm-numbers__gcd_composed-hard-88", "pool": "math", "split": "train", "question": "Let l be (2 + -7 - -3) + 328. Suppose -1334 = -4*h - 4*i - i, h - l = -5*i. Suppose g = 4*r + 30, -2*g - r = -3*r - 78. Calculate the highest common divisor of h and g.", "unit": "dimensionless", "value": "42", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-89"}}
{"id": "dm-numbers__gcd_composed-hard-89", "pool": "math", "split": "train", "question": "Suppose 5*x + 5*l - 40 = 0, 9*l = 6*l - 3. Let t be (x + -3)/((-1)/(-6)). What is the highest common factor of 48 and t?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-90"}}
{"id": "dm-numbers__gcd_composed-hard-90", "pool": "math", "split": "train", "question": "Let z be (26 - (-2 + -1))*(-6 - -1). Let k = 306 + z. Calculate the highest common divisor of 115 and k.", "unit": "dimensionless", "value": "23", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-91"}}
{"id": "dm-numbers__gcd_composed-hard-91", "pool": "math", "split": "train", "question": "Let v be 2/13 + 99/117. Suppose 6*k = 4*k - 8. Let t be (-6)/48*k*(0 - -14). What is the highest common factor of t and v?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-92"}}
{"id": "dm-numbers__gcd_composed-hard-92", "pool": "math", "split": "train", "question": "Let x(m) = 4*m + 13. Let r(f) = 1 - f. Let d(n) = 6*r(n) + x(n). Let j be d(9). Suppose 0 = -5*a + 179 + j. Calculate the highest common factor of a and 4.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-93"}}
{"id": "dm-numbers__gcd_composed-hard-93", "pool": "math", "split": "train", "question": "Suppose -7*g + 54311 - 9203 = 0. Calculate the highest common factor of 2 and g.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-94"}}
{"id": "dm-numbers__gcd_composed-hard-94", "pool": "math", "split": "train", "question": "Suppose 5*y - y = m + 8, -5*y = -25. Let v(g) = 170 - 3*g. Let o be v(49). Suppose -o*q + 2 = -22*q, -a + 5*q + 2 = 0. Calculate the highest common factor of a and m.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-95"}}
{"id": "dm-numbers__gcd_composed-hard-95", "pool": "math", "split": "train", "question": "Let x(h) = 60*h**2 + 16*h + 77. Let z be x(7). What is the highest common divisor of 84 and z?", "unit": "dimensionless", "value": "21", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-96"}}
{"id": "dm-numbers__gcd_composed-hard-96", "pool": "math", "split": "train", "question": "Suppose 73*c = 280 + 596. Suppose y + 4 - c = -5*b, 2*y - 3*b - 16 = 0. Suppose -5*g = -4*x - 24, -3*x - 2*x - 1 = g. What is the greatest common factor of g and y?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-97"}}
{"id": "dm-numbers__gcd_composed-hard-97", "pool": "math", "split": "train", "question": "Let n(r) = r**3 + 20*r**2 + 2*r + 47. Let v(m) = 4*m**3 + 60*m**2 + 7*m + 142. Let b(q) = 7*n(q) - 2*v(q). Let z be b(20). Let a = 22 - 4. Calculate the highest common divisor of z and a.", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-98"}}
{"id": "dm-numbers__gcd_composed-hard-98", "pool": "math", "split": "train", "question": "Suppose -3*m + 4917 = 5*w, m + 1636 = -w + 2619. Calculate the greatest common divisor of 40 and w.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-99"}}
{"id": "dm-numbers__gcd_composed-hard-99", "pool": "math", "split": "train", "question": "Let l = -7591 + 7629. Calculate the highest common divisor of 90 and l.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-100"}}
{"id": "dm-numbers__gcd_composed-hard-100", "pool": "math", "split": "train", "question": "Let y = -26 - -18. Let x = y - -56. What is the highest common divisor of 6 and x?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-101"}}
{"id": "dm-numbers__gcd_composed-hard-101", "pool": "math", "split": "train", "question": "Suppose 2*a + 190 = 2*l, -4*a - 4*l = -3*a + 90. Let w = a - -132. Let m = -752 + 809. Calculate the greatest common factor of w and m.", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-102"}}
{"id": "dm-numbers__gcd_composed-hard-102", "pool": "math", "split": "train", "question": "Let k(z) be the first derivative of 5*z**3/3 - z**2/2 + 1. Let m be k(-1). Let g = -4812 - -4818. Calculate the highest common factor of g and m.", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-103"}}
{"id": "dm-numbers__gcd_composed-hard-103", "pool": "math", "split": "train", "question": "Suppose -19 + 11 = -t. Let o be (t/(-3))/(-4) - 9/(-27). Let b be o/4 - (-94)/8*1. Calculate the highest common factor of 3 and b.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-104"}}
{"id": "dm-numbers__gcd_composed-hard-104", "pool": "math", "split": "train", "question": "Suppose -114 + 36 = -13*t. Suppose -b + t = b, 3*b = 3*f - 27. Let k = 49 + 47. Calculate the greatest common divisor of f and k.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-105"}}
{"id": "dm-numbers__gcd_composed-hard-105", "pool": "math", "split": "train", "question": "Let r(g) = -g**2 + 5*g - 10. Let l be r(9). Let k = 50 + l. Suppose 44 = 2*c + k*w, 3*c - 58 = w - 5*w. Calculate the greatest common factor of 126 and c.", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-106"}}
{"id": "dm-numbers__gcd_composed-hard-106", "pool": "math", "split": "train", "question": "Suppose 0 = 412*r + 12641 - 106577. Suppose 3*s = -5*p + 113, 3*p + p = 3*s - 104. What is the highest common factor of s and r?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-107"}}
{"id": "dm-numbers__gcd_composed-hard-107", "pool": "math", "split": "train", "question": "Let v = 1503 - 674. Suppose 0 = -p + 6*p - 3*k - 2071, -2*p + k + v = 0. What is the greatest common factor of 39 and p?", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-108"}}
{"id": "dm-numbers__gcd_composed-hard-108", "pool": "math", "split": "train", "question": "Suppose 0 = 5*r - 3057 - 5083. Suppose 821*w - 832*w = -484. Calculate the greatest common divisor of w and r.", "unit": "dimensionless", "value": "44", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-109"}}
{"id": "dm-numbers__gcd_composed-hard-109", "pool": "math", "split": "train", "question": "Suppose -24624 = 4351*k - 4370*k. What is the highest common factor of k and 96?", "unit": "dimensionless", "value": "48", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-110"}}
{"id": "dm-numbers__gcd_composed-hard-110", "pool": "math", "split": "train", "question": "Let y be 31 + (9 - 4) - -3. Let l be 584/6 - 52/y. Calculate the highest common factor of l and 24.", "unit": "dimensionless", "value": "24", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-111"}}
{"id": "dm-numbers__gcd_composed-hard-111", "pool": "math", "split": "train", "question": "Let l be ((-2)/4)/(6/468*-13). What is the highest common divisor of 223 and l?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-112"}}
{"id": "dm-numbers__gcd_composed-hard-112", "pool": "math", "split": "train", "question": "Suppose 2*y = 39 + 59. Let t be 994/y + (-4)/14. Suppose -5*b = 4*r - 104, -3*b - 4*r = 25 - 89. Calculate the greatest common factor of t and b.", "unit": "dimensionless", "value": "20", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-113"}}
{"id": "dm-numbers__gcd_composed-hard-113", "pool": "math", "split": "train", "question": "Let v(g) = -g**3 + 13*g**2 + 11*g + 21. Let q be v(14). Let d = q + 25. Suppose -d*i - i = -70. Calculate the highest common factor of i and 21.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-114"}}
{"id": "dm-numbers__gcd_composed-hard-114", "pool": "math", "split": "train", "question": "Let y = 19644 + -9164. Calculate the highest common factor of y and 10.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-115"}}
{"id": "dm-numbers__gcd_composed-hard-115", "pool": "math", "split": "train", "question": "Suppose 2*r = 5*v - 775, 361 = -5*v - r + 1136. Let m be (-5 + 58/10 + 0)*v. What is the highest common factor of 558 and m?", "unit": "dimensionless", "value": "62", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-116"}}
{"id": "dm-numbers__gcd_composed-hard-116", "pool": "math", "split": "train", "question": "Let w be 1 + 2 + (-2)/(-2)*0. Suppose -5*p + 0*i + 4*i + 190 = 0, 3*p - w*i - 117 = 0. Let k(s) = 169*s**3 + s**2 + s - 1. Let o be k(1). Calculate the highest common divisor of p and o.", "unit": "dimensionless", "value": "34", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-117"}}
{"id": "dm-numbers__gcd_composed-hard-117", "pool": "math", "split": "train", "question": "Suppose l - 126 = -3*l - 5*r, -2*l + 62 = 3*r. Suppose -l*i + 40*i - 480 = 0. Suppose q + 4*p - 18 = 6*p, p - 63 = -4*q. Calculate the highest common divisor of q and i.", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-118"}}
{"id": "dm-numbers__gcd_composed-hard-118", "pool": "math", "split": "train", "question": "Let l be 16/56 + (-3 - (-618)/(-7)). Let j = l + 111. What is the greatest common factor of 30 and j?", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-119"}}
{"id": "dm-numbers__gcd_composed-hard-119", "pool": "math", "split": "train", "question": "Let c be ((130/(-15))/((-2)/(-9)))/(12/(-136)). Calculate the greatest common divisor of 238 and c.", "unit": "dimensionless", "value": "34", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-120"}}
{"id": "dm-numbers__gcd_composed-hard-120", "pool": "math", "split": "train", "question": "Let m be 0*6/96*-4. Suppose m = 2*n + 7 - 367. Let d(f) = -3*f - 1. Let t be d(-7). Calculate the greatest common divisor of t and n.", "unit": "dimensionless", "value": "20", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-121"}}
{"id": "dm-numbers__gcd_composed-hard-121", "pool": "math", "split": "train", "question": "Suppose 3*c = -2*k + 84, 2*c - 5*k - 37 = -0*c. Suppose -o = -n - 11, -o - c = -3*o + 4*n. Suppose -o*j = -5*j - 448. What is the highest common divisor of 28 and j?", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-122"}}
{"id": "dm-numbers__gcd_composed-hard-122", "pool": "math", "split": "train", "question": "Suppose -5*n - 21 = -2*t, 5*t - 2*n - 40 - 44 = 0. Let y = 15 - 12. Suppose y = -v + 12. Calculate the highest common factor of v and t.", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-123"}}
{"id": "dm-numbers__gcd_composed-hard-123", "pool": "math", "split": "train", "question": "Suppose 4*r + 3*z = 893, 2*r - 2*z - 240 - 196 = 0. Let t = -155 + r. What is the greatest common divisor of 12 and t?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-124"}}
{"id": "dm-numbers__gcd_composed-hard-124", "pool": "math", "split": "train", "question": "Let o(j) = 1662 - 194*j. Let p be o(8). Calculate the highest common factor of p and 14410.", "unit": "dimensionless", "value": "110", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-125"}}
{"id": "dm-numbers__gcd_composed-hard-125", "pool": "math", "split": "train", "question": "Let m(x) = 2*x**3 + x**2 + 4*x - 3. Let s be m(2). Let d = -350 - -355. What is the highest common divisor of s and d?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-126"}}
{"id": "dm-numbers__gcd_composed-hard-126", "pool": "math", "split": "train", "question": "Let w(r) = 4*r + 25. Let f be w(-8). Let j be (3 + 0)/(-6 - f). Suppose -j*t = 2*z - 90, -2*t + 131 = 3*t - 3*z. Calculate the highest common divisor of 112 and t.", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-127"}}
{"id": "dm-numbers__gcd_composed-hard-127", "pool": "math", "split": "train", "question": "Suppose -18*h + 13*h + 55 = 0. Let c be (3/2)/(39/52). Calculate the highest common divisor of c and h.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-128"}}
{"id": "dm-numbers__gcd_composed-hard-128", "pool": "math", "split": "train", "question": "Let d(m) = -m**3 + 17*m**2 + 9*m - 44. Let h be d(12). Calculate the greatest common factor of h and 294.", "unit": "dimensionless", "value": "98", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-129"}}
{"id": "dm-numbers__gcd_composed-hard-129", "pool": "math", "split": "train", "question": "Let i(w) = 3190 - 1423*w. Let d be i(2). Calculate the highest common divisor of d and 2838.", "unit": "dimensionless", "value": "86", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-130"}}
{"id": "dm-numbers__gcd_composed-hard-130", "pool": "math", "split": "train", "question": "Suppose 0 = -11*r + 6*r + 700. Let s(m) = 3*m**3 + 2*m**2 + m - 2. Let a be s(1). Let p be (12/(-10))/(a - (-1698)/(-420)). What is the greatest common factor of r and p?", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-131"}}
{"id": "dm-numbers__gcd_composed-hard-131", "pool": "math", "split": "train", "question": "Let f(b) = 4*b**2 + 237*b - 140. Let l be f(-60). Calculate the greatest common factor of 88 and l.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-132"}}
{"id": "dm-numbers__gcd_composed-hard-132", "pool": "math", "split": "train", "question": "Suppose 0 = 4*g, j - 8 = -j - 2*g. Let t be (1 - j)/(2 - 1183/585). Calculate the highest common factor of t and 5.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-133"}}
{"id": "dm-numbers__gcd_composed-hard-133", "pool": "math", "split": "train", "question": "Suppose 208 = -108*l + 100*l. Let o = 1 - 2. Let d = o - l. Calculate the greatest common divisor of d and 225.", "unit": "dimensionless", "value": "25", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-134"}}
{"id": "dm-numbers__gcd_composed-hard-134", "pool": "math", "split": "train", "question": "Let k be (-3)/7 + 155/35. Let f be 4/(-8) - ((-137)/2 + k). What is the greatest common divisor of f and 4?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-135"}}
{"id": "dm-numbers__gcd_composed-hard-135", "pool": "math", "split": "train", "question": "Let l = 784 - 472. Calculate the greatest common divisor of l and 2964.", "unit": "dimensionless", "value": "156", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-136"}}
{"id": "dm-numbers__gcd_composed-hard-136", "pool": "math", "split": "train", "question": "Let w(s) = -s**3 + 10*s**2 + 13*s. Let l be w(9). Let f(m) = 2*m**3 + 15*m**2 - 158*m - 51. Let c be f(7). Calculate the greatest common factor of l and c.", "unit": "dimensionless", "value": "66", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-137"}}
{"id": "dm-numbers__gcd_composed-hard-137", "pool": "math", "split": "train", "question": "Let t = 232 + -132. Suppose 5*v - 127 = -2*c, 8*c = -2*v + 10*c + 48. What is the greatest common divisor of t and v?", "unit": "dimensionless", "value": "25", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-138"}}
{"id": "dm-numbers__gcd_composed-hard-138", "pool": "math", "split": "train", "question": "Let d(p) be the first derivative of -p - 13 - 15/2*p**2. Let q be d(-5). Calculate the highest common divisor of q and 185.", "unit": "dimensionless", "value": "37", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-139"}}
{"id": "dm-numbers__gcd_composed-hard-139", "pool": "math", "split": "train", "question": "Suppose -40*x + 44*x = -3*l + 1608, -x + 1590 = 3*l. Calculate the greatest common factor of 3300 and l.", "unit": "dimensionless", "value": "132", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-140"}}
{"id": "dm-numbers__gcd_composed-hard-140", "pool": "math", "split": "train", "question": "Let k(m) be the first derivative of 12 - 9*m**2 + 1/4*m**4 + 16/3*m**3 - 14*m. Let w be k(-17). Calculate the highest common factor of w and 24.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-141"}}
{"id": "dm-numbers__gcd_composed-hard-141", "pool": "math", "split": "train", "question": "Let w(o) = -337*o - 11. Let v be w(-2). Suppose 0 = -5*x + 342 + v. Suppose -55 = -16*r + x. Calculate the highest common divisor of 2 and r.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-142"}}
{"id": "dm-numbers__gcd_composed-hard-142", "pool": "math", "split": "train", "question": "Let w = -51 + 75. Suppose -9*r + 21*r = -w. Let d be 2 - ((r - -2) + 1)/1. What is the highest common factor of d and 16?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-143"}}
{"id": "dm-numbers__gcd_composed-hard-143", "pool": "math", "split": "train", "question": "Let x be (-1)/2 + 15834/52. Let a = x - 292. Suppose -4*l = 2*z - 200, -5*l = z - 32 - 56. What is the highest common factor of a and z?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-144"}}
{"id": "dm-numbers__gcd_composed-hard-144", "pool": "math", "split": "train", "question": "Suppose 4*g + 50 = 3*k, 0 = -4*k + 2*g + 2 + 58. Let y(f) = f + 2. Let d be y(-6). Let r = d + k. What is the highest common divisor of r and 30?", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-145"}}
{"id": "dm-numbers__gcd_composed-hard-145", "pool": "math", "split": "train", "question": "Let o(c) = 19*c + 401. Let w be o(-7). Calculate the highest common divisor of 44 and w.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-146"}}
{"id": "dm-numbers__gcd_composed-hard-146", "pool": "math", "split": "train", "question": "Suppose 0 = -g, j + 4*g = -2*j - 0*j + 108. What is the greatest common factor of j and 3258?", "unit": "dimensionless", "value": "18", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-147"}}
{"id": "dm-numbers__gcd_composed-hard-147", "pool": "math", "split": "train", "question": "Suppose 4*r = 3*n + 144, 44*n = 2*r + 49*n - 98. Suppose 2*p + r*p - 164 = 0. Suppose -5*k - 3*l + 17 = 0, 2*l = -0*k + k - 6. Calculate the greatest common divisor of k and p.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-148"}}
{"id": "dm-numbers__gcd_composed-hard-148", "pool": "math", "split": "train", "question": "Let b be -2*(-214)/16 + (-4)/(-16). Suppose o - 27 = 5*h, -154 = -4*o + h - b. Calculate the highest common factor of o and 4.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-149"}}
{"id": "dm-numbers__gcd_composed-hard-149", "pool": "math", "split": "train", "question": "Let r be (2 + (-9952)/(-16))*8/6. Let t be 208/(-6)*(-6)/2. What is the highest common divisor of t and r?", "unit": "dimensionless", "value": "104", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-150"}}
{"id": "dm-numbers__gcd_composed-hard-150", "pool": "math", "split": "train", "question": "Suppose -6*j + 11*j = 4*g - 254, 0 = 5*g + 5*j - 340. Suppose 0 = -35*k + 1475 + 15465. Calculate the greatest common factor of k and g.", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-151"}}
{"id": "dm-numbers__gcd_composed-hard-151", "pool": "math", "split": "train", "question": "Suppose -10*v + 393 = 393. Suppose 5*c - 5*d - 3885 = 0, -d + 7 - 3 = v. Calculate the greatest common divisor of c and 11.", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-152"}}
{"id": "dm-numbers__gcd_composed-hard-152", "pool": "math", "split": "train", "question": "Suppose -318*i - 53245 = 3677. Suppose -2*o + 668 = -5*v, -386 - 978 = -4*o - 4*v. Let r = o + i. What is the greatest common factor of 10 and r?", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-153"}}
{"id": "dm-numbers__gcd_composed-hard-153", "pool": "math", "split": "train", "question": "Suppose -4*x - 2*o + 46 = 0, 0 = -2*o - 1 - 1. Let n = 55 + 101. Calculate the greatest common divisor of n and x.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-154"}}
{"id": "dm-numbers__gcd_composed-hard-154", "pool": "math", "split": "train", "question": "Let u be (-76 + 3)/(-4 - (-21)/6). Let p = u - 131. Suppose -3*n + 114 = p. Calculate the greatest common divisor of 132 and n.", "unit": "dimensionless", "value": "33", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-155"}}
{"id": "dm-numbers__gcd_composed-hard-155", "pool": "math", "split": "train", "question": "Let f be 38/8*8*(-5118)/(-12). Calculate the greatest common divisor of 19 and f.", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-156"}}
{"id": "dm-numbers__gcd_composed-hard-156", "pool": "math", "split": "train", "question": "Let s(n) = 94 - 4*n. Let b be s(27). Let z be (-7 - b)/(1*2/96). What is the greatest common divisor of 21 and z?", "unit": "dimensionless", "value": "21", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-157"}}
{"id": "dm-numbers__gcd_composed-hard-157", "pool": "math", "split": "train", "question": "Suppose l + l = 14. Suppose 29 = 2*a + 25. Suppose 4*j = 5*v + 23, j - 7*v = -a*v + 2. What is the greatest common factor of l and j?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-158"}}
{"id": "dm-numbers__gcd_composed-hard-158", "pool": "math", "split": "train", "question": "Suppose 2*j = 4*u - 0*j + 5542, -5*j = 4*u + 5521. Let x = u + 1978. What is the highest common divisor of 22 and x?", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-159"}}
{"id": "dm-numbers__gcd_composed-hard-159", "pool": "math", "split": "train", "question": "Suppose -w + 75 = 3*p + 2*w, 2*p - 53 = -5*w. Suppose 18*z = p*z - 528. What is the highest common divisor of z and 11?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-160"}}
{"id": "dm-numbers__gcd_composed-hard-160", "pool": "math", "split": "train", "question": "Let o(s) = 6*s**2 - 5*s + 3. Let r be o(3). Suppose 0 = -2*a + 2*h + 416, 5*a - 165 = -3*h + 891. Calculate the greatest common divisor of r and a.", "unit": "dimensionless", "value": "42", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-161"}}
{"id": "dm-numbers__gcd_composed-hard-161", "pool": "math", "split": "train", "question": "Suppose 5*y + z - 2028 = 2*z, 0 = 3*z + 9. Let h be (18/4)/(4/40). What is the greatest common divisor of h and y?", "unit": "dimensionless", "value": "45", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-162"}}
{"id": "dm-numbers__gcd_composed-hard-162", "pool": "math", "split": "train", "question": "Suppose 41977 = 20*h - 15623. Calculate the highest common divisor of h and 90.", "unit": "dimensionless", "value": "90", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-163"}}
{"id": "dm-numbers__gcd_composed-hard-163", "pool": "math", "split": "train", "question": "Let y be ((-4818)/(-511))/(1/14). What is the greatest common divisor of y and 228?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-164"}}
{"id": "dm-numbers__gcd_composed-hard-164", "pool": "math", "split": "train", "question": "Let h be 59*(-4 - -3) + 1. Let a = -42 - h. Let l be (8/a)/(1/6)*1. Calculate the greatest common divisor of 3 and l.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-165"}}
{"id": "dm-numbers__gcd_composed-hard-165", "pool": "math", "split": "train", "question": "Let h = -9 + 21. Let q(u) be the first derivative of 2*u**2 - 19*u + 401. Let i be q(h). Calculate the greatest common factor of i and 29.", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-166"}}
{"id": "dm-numbers__gcd_composed-hard-166", "pool": "math", "split": "train", "question": "Suppose 8*l + 1930 = 13*l + 2*d, 4*d + 748 = 2*l. Calculate the greatest common divisor of l and 12.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-167"}}
{"id": "dm-numbers__gcd_composed-hard-167", "pool": "math", "split": "train", "question": "Suppose -12*i - 3*o = -13*i - 5, 5*o = -4*i + 14. Suppose 0 = -4*l + 5*b - 47, 2*l - 3*b = 5*l + 69. Let r be -5*(l - -3) - (i + 2). What is the highest common factor of 8 and r?", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-168"}}
{"id": "dm-numbers__gcd_composed-hard-168", "pool": "math", "split": "train", "question": "Suppose 4*h - 115 = -2*l - 89, 0 = 5*l - 5*h - 80. What is the highest common factor of l and 27795?", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-169"}}
{"id": "dm-numbers__gcd_composed-hard-169", "pool": "math", "split": "train", "question": "Let k = -50 + 50. Suppose k = 3*l - 5*f - 100, -3*l + 80 + 27 = 2*f. What is the highest common divisor of 5 and l?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-170"}}
{"id": "dm-numbers__gcd_composed-hard-170", "pool": "math", "split": "train", "question": "Let i = 23 + -14. Suppose -10*n + i*n - 273 = -4*g, n - 196 = -3*g. What is the greatest common divisor of g and 335?", "unit": "dimensionless", "value": "67", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-171"}}
{"id": "dm-numbers__gcd_composed-hard-171", "pool": "math", "split": "train", "question": "Suppose -2*m = -3*f - 52, -2*m + 18 = -3*m - 4*f. Let k(u) = 3*u. Let b be k(2). Suppose -b = -n + 8. What is the highest common divisor of m and n?", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-172"}}
{"id": "dm-numbers__gcd_composed-hard-172", "pool": "math", "split": "train", "question": "Let b(x) = -2. Let y(p) = 6*p - 44. Let d(u) = -2*b(u) - y(u). Let k be d(6). Calculate the highest common divisor of 132 and k.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-173"}}
{"id": "dm-numbers__gcd_composed-hard-173", "pool": "math", "split": "train", "question": "Let q = 57 + -68. Let l(n) = -13*n - 32. Let x be l(q). Let z = x - 72. Calculate the highest common divisor of z and 156.", "unit": "dimensionless", "value": "39", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-174"}}
{"id": "dm-numbers__gcd_composed-hard-174", "pool": "math", "split": "train", "question": "Let r(u) = 194*u**2 + 39. Let o be r(-2). What is the highest common divisor of o and 5?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-175"}}
{"id": "dm-numbers__gcd_composed-hard-175", "pool": "math", "split": "train", "question": "Let q be (-2 + 3)*(154 - -2). Suppose 3*k = 99 + q. Suppose 4*l - 59 - 9 = 0. Calculate the greatest common factor of k and l.", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-176"}}
{"id": "dm-numbers__gcd_composed-hard-176", "pool": "math", "split": "train", "question": "Suppose -3*u + i = 2*i - 326, -2*u - 2*i + 212 = 0. Let q = -55 + 105. Suppose 5 = 2*w + 2*y - 25, -q = -4*w - 2*y. Calculate the greatest common divisor of u and w.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-177"}}
{"id": "dm-numbers__gcd_composed-hard-177", "pool": "math", "split": "train", "question": "Let o = -851 - -216. Let x = o + 654. Calculate the highest common factor of 19 and x.", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-178"}}
{"id": "dm-numbers__gcd_composed-hard-178", "pool": "math", "split": "train", "question": "Suppose -4*k + 100 = -5*h, -68*k = -66*k - 5*h - 40. What is the greatest common factor of 670 and k?", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-179"}}
{"id": "dm-numbers__gcd_composed-hard-179", "pool": "math", "split": "train", "question": "Suppose 1588 - 517 = 3*n. Let y = -313 + n. Calculate the highest common divisor of 8 and y.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-180"}}
{"id": "dm-numbers__gcd_composed-hard-180", "pool": "math", "split": "train", "question": "Let r(o) = 134*o - 304. Let v be r(12). Calculate the greatest common divisor of 8 and v.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-181"}}
{"id": "dm-numbers__gcd_composed-hard-181", "pool": "math", "split": "train", "question": "Let z = -136167 - -136198. Let q = 176 - 12. Suppose 5*x - q = -3*g, x - 4*g = -g + 22. Calculate the highest common factor of x and z.", "unit": "dimensionless", "value": "31", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-182"}}
{"id": "dm-numbers__gcd_composed-hard-182", "pool": "math", "split": "train", "question": "Suppose 8*w - 2 = 10*w, 5*z - 5*w = 485. Let c = 120 - z. Calculate the greatest common factor of 6 and c.", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-183"}}
{"id": "dm-numbers__gcd_composed-hard-183", "pool": "math", "split": "train", "question": "Let p = 698 + -702. Let q be (276/23)/(p/(-30)). What is the greatest common factor of q and 990?", "unit": "dimensionless", "value": "90", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-184"}}
{"id": "dm-numbers__gcd_composed-hard-184", "pool": "math", "split": "train", "question": "Suppose -2*t + 124 = 18*b - 16*b, -8*b + 181 = 3*t. What is the greatest common factor of 224 and t?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-185"}}
{"id": "dm-numbers__gcd_composed-hard-185", "pool": "math", "split": "train", "question": "Let w(p) = -p**2 + 3*p + 15. Let c be w(11). Let o = 103 + c. Suppose 4*i - 159 - 321 = 0. Calculate the greatest common divisor of i and o.", "unit": "dimensionless", "value": "30", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-186"}}
{"id": "dm-numbers__gcd_composed-hard-186", "pool": "math", "split": "train", "question": "Suppose 0 = 2*w + 2*l + 8, -3*w - 8 = 2*w + 2*l. Let d be (-54)/(-4) + w + 3/(-6). Suppose -10*h + d*h = 42. What is the highest common divisor of 98 and h?", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-187"}}
{"id": "dm-numbers__gcd_composed-hard-187", "pool": "math", "split": "train", "question": "Let n(i) be the third derivative of -i**5/60 + 11*i**4/24 - i**3 - 2*i**2. Let f be n(7). Suppose 152*b - 154*b = -22. What is the greatest common divisor of b and f?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-188"}}
{"id": "dm-numbers__gcd_composed-hard-188", "pool": "math", "split": "train", "question": "Let m(k) = -175*k + 19*k**2 + 143*k - 6 + 7*k**2 + 2*k**3. Let v be m(-14). What is the highest common factor of 35 and v?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-189"}}
{"id": "dm-numbers__gcd_composed-hard-189", "pool": "math", "split": "train", "question": "Suppose -3*m + 22 = -2*u, 2*u + 2*u = -3*m - 26. Let l be 4 - (-1 - u) - -9. Let p = 131 - 125. Calculate the highest common factor of p and l.", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-190"}}
{"id": "dm-numbers__gcd_composed-hard-190", "pool": "math", "split": "train", "question": "Let c(a) = 318*a + 386. Let o be c(2). What is the greatest common divisor of 14 and o?", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-191"}}
{"id": "dm-numbers__gcd_composed-hard-191", "pool": "math", "split": "train", "question": "Suppose -134328 = -40*s - 9888. What is the highest common divisor of s and 34?", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-192"}}
{"id": "dm-numbers__gcd_composed-hard-192", "pool": "math", "split": "train", "question": "Let i(g) = 27 - 9*g. Let x be i(-31). Calculate the highest common divisor of 54 and x.", "unit": "dimensionless", "value": "18", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-193"}}
{"id": "dm-numbers__gcd_composed-hard-193", "pool": "math", "split": "train", "question": "Suppose -9*m = 66588 - 71556. Calculate the greatest common divisor of 5704 and m.", "unit": "dimensionless", "value": "184", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-194"}}
{"id": "dm-numbers__gcd_composed-hard-194", "pool": "math", "split": "train", "question": "Suppose -4*v + 53 = 5*b, -2*v - 7 = -b - 4*v. What is the highest common factor of 1781 and b?", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-195"}}
{"id": "dm-numbers__gcd_composed-hard-195", "pool": "math", "split": "train", "question": "Let q(c) = 117*c - 36. Let x be q(1). Calculate the greatest common divisor of 8451 and x.", "unit": "dimensionless", "value": "27", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-196"}}
{"id": "dm-numbers__gcd_composed-hard-196", "pool": "math", "split": "train", "question": "Let i(l) = 87 - 30*l. Let u be i(-6). Let m = u + -241. What is the greatest common divisor of 78 and m?", "unit": "dimensionless", "value": "26", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-197"}}
{"id": "dm-numbers__gcd_composed-hard-197", "pool": "math", "split": "train", "question": "Suppose -51 = -h + 5*x, -2*h + 7*x = 8*x - 47. Let u be 1*-2*276/6. Let p be u/(-6)*39/h. What is the highest common divisor of 184 and p?", "unit": "dimensionless", "value": "23", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-198"}}
{"id": "dm-numbers__gcd_composed-hard-198", "pool": "math", "split": "train", "question": "Suppose 2*s + 4*x - 51 = 9, 0 = -2*x + 4. What is the highest common factor of s and 26?", "unit": "dimensionless", "value": "26", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-199"}}
{"id": "dm-numbers__gcd_composed-hard-199", "pool": "math", "split": "train", "question": "Suppose 0 = -6*d + 17 + 1. Suppose 0 = -d*q + 3*n + 498, -5*q = 5*n - 300 - 500. Suppose q = 6*p - 17. What is the highest common factor of 6 and p?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-200"}}
{"id": "dm-numbers__gcd_composed-hard-200", "pool": "math", "split": "train", "question": "Let p(g) = g**3 + 43*g**2 + 4*g + 150. Let z be p(-43). Let d be (-7*(-3)/(-6))/(z/44). Let l(o) = o**3 + 5*o**2 - 5*o + 7. Let u be l(-6). What is the highest common divisor of u and d?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-201"}}
{"id": "dm-numbers__gcd_composed-hard-201", "pool": "math", "split": "train", "question": "Let g(v) = v**3 - 11*v**2 - 5*v - 3. Let n be g(11). Let z = n - -25. Let t be ((-3)/3)/2*-6 - z. Calculate the greatest common factor of 396 and t.", "unit": "dimensionless", "value": "36", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-202"}}
{"id": "dm-numbers__gcd_composed-hard-202", "pool": "math", "split": "train", "question": "Suppose 11*m = -9*m + 260. Suppose -5*h + 0 = -3*d - m, 0 = d + 4*h - 24. What is the highest common factor of d and 34?", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-203"}}
{"id": "dm-numbers__gcd_composed-hard-203", "pool": "math", "split": "train", "question": "Let u = 4 + 5. Suppose 3*v = -4*d + 15, -3*v + 2*v + u = 2*d. Let w(b) = 2*b**2 - 3*b + 6. Let p be w(d). Calculate the highest common divisor of 24 and p.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-204"}}
{"id": "dm-numbers__gcd_composed-hard-204", "pool": "math", "split": "train", "question": "Let m(w) = 6*w + 1920. Let a be m(-26). Calculate the greatest common factor of 324 and a.", "unit": "dimensionless", "value": "36", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-205"}}
{"id": "dm-numbers__gcd_composed-hard-205", "pool": "math", "split": "train", "question": "Let u = 13606 + -12760. Calculate the greatest common factor of u and 3.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-206"}}
{"id": "dm-numbers__gcd_composed-hard-206", "pool": "math", "split": "train", "question": "Let h = 5226 - 3525. Calculate the highest common factor of h and 252.", "unit": "dimensionless", "value": "63", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-207"}}
{"id": "dm-numbers__gcd_composed-hard-207", "pool": "math", "split": "train", "question": "Suppose 4*u + 17 = 13. Let a be (u + (-10)/(-5))/((-2)/(-56)). Let z be 0 - (9/(-12) - 445/4). Calculate the greatest common divisor of z and a.", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-208"}}
{"id": "dm-numbers__gcd_composed-hard-208", "pool": "math", "split": "train", "question": "Let r(b) = b**3 + 7*b**2 + 12*b + 232. Let g be r(-8). What is the greatest common divisor of g and 774?", "unit": "dimensionless", "value": "18", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-209"}}
{"id": "dm-numbers__gcd_composed-hard-209", "pool": "math", "split": "train", "question": "Let h(t) = t**2 - 30*t + 113. Let z be ((-3)/(-21) + 61/14)*6. Let k be h(z). What is the greatest common factor of k and 32?", "unit": "dimensionless", "value": "32", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-210"}}
{"id": "dm-numbers__gcd_composed-hard-210", "pool": "math", "split": "train", "question": "Suppose -37*f - 772365 = -24*f - 44*f. What is the greatest common factor of f and 165?", "unit": "dimensionless", "value": "165", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-211"}}
{"id": "dm-numbers__gcd_composed-hard-211", "pool": "math", "split": "train", "question": "Let b be (-2*3/(-18))/((-2)/(-48)). Let t be b + (-6 - -5) + -2. What is the highest common factor of 11 and t?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-212"}}
{"id": "dm-numbers__gcd_composed-hard-212", "pool": "math", "split": "train", "question": "Let f be ((-1720)/(-688))/(1/1544). Calculate the highest common factor of 50 and f.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-213"}}
{"id": "dm-numbers__gcd_composed-hard-213", "pool": "math", "split": "train", "question": "Let m(u) = -9*u**3 + u**2 + u - 2. Let y be m(-2). Suppose v + v = y. Suppose 10*h - 4*l = 268, l + 54 = 4*h - 49. What is the highest common divisor of v and h?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-214"}}
{"id": "dm-numbers__gcd_composed-hard-214", "pool": "math", "split": "train", "question": "Let x = 63 - 179. Let p = -85 - x. What is the highest common divisor of 248 and p?", "unit": "dimensionless", "value": "31", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-215"}}
{"id": "dm-numbers__gcd_composed-hard-215", "pool": "math", "split": "train", "question": "Suppose 2*h - o = 23648, h = 117*o - 112*o + 11833. Calculate the greatest common factor of 21 and h.", "unit": "dimensionless", "value": "21", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-216"}}
{"id": "dm-numbers__gcd_composed-hard-216", "pool": "math", "split": "train", "question": "Let w be (-2)/(-8)*-33 - (-3)/12. Let f be (-18)/w + -2 + (-1438)/(-8). Calculate the highest common divisor of f and 20.", "unit": "dimensionless", "value": "20", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-217"}}
{"id": "dm-numbers__gcd_composed-hard-217", "pool": "math", "split": "train", "question": "Suppose 0 = 4*j + 5*s - 3*s + 8, 2*j + 2*s + 8 = 0. Suppose 3*i - 60 - 606 = j. What is the greatest common factor of i and 37?", "unit": "dimensionless", "value": "37", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-218"}}
{"id": "dm-numbers__gcd_composed-hard-218", "pool": "math", "split": "train", "question": "Suppose -5*v - 4*j = -2*j - 184, -2*j + 76 = 2*v. Let f be 11 - (2/6)/(24/504). Calculate the greatest common divisor of v and f.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-219"}}
{"id": "dm-numbers__gcd_composed-hard-219", "pool": "math", "split": "train", "question": "Let s = 1224 - 1110. What is the highest common factor of s and 304?", "unit": "dimensionless", "value": "38", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-220"}}
{"id": "dm-numbers__gcd_composed-hard-220", "pool": "math", "split": "train", "question": "Let g(l) = -11*l**3 - 3*l**2 + 2*l - 4. Let d be g(-3). Let f = 128 + -9. Suppose -b - 15 = -f. What is the highest common factor of d and b?", "unit": "dimensionless", "value": "52", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-221"}}
{"id": "dm-numbers__gcd_composed-hard-221", "pool": "math", "split": "train", "question": "Let t(f) = -9*f**3 - 6*f**2 - 4. Let i(y) = -y**3 - y**2 - 1. Let m = -22 + 16. Let g(c) = m*i(c) + t(c). Let w be g(-2). What is the highest common factor of w and 65?", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-222"}}
{"id": "dm-numbers__gcd_composed-hard-222", "pool": "math", "split": "train", "question": "Let j = 27083 - 25724. Calculate the highest common divisor of j and 207.", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-223"}}
{"id": "dm-numbers__gcd_composed-hard-223", "pool": "math", "split": "train", "question": "Let y be ((-10200)/18 - -2)*(0 - 3). What is the highest common divisor of 182 and y?", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-224"}}
{"id": "dm-numbers__gcd_composed-hard-224", "pool": "math", "split": "train", "question": "Suppose 4*c = 3*v - 3, 5*v = -4*c + v - 24. Let o be 15/(-10)*(-1400)/60. Let m = o - c. Calculate the greatest common factor of 114 and m.", "unit": "dimensionless", "value": "38", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-225"}}
{"id": "dm-numbers__gcd_composed-hard-225", "pool": "math", "split": "train", "question": "Let j(k) = k**3 - 3*k**2 - 5*k + 22. Let z be j(10). What is the greatest common divisor of 256 and z?", "unit": "dimensionless", "value": "32", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-226"}}
{"id": "dm-numbers__gcd_composed-hard-226", "pool": "math", "split": "train", "question": "Let a(y) = -y**3 - 56*y**2 + 207*y - 78. Let i be a(-61). Calculate the greatest common factor of 100 and i.", "unit": "dimensionless", "value": "100", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-227"}}
{"id": "dm-numbers__gcd_composed-hard-227", "pool": "math", "split": "train", "question": "Let g be 42*(-4)/8*1. Let t(o) = o**2 + 28*o + 52. Let h be t(g). Let q = 161 + h. Calculate the highest common divisor of q and 22.", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-228"}}
{"id": "dm-numbers__gcd_composed-hard-228", "pool": "math", "split": "train", "question": "Suppose 4*z - 32 = 2*z. Suppose -23*m + 40 = -21*m. Suppose 16 = -19*v + m*v. What is the greatest common factor of z and v?", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-229"}}
{"id": "dm-numbers__gcd_composed-hard-229", "pool": "math", "split": "train", "question": "Suppose -9*w + 13*w + 2*h = 584, 5*w + h - 724 = 0. Calculate the greatest common factor of w and 135.", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-230"}}
{"id": "dm-numbers__gcd_composed-hard-230", "pool": "math", "split": "train", "question": "Suppose -2*m + 136 = 3*p, 0 = 67*p - 69*p + m + 107. Calculate the highest common factor of p and 1280.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-231"}}
{"id": "dm-numbers__gcd_composed-hard-231", "pool": "math", "split": "train", "question": "Suppose 0 = 19*v - 854 + 170. Suppose -10 = 8*k - 9*k. Let c(f) = f**2 - 8*f - 8. Let m be c(k). What is the highest common divisor of v and m?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-232"}}
{"id": "dm-numbers__gcd_composed-hard-232", "pool": "math", "split": "train", "question": "Let h be 2*(4 + -8 + 1 + 4). Suppose -h*w + 1230 = 2*z, -4*w + 9 + 3 = 0. What is the highest common factor of 68 and z?", "unit": "dimensionless", "value": "68", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-233"}}
{"id": "dm-numbers__gcd_composed-hard-233", "pool": "math", "split": "train", "question": "Suppose -82 = -2*j - 4*z, -459*z = 4*j - 458*z - 178. Calculate the greatest common divisor of 25 and j.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-234"}}
{"id": "dm-numbers__gcd_composed-hard-234", "pool": "math", "split": "train", "question": "Let p(y) = 26*y**3 - 180*y**2 - 5*y - 7. Let d be p(7). What is the greatest common factor of d and 434?", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-235"}}
{"id": "dm-numbers__gcd_composed-hard-235", "pool": "math", "split": "train", "question": "Suppose 0 = 2*q - f - 2158, 0 = 2*q + 2*f - 147 - 2035. Calculate the highest common divisor of q and 9.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-236"}}
{"id": "dm-numbers__gcd_composed-hard-236", "pool": "math", "split": "train", "question": "Let f(y) be the first derivative of 14 + 43/3*y**3 + 1/2*y**4 - 16*y + 10*y**2. Let s be f(-21). What is the greatest common divisor of 5 and s?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-237"}}
{"id": "dm-numbers__gcd_composed-hard-237", "pool": "math", "split": "train", "question": "Let w = -3879 + 4110. Suppose p - 2*k - 32 = 0, p + 4*k - 42 = 20. What is the greatest common divisor of w and p?", "unit": "dimensionless", "value": "21", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-238"}}
{"id": "dm-numbers__gcd_composed-hard-238", "pool": "math", "split": "train", "question": "Let t = -32 - -36. Suppose t*i = 15 - 3. Suppose -32 = i*k - 4*k + u, -u - 98 = -3*k. What is the highest common divisor of 3 and k?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-239"}}
{"id": "dm-numbers__gcd_composed-hard-239", "pool": "math", "split": "train", "question": "Let w be ((-17)/(17/4) - -6)*(-3)/(-6). Calculate the highest common divisor of 109 and w.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-240"}}
{"id": "dm-numbers__gcd_composed-hard-240", "pool": "math", "split": "train", "question": "Let v = 2829 - 1683. Calculate the greatest common divisor of v and 8.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-241"}}
{"id": "dm-numbers__gcd_composed-hard-241", "pool": "math", "split": "train", "question": "Let l = 3327 + -3297. Calculate the greatest common divisor of l and 30.", "unit": "dimensionless", "value": "30", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-242"}}
{"id": "dm-numbers__gcd_composed-hard-242", "pool": "math", "split": "train", "question": "Let v(z) = z**3 + 10*z**2 + 16. Let d(t) = t**3 + 10*t**2 + 15. Let u(q) = 7*d(q) - 6*v(q). Let f be u(-10). Calculate the greatest common divisor of 5 and f.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-243"}}
{"id": "dm-numbers__gcd_composed-hard-243", "pool": "math", "split": "train", "question": "Let i be (3*3/9)/(76/4864). Calculate the greatest common divisor of i and 1016.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-244"}}
{"id": "dm-numbers__gcd_composed-hard-244", "pool": "math", "split": "train", "question": "Let n be -1*(-20)/(-8)*-2. Let m be (-164)/(-4) + n/(-15)*0. Calculate the greatest common factor of 205 and m.", "unit": "dimensionless", "value": "41", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-245"}}
{"id": "dm-numbers__gcd_composed-hard-245", "pool": "math", "split": "train", "question": "Suppose 10 - 25 = -3*x. Let r = -3 + x. Let w(t) = -t**3 + 5*t**2 + t + 4. Let g be w(0). Calculate the highest common divisor of g and r.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-246"}}
{"id": "dm-numbers__gcd_composed-hard-246", "pool": "math", "split": "train", "question": "Let k be (-14)/(-3)*4902/133. Suppose y = -8*u + 6*u + 52, -3*y - 2*u + k = 0. What is the greatest common factor of y and 120?", "unit": "dimensionless", "value": "60", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-247"}}
{"id": "dm-numbers__gcd_composed-hard-247", "pool": "math", "split": "train", "question": "Let l(a) = -779*a - 93. Let m be l(-2). What is the highest common divisor of m and 5?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-248"}}
{"id": "dm-numbers__gcd_composed-hard-248", "pool": "math", "split": "train", "question": "Let a be 2 - (-306)/(-3)*-1. Suppose 901 + 1127 = 13*y. Calculate the greatest common factor of a and y.", "unit": "dimensionless", "value": "52", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-249"}}
{"id": "dm-numbers__gcd_composed-hard-249", "pool": "math", "split": "train", "question": "Let b = -340 + 344. Suppose 0 = b*a + 16, y - 5*a - 92 - 552 = 0. Calculate the highest common factor of y and 16.", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-250"}}
{"id": "dm-numbers__gcd_composed-hard-250", "pool": "math", "split": "train", "question": "Let w(k) = -k**2 + 8*k + 6. Let s be w(9). Let x(b) = -2*b**2 - 5*b - 3. Let p(n) = n**2 - n - 2. Let r(z) = s*p(z) - x(z). Let a be r(6). Calculate the greatest common divisor of a and 105.", "unit": "dimensionless", "value": "21", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-251"}}
{"id": "dm-numbers__gcd_composed-hard-251", "pool": "math", "split": "train", "question": "Suppose -3*d + 65 + 58 = -3*r, -4*d - r = -184. Let k = 78 + -38. Suppose 2*p = 5*p + 5*t, 5*p - k = 5*t. What is the highest common factor of d and p?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-252"}}
{"id": "dm-numbers__gcd_composed-hard-252", "pool": "math", "split": "train", "question": "Let p be (-187 - 1)/((-4)/26). Suppose 4*r = f + 110, 3*r - 84 - 18 = 4*f. Calculate the highest common factor of r and p.", "unit": "dimensionless", "value": "26", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-253"}}
{"id": "dm-numbers__gcd_composed-hard-253", "pool": "math", "split": "train", "question": "Let s(k) = k**3 - 11*k**2 - 40*k - 10. Let m be s(14). Suppose 2*y - n - 53 = -2*y, -3*n + 33 = 4*y. What is the highest common divisor of y and m?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-254"}}
{"id": "dm-numbers__gcd_composed-hard-254", "pool": "math", "split": "train", "question": "Let m be (24/(-40))/(((-6)/345)/2). What is the highest common divisor of m and 368?", "unit": "dimensionless", "value": "23", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-255"}}
{"id": "dm-numbers__gcd_composed-hard-255", "pool": "math", "split": "train", "question": "Let q be 3 + 2 + 6*5. Let n = q + -19. Suppose -197 = -3*i + 7*p - 6*p, -5*p = -2*i + 153. What is the highest common divisor of i and n?", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-256"}}
{"id": "dm-numbers__gcd_composed-hard-256", "pool": "math", "split": "train", "question": "Let o be 3/7 + 405/35. Suppose 0 = 4*b - 5*j - 24, -4*j + o = -4. Suppose 0 = -s - y + b + 17, -4*y = -3*s + 56. What is the greatest common divisor of s and 3?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-257"}}
{"id": "dm-numbers__gcd_composed-hard-257", "pool": "math", "split": "train", "question": "Let b(x) = -62*x - 2. Let w be b(-1). Suppose -w - 34 = -2*p. What is the highest common divisor of p and 423?", "unit": "dimensionless", "value": "47", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-258"}}
{"id": "dm-numbers__gcd_composed-hard-258", "pool": "math", "split": "train", "question": "Let t(u) = -u**3 - 7*u**2 + 7. Let p be t(-7). Let r be (4/6)/(18/(-189)). Let q = r - -35. Calculate the greatest common factor of p and q.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-259"}}
{"id": "dm-numbers__gcd_composed-hard-259", "pool": "math", "split": "train", "question": "Let m(c) = 7*c + 3. Let n be m(3). Let a(z) be the first derivative of 3*z**2/2 + 72*z + 9. Let w be a(-23). What is the highest common factor of w and n?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-260"}}
{"id": "dm-numbers__gcd_composed-hard-260", "pool": "math", "split": "train", "question": "Let v(c) = 2*c**2 - 6*c - 7. Let t be v(5). Let j(m) be the second derivative of -m**5/20 + 7*m**4/6 - 5*m**3/3 - 9*m**2/2 + m - 152. Let z be j(t). Calculate the highest common divisor of z and 10.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-261"}}
{"id": "dm-numbers__gcd_composed-hard-261", "pool": "math", "split": "train", "question": "Let w = -15028 - -18981. Calculate the highest common divisor of 268 and w.", "unit": "dimensionless", "value": "67", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-262"}}
{"id": "dm-numbers__gcd_composed-hard-262", "pool": "math", "split": "train", "question": "Let d = -26304 - -37084. What is the highest common divisor of d and 14?", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-263"}}
{"id": "dm-numbers__gcd_composed-hard-263", "pool": "math", "split": "train", "question": "Suppose -510 = -5*m + 2*i, -160 = -5*m - 2*i + 350. Suppose 3*s = 5*o - 0*o + m, 2*o = -5*s + 139. Calculate the greatest common factor of 87 and s.", "unit": "dimensionless", "value": "29", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-264"}}
{"id": "dm-numbers__gcd_composed-hard-264", "pool": "math", "split": "train", "question": "Suppose n + 4*l - 60 = 0, -16 = -3*n - l + 131. Let o(j) = -5*j - 3. Let q be o(-1). Let i be ((-16)/(-1) - 0)/q. Calculate the greatest common factor of n and i.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-265"}}
{"id": "dm-numbers__gcd_composed-hard-265", "pool": "math", "split": "train", "question": "Suppose 16*g + 292 = -1340. Let j = g + 108. Calculate the highest common factor of 9 and j.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-266"}}
{"id": "dm-numbers__gcd_composed-hard-266", "pool": "math", "split": "train", "question": "Suppose 0 = 3*t - 3*w - 111, w + 82 = 30*t - 28*t. Calculate the highest common divisor of 8649 and t.", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-267"}}
{"id": "dm-numbers__gcd_composed-hard-267", "pool": "math", "split": "train", "question": "Let x be (110/7)/((50/(-385))/(-10)). What is the highest common factor of 30 and x?", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-268"}}
{"id": "dm-numbers__gcd_composed-hard-268", "pool": "math", "split": "train", "question": "Let s(q) = -q**3 + 66*q**2 - 121*q - 1343. Let o be s(63). Calculate the greatest common factor of o and 17.", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-269"}}
{"id": "dm-numbers__gcd_composed-hard-269", "pool": "math", "split": "train", "question": "Let w(r) = 12*r**3 + 19*r + 34. Let p be w(11). What is the greatest common factor of 45 and p?", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-270"}}
{"id": "dm-numbers__gcd_composed-hard-270", "pool": "math", "split": "train", "question": "Let i(d) = -d**3 + d**2 + d - 2. Let u(p) = 4*p**3 - 10*p**2 + 9*p + 62. Let x(r) = -5*i(r) - u(r). Let z be x(-5). What is the greatest common divisor of z and 66?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-271"}}
{"id": "dm-numbers__gcd_composed-hard-271", "pool": "math", "split": "train", "question": "Suppose -64 = -o - 2*z - 14, 0 = -3*z + 3. Calculate the highest common factor of 3088 and o.", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-272"}}
{"id": "dm-numbers__gcd_composed-hard-272", "pool": "math", "split": "train", "question": "Suppose 0 = -2*a - 5*u + 14 - 58, -2*a - u = 28. Let q be 96*(2 + (-40)/a). Suppose -100 - q = -12*s. Calculate the highest common factor of 51 and s.", "unit": "dimensionless", "value": "51", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-273"}}
{"id": "dm-numbers__gcd_composed-hard-273", "pool": "math", "split": "train", "question": "Let v = 140 + -140. Let a(b) be the second derivative of -b**5/10 - b**3/3 + 3*b**2 + 2*b. Let y be a(v). Calculate the greatest common factor of y and 15.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-274"}}
{"id": "dm-numbers__gcd_composed-hard-274", "pool": "math", "split": "train", "question": "Let h = -588 - -1380. Calculate the greatest common divisor of 72 and h.", "unit": "dimensionless", "value": "72", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-275"}}
{"id": "dm-numbers__gcd_composed-hard-275", "pool": "math", "split": "train", "question": "Let n(o) = -o - 19. Let i be n(-30). Suppose i*g - 917 = -125. Suppose 3*t - 1 = 26. What is the greatest common factor of g and t?", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-276"}}
{"id": "dm-numbers__gcd_composed-hard-276", "pool": "math", "split": "train", "question": "Let m(x) = x**3 + 13*x**2 - 9*x - 114. Let s be m(-13). Suppose s*v = 14*v - 396. What is the highest common factor of 54 and v?", "unit": "dimensionless", "value": "18", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-277"}}
{"id": "dm-numbers__gcd_composed-hard-277", "pool": "math", "split": "train", "question": "Suppose 0 = 126*w - 163*w + 13727. Calculate the greatest common factor of 70 and w.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-278"}}
{"id": "dm-numbers__gcd_composed-hard-278", "pool": "math", "split": "train", "question": "Let c(r) = r**3 - 6*r**2 + 4. Let k be 5 + (-3)/3 + -2. Suppose k*x - w = 8, -9 = -3*x - 3*w + 21. Let j be c(x). Calculate the highest common factor of j and 10.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-279"}}
{"id": "dm-numbers__gcd_composed-hard-279", "pool": "math", "split": "train", "question": "Suppose -i + 4*m + 32 = 0, 516*i + 91 = 521*i + 3*m. Let j = 10 + -6. Let h be j*12*10/30. Calculate the highest common factor of i and h.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-280"}}
{"id": "dm-numbers__gcd_composed-hard-280", "pool": "math", "split": "train", "question": "Let m(q) = q**3 + 40*q**2 + 7*q + 42. Let x be m(-12). Calculate the greatest common divisor of 84 and x.", "unit": "dimensionless", "value": "42", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-281"}}
{"id": "dm-numbers__gcd_composed-hard-281", "pool": "math", "split": "train", "question": "Let t = -27 - -29. Let x be t*3/8*4. Suppose 144 = x*k - k. What is the greatest common factor of 8 and k?", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-282"}}
{"id": "dm-numbers__gcd_composed-hard-282", "pool": "math", "split": "train", "question": "Suppose -g + 7849 = 5*p - 3*g, 14*g - 3258 = -2*p. Calculate the highest common divisor of 605 and p.", "unit": "dimensionless", "value": "121", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-283"}}
{"id": "dm-numbers__gcd_composed-hard-283", "pool": "math", "split": "train", "question": "Let b be 500/(-24)*-19 - (-2)/12. Suppose 360*o + b = 371*o. What is the greatest common divisor of 12 and o?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-284"}}
{"id": "dm-numbers__gcd_composed-hard-284", "pool": "math", "split": "train", "question": "Let a(g) = 3*g**3 - 52*g**2 - 35*g - 16. Let f be a(18). Let q(r) = -1 + 8 + 4 + r**2 + 9*r. Let b be q(-8). Calculate the greatest common divisor of f and b.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-285"}}
{"id": "dm-numbers__gcd_composed-hard-285", "pool": "math", "split": "train", "question": "Let y = -163 + 211. Suppose -3*o - 3*a = -156, y = o - 0*o - 3*a. Calculate the highest common divisor of 102 and o.", "unit": "dimensionless", "value": "51", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-286"}}
{"id": "dm-numbers__gcd_composed-hard-286", "pool": "math", "split": "train", "question": "Suppose q + 4*q = 550. Suppose 4*t = 5*m - 66, -2*m - 7*t + 8 = -4*t. Calculate the highest common divisor of q and m.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-287"}}
{"id": "dm-numbers__gcd_composed-hard-287", "pool": "math", "split": "train", "question": "Let y be (8/5)/((-57)/15 + 4). Let q be (y/(-6))/(16/120). Let x be 1 + (-394)/q + (-16)/40. What is the greatest common divisor of x and 5?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-288"}}
{"id": "dm-numbers__gcd_composed-hard-288", "pool": "math", "split": "train", "question": "Let l be 4/(28/3885) - (2 - 2). Suppose 0 = -3*c + 2*i + 332, 0*c - 3*i = -5*c + l. Calculate the greatest common factor of 76 and c.", "unit": "dimensionless", "value": "38", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-289"}}
{"id": "dm-numbers__gcd_composed-hard-289", "pool": "math", "split": "train", "question": "Suppose -73*g = 104 - 834. Calculate the highest common factor of g and 970.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-290"}}
{"id": "dm-numbers__gcd_composed-hard-290", "pool": "math", "split": "train", "question": "Let k = 13189 + -12829. What is the highest common divisor of 1125 and k?", "unit": "dimensionless", "value": "45", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-291"}}
{"id": "dm-numbers__gcd_composed-hard-291", "pool": "math", "split": "train", "question": "Suppose 3*z = j + 16, -201*j + 36 = 3*z - 198*j. Let i be 2 - 9*(0 - 13). Calculate the highest common factor of z and i.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-292"}}
{"id": "dm-numbers__gcd_composed-hard-292", "pool": "math", "split": "train", "question": "Suppose 5*c + 20 = 2*f - 6, 0 = 3*f + 2*c - 1. Suppose j + 6 = 4*j - f*o, 16 = -4*j - 4*o. Let q be (-2 - -5)*j + 123. What is the greatest common factor of 30 and q?", "unit": "dimensionless", "value": "30", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-293"}}
{"id": "dm-numbers__gcd_composed-hard-293", "pool": "math", "split": "train", "question": "Let m be ((-96)/(-10))/((-297)/(-90) - 3). Let k be (38/4)/(3/30). Suppose 27*r = m*r - k. Calculate the greatest common divisor of 38 and r.", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-294"}}
{"id": "dm-numbers__gcd_composed-hard-294", "pool": "math", "split": "train", "question": "Let o be (3/(-9) + (-88)/132)*(-114)/2. Let n(q) = q**2 - 2*q + 2. Let c be n(2). Suppose -7*y + c*y + 187 = -m, -4*y + 3*m + 143 = 0. What is the highest common divisor of y and o?", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-295"}}
{"id": "dm-numbers__gcd_composed-hard-295", "pool": "math", "split": "train", "question": "Let g(n) = -2*n**3 + 6 + 12 + n**3 - 24 - n - 7*n**2. Let d be g(-7). Let s be (-19)/(d/(-3)*3) + 0. What is the highest common factor of 171 and s?", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-296"}}
{"id": "dm-numbers__gcd_composed-hard-296", "pool": "math", "split": "train", "question": "Let u be 3 - 10 - (-2 - 21/(-6))*-50. What is the highest common factor of 324 and u?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-297"}}
{"id": "dm-numbers__gcd_composed-hard-297", "pool": "math", "split": "train", "question": "Suppose -11*q = 238 - 898. Let u be 13 + -32 + (-2)/1. Let r = u + 61. What is the greatest common factor of r and q?", "unit": "dimensionless", "value": "20", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-298"}}
{"id": "dm-numbers__gcd_composed-hard-298", "pool": "math", "split": "train", "question": "Let j(l) = -l**3 + 12*l**2 + 14*l - 15. Let t be j(13). Let s be (7 - -742) + 10/t. Calculate the highest common factor of s and 24.", "unit": "dimensionless", "value": "24", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-299"}}
{"id": "dm-numbers__gcd_composed-hard-299", "pool": "math", "split": "train", "question": "Let w(o) = o**3 - 29*o**2 + 55*o + 40. Let u be w(27). What is the greatest common factor of 5092 and u?", "unit": "dimensionless", "value": "67", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-300"}}
{"id": "dm-numbers__gcd_composed-hard-300", "pool": "math", "split": "train", "question": "Suppose 59*z = -80*z + 119*z + 7100. Calculate the greatest common factor of z and 55.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-301"}}
{"id": "dm-numbers__gcd_composed-hard-301", "pool": "math", "split": "train", "question": "Let r be 2820/(-423)*((-725)/35 - 4/14). What is the highest common divisor of 2128 and r?", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-302"}}
{"id": "dm-numbers__gcd_composed-hard-302", "pool": "math", "split": "train", "question": "Suppose 3*z + 76 = 3*q + 4, 0 = 3*z - 9. Suppose -6*j + j = h - q, -3*h - 2*j = -16. Suppose h*t - 36 = 12. Calculate the greatest common factor of 36 and t.", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-303"}}
{"id": "dm-numbers__gcd_composed-hard-303", "pool": "math", "split": "train", "question": "Let g(v) = 2*v**2 + 323*v + 329*v + 15 - 655*v. Let y be g(5). Calculate the highest common factor of y and 450.", "unit": "dimensionless", "value": "50", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-304"}}
{"id": "dm-numbers__gcd_composed-hard-304", "pool": "math", "split": "train", "question": "Suppose t = -4*s + 22, -11 = -t + 4*s + 27. Suppose 113*v - 80*v = -2331 + 11241. What is the greatest common divisor of t and v?", "unit": "dimensionless", "value": "30", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-305"}}
{"id": "dm-numbers__gcd_composed-hard-305", "pool": "math", "split": "train", "question": "Let u = 7748 - 7720. Calculate the greatest common divisor of 3206 and u.", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-306"}}
{"id": "dm-numbers__gcd_composed-hard-306", "pool": "math", "split": "train", "question": "Let n(b) = -b**3 - 86*b**2 - 94*b - 673. Let d be n(-85). Calculate the highest common factor of 23 and d.", "unit": "dimensionless", "value": "23", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-307"}}
{"id": "dm-numbers__gcd_composed-hard-307", "pool": "math", "split": "train", "question": "Suppose -7*p = -2*l - 541, -5*p + 387 = -10*l + 8*l. What is the highest common divisor of 429 and p?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-308"}}
{"id": "dm-numbers__gcd_composed-hard-308", "pool": "math", "split": "train", "question": "Suppose 49*c = 19376 + 3948. Let q = c - 432. Calculate the greatest common factor of 198 and q.", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-309"}}
{"id": "dm-numbers__gcd_composed-hard-309", "pool": "math", "split": "train", "question": "Let a(m) = -4*m**3 - 14*m**2 - m + 10. Let v(n) = 9*n**3 + 29*n**2 + 3*n - 19. Let z(i) = 5*a(i) + 2*v(i). Let y be z(-6). What is the highest common divisor of y and 90?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-310"}}
{"id": "dm-numbers__gcd_composed-hard-310", "pool": "math", "split": "train", "question": "Suppose -3*d - 45*g + 40*g = -19983, -2*g + 13318 = 2*d. What is the highest common divisor of 104 and d?", "unit": "dimensionless", "value": "104", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-311"}}
{"id": "dm-numbers__gcd_composed-hard-311", "pool": "math", "split": "train", "question": "Suppose -326 = -2*b + y - 216, -3*y = 18. What is the greatest common factor of b and 12428?", "unit": "dimensionless", "value": "52", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-312"}}
{"id": "dm-numbers__gcd_composed-hard-312", "pool": "math", "split": "train", "question": "Let z = 15745 - 8525. Calculate the greatest common factor of 20 and z.", "unit": "dimensionless", "value": "20", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-313"}}
{"id": "dm-numbers__gcd_composed-hard-313", "pool": "math", "split": "train", "question": "Suppose -10*t = -12*t - 2*i + 98, -3*i + 198 = 4*t. Calculate the highest common factor of 986 and t.", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-314"}}
{"id": "dm-numbers__gcd_composed-hard-314", "pool": "math", "split": "train", "question": "Let d = 31 - 3. Let n(r) = 3*r**2 + 26*r + 175. Let g be n(-11). Calculate the highest common factor of d and g.", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-315"}}
{"id": "dm-numbers__gcd_composed-hard-315", "pool": "math", "split": "train", "question": "Suppose 8*b - 17694 = 17*b. Let q = b + 3097. Suppose -3*x = -3*u - q, -3*x + 2*x - 5*u + 371 = 0. Calculate the greatest common divisor of x and 47.", "unit": "dimensionless", "value": "47", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-316"}}
{"id": "dm-numbers__gcd_composed-hard-316", "pool": "math", "split": "train", "question": "Suppose -74 = 34*k - 210. Suppose -3*s - k*h = -2989, -2*h + 4*h + 4000 = 4*s. Calculate the highest common divisor of s and 37.", "unit": "dimensionless", "value": "37", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-317"}}
{"id": "dm-numbers__gcd_composed-hard-317", "pool": "math", "split": "train", "question": "Let x = -165 + 573. Suppose 31*y - 1398 = 1764. What is the greatest common divisor of y and x?", "unit": "dimensionless", "value": "102", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-318"}}
{"id": "dm-numbers__gcd_composed-hard-318", "pool": "math", "split": "train", "question": "Let x be 6/(-4)*8/(-6). Let a(g) = -g**2 + 168*g - 1705. Let r be a(11). What is the highest common factor of x and r?", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-319"}}
{"id": "dm-numbers__gcd_composed-hard-319", "pool": "math", "split": "train", "question": "Suppose -3*a + 37 = -26. Let q be (-135)/(a/(-35) + 2/(-5)). What is the greatest common factor of 15 and q?", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-320"}}
{"id": "dm-numbers__gcd_composed-hard-320", "pool": "math", "split": "train", "question": "Let r be 1 + 17 + 1*(3 + -4). Let n = 26 - r. Suppose 2*c - 6*c + 12 = 0. What is the highest common factor of n and c?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-321"}}
{"id": "dm-numbers__gcd_composed-hard-321", "pool": "math", "split": "train", "question": "Suppose s - 604 = -2*i, 15*s - 12*s - 2*i - 1796 = 0. What is the greatest common divisor of 64 and s?", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-322"}}
{"id": "dm-numbers__gcd_composed-hard-322", "pool": "math", "split": "train", "question": "Suppose 3*y + 631 = s + 3035, 4*y + s - 3196 = 0. Calculate the highest common factor of 2500 and y.", "unit": "dimensionless", "value": "100", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-323"}}
{"id": "dm-numbers__gcd_composed-hard-323", "pool": "math", "split": "train", "question": "Let w be (4/8)/((-6)/420). Let l = 35 + w. Suppose -5*c - 2*c + 238 = l. Calculate the greatest common divisor of 85 and c.", "unit": "dimensionless", "value": "17", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-324"}}
{"id": "dm-numbers__gcd_composed-hard-324", "pool": "math", "split": "train", "question": "Suppose 239861*w - 239887*w = -2340. Let t = -190 - -310. What is the greatest common divisor of t and w?", "unit": "dimensionless", "value": "30", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-325"}}
{"id": "dm-numbers__gcd_composed-hard-325", "pool": "math", "split": "train", "question": "Let f(r) = r**2 + 25*r + 52. Let l be f(-8). Let w be (l/(-15))/((-161)/35 - -5). What is the greatest common factor of 7 and w?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-326"}}
{"id": "dm-numbers__gcd_composed-hard-326", "pool": "math", "split": "train", "question": "Let q(o) = -369*o**2 + 12919*o - 60. Let t be q(35). Let f = 17 - 12. Calculate the highest common divisor of f and t.", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-327"}}
{"id": "dm-numbers__gcd_composed-hard-327", "pool": "math", "split": "train", "question": "Let t = -14594 - -28464. What is the greatest common divisor of t and 10?", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-328"}}
{"id": "dm-numbers__gcd_composed-hard-328", "pool": "math", "split": "train", "question": "Suppose 25*d + 48782 = 52132. Let v = -54 - -255. What is the greatest common factor of d and v?", "unit": "dimensionless", "value": "67", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-329"}}
{"id": "dm-numbers__gcd_composed-hard-329", "pool": "math", "split": "train", "question": "Let f = 2765 - 1778. Suppose -3*v + 846 = 15*v. Calculate the highest common divisor of f and v.", "unit": "dimensionless", "value": "47", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-330"}}
{"id": "dm-numbers__gcd_composed-hard-330", "pool": "math", "split": "train", "question": "Let p be 189/18*(10/3)/(-5). Let l be 3*2 - (-3 - -1). Let s = l - p. Calculate the highest common factor of 15 and s.", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-331"}}
{"id": "dm-numbers__gcd_composed-hard-331", "pool": "math", "split": "train", "question": "Let o = 113 + -38. Let i = o + -31. Let k be i*(8/16 + (-1)/(-2)). Calculate the highest common factor of k and 4.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-332"}}
{"id": "dm-numbers__gcd_composed-hard-332", "pool": "math", "split": "train", "question": "Suppose -992 + 980 = -3*y. Calculate the highest common divisor of 2188 and y.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-333"}}
{"id": "dm-numbers__gcd_composed-hard-333", "pool": "math", "split": "train", "question": "Let c(x) = 10*x**2 + 5*x + 12. Let h(d) = 9*d**2 + 3*d + 11. Let z(g) = -5*c(g) + 6*h(g). Let f be z(-6). Let t(j) = -j**3 + 15*j**2 - 11*j - 18. Let o be t(14). What is the greatest common factor of o and f?", "unit": "dimensionless", "value": "24", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-334"}}
{"id": "dm-numbers__gcd_composed-hard-334", "pool": "math", "split": "train", "question": "Suppose -3*q + 8 = -7. Let z(j) = 2*j**3 - 4*j**2 - 14*j + 8. Let u be z(q). Suppose 2*r + 5*b = u, -5*r + 0*b + 2*b + 191 = 0. Calculate the highest common divisor of r and 26.", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-335"}}
{"id": "dm-numbers__gcd_composed-hard-335", "pool": "math", "split": "train", "question": "Let g = 3079 - 2371. What is the highest common divisor of g and 48?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-336"}}
{"id": "dm-numbers__gcd_composed-hard-336", "pool": "math", "split": "train", "question": "Let s = -1226 - -2790. Calculate the highest common factor of 138 and s.", "unit": "dimensionless", "value": "46", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-337"}}
{"id": "dm-numbers__gcd_composed-hard-337", "pool": "math", "split": "train", "question": "Let y(x) = 60*x**2 - 11*x - 12. Let b be y(3). Calculate the highest common divisor of 99 and b.", "unit": "dimensionless", "value": "99", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-338"}}
{"id": "dm-numbers__gcd_composed-hard-338", "pool": "math", "split": "train", "question": "Let h(z) = 1657*z**3 + 8*z**2 + 12*z - 19. Let n be h(1). Calculate the highest common factor of n and 4.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-339"}}
{"id": "dm-numbers__gcd_composed-hard-339", "pool": "math", "split": "train", "question": "Let g be -2*1 + (-1 - -15). Suppose -26*d - 1289 + 9193 = 0. Suppose d = g*m - 8*m. Calculate the highest common factor of 19 and m.", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-340"}}
{"id": "dm-numbers__gcd_composed-hard-340", "pool": "math", "split": "train", "question": "Let f = 2658 + 9559. Calculate the highest common divisor of f and 19.", "unit": "dimensionless", "value": "19", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-341"}}
{"id": "dm-numbers__gcd_composed-hard-341", "pool": "math", "split": "train", "question": "Let p(h) = 656*h - 3162. Let l be p(6). Suppose 0 = -2*m - b + 41, 2*m + 0*b = -3*b + 51. Calculate the greatest common divisor of m and l.", "unit": "dimensionless", "value": "18", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-342"}}
{"id": "dm-numbers__gcd_composed-hard-342", "pool": "math", "split": "train", "question": "Suppose 20 = 2*q + 2*b, 4*q + 4*b = 9*q - 14. Let u be ((-40)/q)/(132/(-198)). Calculate the highest common divisor of u and 130.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-343"}}
{"id": "dm-numbers__gcd_composed-hard-343", "pool": "math", "split": "train", "question": "Let g(t) = -4*t - 9. Let c(j) = 7*j + 18. Let r(a) = 6*c(a) + 11*g(a). Let p be r(-8). Let h = 114757 - 114732. Calculate the greatest common factor of p and h.", "unit": "dimensionless", "value": "25", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-344"}}
{"id": "dm-numbers__gcd_composed-hard-344", "pool": "math", "split": "train", "question": "Let k(r) be the third derivative of r**6/120 + 2*r**5/5 + 41*r**4/24 + 11*r**3/6 + 77*r**2. Let t be k(-22). What is the greatest common divisor of 7 and t?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-345"}}
{"id": "dm-numbers__gcd_composed-hard-345", "pool": "math", "split": "train", "question": "Suppose v - 23 = 5*y, 0 = 5*v + 3*y + 3 - 90. Let p(x) = -5*x**3 - 2*x**2 - 2*x + 3. Let a be p(-3). Calculate the greatest common divisor of v and a.", "unit": "dimensionless", "value": "18", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-346"}}
{"id": "dm-numbers__gcd_composed-hard-346", "pool": "math", "split": "train", "question": "Let z = 1092 - 722. Let t(y) = -y**3 - 6*y**2 - 4*y + 13. Let f be t(-6). Calculate the greatest common factor of f and z.", "unit": "dimensionless", "value": "37", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-347"}}
{"id": "dm-numbers__gcd_composed-hard-347", "pool": "math", "split": "train", "question": "Let d be ((-70)/49*-3 - -12)*(415 + -2). Calculate the highest common factor of d and 114.", "unit": "dimensionless", "value": "114", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-348"}}
{"id": "dm-numbers__gcd_composed-hard-348", "pool": "math", "split": "train", "question": "Let t(i) be the second derivative of -5*i**3/6 - 29*i**2/2 + 10*i. Let c be t(4). Let h = c + 65. What is the highest common factor of h and 4?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-349"}}
{"id": "dm-numbers__gcd_composed-hard-349", "pool": "math", "split": "train", "question": "Let a(o) = o + 10. Let x be a(-9). Calculate the highest common divisor of 9 and x.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-350"}}
{"id": "dm-numbers__gcd_composed-hard-350", "pool": "math", "split": "train", "question": "Let j(v) = -2*v**3 - 12*v**2 - 4*v - 27. Let l be j(-6). Let o be l*(-12)/10*(-35)/(-21). Calculate the highest common divisor of 45 and o.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-351"}}
{"id": "dm-numbers__gcd_composed-hard-351", "pool": "math", "split": "train", "question": "Let b = 155 - 155. Suppose -4*v - 5*m + 231 = b, 0 = -5*v - 2*m - 2*m + 282. Suppose -5*d = 3*a - v, -5*d - a = -80 + 22. What is the greatest common divisor of 78 and d?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-352"}}
{"id": "dm-numbers__gcd_composed-hard-352", "pool": "math", "split": "train", "question": "Let q(a) = -196*a - 974. Let t be q(-5). Calculate the greatest common divisor of t and 6234.", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-353"}}
{"id": "dm-numbers__gcd_composed-hard-353", "pool": "math", "split": "train", "question": "Suppose 36 = 20*c - 19*c + 4*i, 0 = c + 2*i - 34. Suppose -54 = 2*v - 5*f, -v = v + 5*f + 14. Let s be (13 + v)/(2/(-16)). What is the highest common factor of s and c?", "unit": "dimensionless", "value": "32", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-354"}}
{"id": "dm-numbers__gcd_composed-hard-354", "pool": "math", "split": "train", "question": "Suppose s + 33 = 3*a, -39*a = -3*s - 38*a - 59. Let f be ((-4)/s)/(13/936). What is the greatest common factor of 88 and f?", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-355"}}
{"id": "dm-numbers__gcd_composed-hard-355", "pool": "math", "split": "train", "question": "Suppose 3*b - 3*r = 210, b + 16 = 3*r + 70. What is the greatest common factor of 9542 and b?", "unit": "dimensionless", "value": "26", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-356"}}
{"id": "dm-numbers__gcd_composed-hard-356", "pool": "math", "split": "train", "question": "Suppose -w - 2101 = -3*d, -w - w = -10. Let b(v) = -v**2 + 3965*v + 39776. Let t be b(-10). What is the highest common factor of d and t?", "unit": "dimensionless", "value": "26", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-357"}}
{"id": "dm-numbers__gcd_composed-hard-357", "pool": "math", "split": "train", "question": "Suppose -104*u + 114*u = -14700. Let f be (-128)/(-6)*u/(-280). Calculate the highest common factor of f and 35.", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-358"}}
{"id": "dm-numbers__gcd_composed-hard-358", "pool": "math", "split": "train", "question": "Let g be ((-154)/(-6) - 14)/(2/468). What is the highest common divisor of g and 84?", "unit": "dimensionless", "value": "42", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-359"}}
{"id": "dm-numbers__gcd_composed-hard-359", "pool": "math", "split": "train", "question": "Let m be (-335)/((39/(-52))/((-3)/(-10))). Calculate the greatest common divisor of 18023 and m.", "unit": "dimensionless", "value": "67", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-360"}}
{"id": "dm-numbers__gcd_composed-hard-360", "pool": "math", "split": "train", "question": "Let o be (4/8)/(6/36). Suppose 25 = 3*w - 4*m, -o*m = -m + 8. Let j be (1 - -20)*8/w. Calculate the highest common divisor of j and 42.", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-361"}}
{"id": "dm-numbers__gcd_composed-hard-361", "pool": "math", "split": "train", "question": "Let f be 4/(-14) - 191/(-7). Let j = 3475 + -2434. Let t = -1005 + j. Calculate the greatest common factor of t and f.", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-362"}}
{"id": "dm-numbers__gcd_composed-hard-362", "pool": "math", "split": "train", "question": "Let c be 8/4 - ((-3 - 6) + 5). Suppose 620 - 854 = -c*f. What is the greatest common factor of f and 130?", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-363"}}
{"id": "dm-numbers__gcd_composed-hard-363", "pool": "math", "split": "train", "question": "Suppose q + 2 = 4, -5*r - 2*q + 179 = 0. Let t = 72 + -29. Suppose 5*f - 69 - 26 = 5*m, 3*m + t = 2*f. What is the highest common factor of r and f?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-364"}}
{"id": "dm-numbers__gcd_composed-hard-364", "pool": "math", "split": "train", "question": "Suppose -10*y - 35 = -15*y. Suppose -10*i - y*i = -1836. Calculate the highest common divisor of 486 and i.", "unit": "dimensionless", "value": "54", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-365"}}
{"id": "dm-numbers__gcd_composed-hard-365", "pool": "math", "split": "train", "question": "Suppose -3*i + 1014 = -4*n, 3*n = 3*i - 635 - 124. Let r be 4/30 + (-26486)/n. Let d = 21 - -5. What is the greatest common factor of r and d?", "unit": "dimensionless", "value": "26", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-366"}}
{"id": "dm-numbers__gcd_composed-hard-366", "pool": "math", "split": "train", "question": "Let h = -13 - -21. Let x(i) = -i**2 + 10*i + 16. Let n be x(8). Let b = h + n. Calculate the greatest common divisor of b and 16.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-367"}}
{"id": "dm-numbers__gcd_composed-hard-367", "pool": "math", "split": "train", "question": "Suppose -v - v = r + 564, 2296 = -4*r + 2*v. Let d be (-620)/(-22) + 104/r. What is the highest common divisor of d and 700?", "unit": "dimensionless", "value": "28", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-368"}}
{"id": "dm-numbers__gcd_composed-hard-368", "pool": "math", "split": "train", "question": "Let p = 204 - 208. Let i(o) = 5*o + 60. Let d be i(p). Calculate the greatest common divisor of d and 30.", "unit": "dimensionless", "value": "10", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-369"}}
{"id": "dm-numbers__gcd_composed-hard-369", "pool": "math", "split": "train", "question": "Suppose 0*d - 12 = -4*d. Let a(i) = 446*i**3 + i**2 - 3*i - 2. Let b be a(2). Suppose -b = o - 3594. Calculate the greatest common divisor of o and d.", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-370"}}
{"id": "dm-numbers__gcd_composed-hard-370", "pool": "math", "split": "train", "question": "Suppose -s + 174 = 4*i, -i - 12 = -s - 58. Let k be (44/88)/(1/i). What is the highest common factor of 198 and k?", "unit": "dimensionless", "value": "22", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-371"}}
{"id": "dm-numbers__gcd_composed-hard-371", "pool": "math", "split": "train", "question": "Suppose 2*k + i + 0*i - 94 = 0, -2*i = k - 44. Let y = -4147 - -4363. What is the greatest common divisor of k and y?", "unit": "dimensionless", "value": "24", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-372"}}
{"id": "dm-numbers__gcd_composed-hard-372", "pool": "math", "split": "train", "question": "Let p be (7648/717)/((-4)/(-6)). What is the greatest common factor of p and 752?", "unit": "dimensionless", "value": "16", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-373"}}
{"id": "dm-numbers__gcd_composed-hard-373", "pool": "math", "split": "train", "question": "Let r be (-1632)/(-14) + 6/14. Let f be (-1925)/91 + (-12)/(-78). Let g = 34 + f. Calculate the highest common factor of r and g.", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-374"}}
{"id": "dm-numbers__gcd_composed-hard-374", "pool": "math", "split": "train", "question": "Let d = -447 + 451. Calculate the highest common divisor of 106 and d.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-375"}}
{"id": "dm-numbers__gcd_composed-hard-375", "pool": "math", "split": "train", "question": "Let y be 517/715*19085 - (-1 - (-24)/26). What is the highest common factor of 46 and y?", "unit": "dimensionless", "value": "46", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-376"}}
{"id": "dm-numbers__gcd_composed-hard-376", "pool": "math", "split": "train", "question": "Let x(v) = v**3 - 45*v**2 - 47*v + 47. Let z(g) = 2*g**3 - 26*g**2 + 5*g - 19. Let n be z(13). Let a be x(n). What is the greatest common divisor of 1 and a?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-377"}}
{"id": "dm-numbers__gcd_composed-hard-377", "pool": "math", "split": "train", "question": "Suppose 5*s = -k + 6, 3*k + 3*s = 5*k - 12. Let p(b) be the third derivative of 7*b**6/120 - b**5/30 + b**4/24 + 2*b**2. Let x be p(1). What is the greatest common divisor of x and k?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-378"}}
{"id": "dm-numbers__gcd_composed-hard-378", "pool": "math", "split": "train", "question": "Suppose -c + 13 = -4*s, 52*s = 48*s - 12. Calculate the highest common factor of 199 and c.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-379"}}
{"id": "dm-numbers__gcd_composed-hard-379", "pool": "math", "split": "train", "question": "Let z be 5618 - ((0 - 30)/(-3) - (-2)/(-2)). Calculate the highest common factor of z and 395.", "unit": "dimensionless", "value": "79", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-380"}}
{"id": "dm-numbers__gcd_composed-hard-380", "pool": "math", "split": "train", "question": "Suppose 3*m = -9, -9*m + 36 = 4*q - 5*m. What is the highest common factor of 384 and q?", "unit": "dimensionless", "value": "12", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-381"}}
{"id": "dm-numbers__gcd_composed-hard-381", "pool": "math", "split": "train", "question": "Suppose 3*b + 4*w - 45 = w, -w = 4*b - 63. Let f(k) = -b*k + 8*k + 9*k + 44. Let j be f(-22). Calculate the highest common divisor of 11 and j.", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-382"}}
{"id": "dm-numbers__gcd_composed-hard-382", "pool": "math", "split": "train", "question": "Let s(f) = 3*f**2 - 3*f + 5. Let a be s(5). Let p be ((-26)/a)/(1/(-10)). Suppose 0*g = 3*g + p*c - 53, 0 = -3*g - 2*c + 43. What is the highest common factor of 11 and g?", "unit": "dimensionless", "value": "11", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-383"}}
{"id": "dm-numbers__gcd_composed-hard-383", "pool": "math", "split": "train", "question": "Let m(f) be the third derivative of -f**6/120 + 2*f**5/15 + f**4 - 10*f**3/3 + 20*f**2. Let c be m(10). Calculate the greatest common divisor of 4 and c.", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-384"}}
{"id": "dm-numbers__gcd_composed-hard-384", "pool": "math", "split": "train", "question": "Suppose -1376 = -15*a - a. Suppose -i - 71 = -a. What is the highest common divisor of i and 135?", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-385"}}
{"id": "dm-numbers__gcd_composed-hard-385", "pool": "math", "split": "train", "question": "Let u(h) = -h**3 + 4*h**2 + 11*h + 9. Let v be u(6). Let a be -18*v*50/45. Let q = a + 129. Calculate the highest common divisor of 23 and q.", "unit": "dimensionless", "value": "23", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-386"}}
{"id": "dm-numbers__gcd_composed-hard-386", "pool": "math", "split": "train", "question": "Let q = 61 - 31. Suppose 5*n - q = -10. Let h be 16/(-10)*(-450)/120. What is the greatest common divisor of h and n?", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-387"}}
{"id": "dm-numbers__gcd_composed-hard-387", "pool": "math", "split": "train", "question": "Let k(q) = -8*q**3 - 56*q**2 - 30*q + 15. Let a be k(-7). Let c(f) = f**3 + 8*f**2 + 7*f + 5. Let j be c(-5). What is the highest common factor of a and j?", "unit": "dimensionless", "value": "45", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-388"}}
{"id": "dm-numbers__gcd_composed-hard-388", "pool": "math", "split": "train", "question": "Let p be 0 + -6 + 8 + -4 - (2 - 476). Calculate the greatest common divisor of 8 and p.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-389"}}
{"id": "dm-numbers__gcd_composed-hard-389", "pool": "math", "split": "train", "question": "Let b = 68 + -66. Suppose 0 = -3*l - 5*w + 11 + 13, 3 = -l + b*w. Suppose -i + 0*i + l*f - 1 = 0, 0 = -i + 2*f. What is the greatest common factor of i and 6?", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-390"}}
{"id": "dm-numbers__gcd_composed-hard-390", "pool": "math", "split": "train", "question": "Let v(q) = q**2 - 7*q - 12. Suppose 3*b + 34 - 19 = 0. Let u be v(b). Calculate the greatest common divisor of 56 and u.", "unit": "dimensionless", "value": "8", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-391"}}
{"id": "dm-numbers__gcd_composed-hard-391", "pool": "math", "split": "train", "question": "Let b(n) = n**2 + 15*n + 9. Let m(j) = j**3 + 2*j**2 - 5. Let z be m(-3). Let k be b(z). Let y be 1/(k + 3 - (-14)/6). What is the greatest common factor of y and 9?", "unit": "dimensionless", "value": "3", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-392"}}
{"id": "dm-numbers__gcd_composed-hard-392", "pool": "math", "split": "train", "question": "Let k = -122 - -139. Suppose 0 = -13*g - k*g + 630. What is the greatest common divisor of 861 and g?", "unit": "dimensionless", "value": "21", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-393"}}
{"id": "dm-numbers__gcd_composed-hard-393", "pool": "math", "split": "train", "question": "Suppose -r + l + l = -17, r - 3*l - 12 = 0. Let d(g) = g**3 + 14*g**2 + 547*g + 6537. Let m be d(-12). Calculate the highest common factor of r and m.", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-394"}}
{"id": "dm-numbers__gcd_composed-hard-394", "pool": "math", "split": "train", "question": "Let p = -196115 + 196141. Suppose 3*a - 707 - 346 = 0. What is the greatest common factor of p and a?", "unit": "dimensionless", "value": "13", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-395"}}
{"id": "dm-numbers__gcd_composed-hard-395", "pool": "math", "split": "train", "question": "Let q(u) = u**3 + 12*u**2 + 16*u + 69. Let r be q(-11). What is the highest common divisor of r and 1379?", "unit": "dimensionless", "value": "7", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-396"}}
{"id": "dm-numbers__gcd_composed-hard-396", "pool": "math", "split": "train", "question": "Let w(v) = -70*v - 798. Let z be w(-12). Suppose -5*g + 280 = -g. Calculate the greatest common divisor of g and z.", "unit": "dimensionless", "value": "14", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-397"}}
{"id": "dm-numbers__gcd_composed-hard-397", "pool": "math", "split": "train", "question": "Let g = -6634 - -6636. Calculate the highest common factor of g and 2374.", "unit": "dimensionless", "value": "2", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-398"}}
{"id": "dm-numbers__gcd_composed-hard-398", "pool": "math", "split": "train", "question": "Let o be ((-90)/14)/(96 + (-272403)/2835). Let u(w) = 10*w**2 - 2*w + 2. Let k be u(3). Let z = k + -26. Calculate the highest common factor of z and o.", "unit": "dimensionless", "value": "15", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-399"}}
{"id": "dm-numbers__gcd_composed-hard-399", "pool": "math", "split": "train", "question": "Suppose 3*v + 230 = 8*v. Suppose 0 = -5*d - 5*g - 80, -2*d + 7*g = 2*g + v. Let a(z) = z**2 + 19*z + 36. Let l be a(d). Calculate the greatest common factor of 27 and l.", "unit": "dimensionless", "value": "9", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-400"}}
{"id": "dm-numbers__gcd_composed-hard-400", "pool": "math", "split": "train", "question": "Suppose 0 = 29*p - 27*p - 32. Let o be (2/2)/((-2)/(-8)). Let h = p + o. What is the highest common divisor of 4 and h?", "unit": "dimensionless", "value": "4", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-401"}}
{"id": "dm-numbers__gcd_composed-hard-401", "pool": "math", "split": "train", "question": "Let x(j) = -2*j**3 - 22*j**2 + 64*j + 936. Let w be x(-14). What is the greatest common factor of 456 and w?", "unit": "dimensionless", "value": "152", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-402"}}
{"id": "dm-numbers__gcd_composed-hard-402", "pool": "math", "split": "train", "question": "Let f be (2/4)/(2/(-88)). Let j(h) = 1 - 11*h. Let d be j(-2). Let n = d + f. What is the greatest common factor of n and 9?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-403"}}
{"id": "dm-numbers__gcd_composed-hard-403", "pool": "math", "split": "train", "question": "Let i(k) = k**2 - 23*k - 32. Let d(z) = -z**3 + 9*z**2 + 21*z + 37. Let a be d(11). Let o be i(a). Calculate the greatest common divisor of 368 and o.", "unit": "dimensionless", "value": "46", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-404"}}
{"id": "dm-numbers__gcd_composed-hard-404", "pool": "math", "split": "train", "question": "Let r be 9*(7 - (1 - -1)). Let n = -131202 + 131207. What is the greatest common divisor of n and r?", "unit": "dimensionless", "value": "5", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-405"}}
{"id": "dm-numbers__gcd_composed-hard-405", "pool": "math", "split": "train", "question": "Let d be (-26064)/(-1267)*1603/2. What is the highest common divisor of d and 72?", "unit": "dimensionless", "value": "72", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-406"}}
{"id": "dm-numbers__gcd_composed-hard-406", "pool": "math", "split": "train", "question": "Let o(t) = t**2 - 17*t - 69. Let b(y) = y**2 - 25*y - 103. Let m(j) = -5*b(j) + 8*o(j). Let f be m(-3). What is the greatest common factor of f and 69?", "unit": "dimensionless", "value": "23", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-407"}}
{"id": "dm-numbers__gcd_composed-hard-407", "pool": "math", "split": "train", "question": "Let v be 24*(6 + 72/(-27)). What is the greatest common factor of 840 and v?", "unit": "dimensionless", "value": "40", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-408"}}
{"id": "dm-numbers__gcd_composed-hard-408", "pool": "math", "split": "train", "question": "Let i(n) = 652*n - 1638. Let y be i(3). What is the greatest common factor of y and 30?", "unit": "dimensionless", "value": "6", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-409"}}
{"id": "dm-numbers__gcd_composed-hard-409", "pool": "math", "split": "train", "question": "Suppose 72*a = 90*a - 8694. What is the highest common divisor of a and 161?", "unit": "dimensionless", "value": "161", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "numbers__gcd_composed", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "numbers__gcd_composed", "level": "hard", "seed": "numbers__gcd_composed-hard-410"}}
{"id": "dm-probability__swr_p_level_set-hard-0", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 v when two letters picked without replacement from zzvhbvz.", "unit": "dimensionless", "value": "0.0476190", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-1"}}
{"id": "dm-probability__swr_p_level_set-hard-1", "pool": "math", "split": "train", "question": "Calculate prob of picking 4 u when four letters picked without replacement from uusssssusssssuussu.", "unit": "dimensionless", "value": "0.00490196", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-2"}}
{"id": "dm-probability__swr_p_level_set-hard-2", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 d and 2 x when four letters picked without replacement from {x: 4, d: 2}.", "unit": "dimensionless", "value": "0.4", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-3"}}
{"id": "dm-probability__swr_p_level_set-hard-3", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 g, 1 z and 1 k when three letters picked without replacement from nkkkrrvvgkknrrvzkkzr.", "unit": "dimensionless", "value": "0.0122807", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-4"}}
{"id": "dm-probability__swr_p_level_set-hard-4", "pool": "math", "split": "train", "question": "What is prob of picking 4 d when four letters picked without replacement from khkkudtoddhdkkk?", "unit": "dimensionless", "value": "0.000732601", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-5"}}
{"id": "dm-probability__swr_p_level_set-hard-5", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {s: 2, x: 1, p: 1, n: 1, y: 1, z: 1}. Give prob of picking 1 p, 1 s and 1 n.", "unit": "dimensionless", "value": "0.0571429", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-6"}}
{"id": "dm-probability__swr_p_level_set-hard-6", "pool": "math", "split": "train", "question": "What is prob of picking 2 y and 1 z when three letters picked without replacement from yuuuzuuyayyuuzu?", "unit": "dimensionless", "value": "0.0263736", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-7"}}
{"id": "dm-probability__swr_p_level_set-hard-7", "pool": "math", "split": "train", "question": "What is prob of picking 2 t and 1 h when three letters picked without replacement from {m: 7, h: 4, t: 7}?", "unit": "dimensionless", "value": "0.102941", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-8"}}
{"id": "dm-probability__swr_p_level_set-hard-8", "pool": "math", "split": "train", "question": "What is prob of picking 2 y, 1 n and 1 i when four letters picked without replacement from bbybyybiiibbninybny?", "unit": "dimensionless", "value": "0.0309598", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-9"}}
{"id": "dm-probability__swr_p_level_set-hard-9", "pool": "math", "split": "train", "question": "Three letters picked without replacement from viviviiviiiv. What is prob of picking 2 i and 1 v?", "unit": "dimensionless", "value": "0.477273", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-10"}}
{"id": "dm-probability__swr_p_level_set-hard-10", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {d: 8, p: 2, k: 2}. What is prob of picking 3 d?", "unit": "dimensionless", "value": "0.254545", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-11"}}
{"id": "dm-probability__swr_p_level_set-hard-11", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {r: 6, o: 1, t: 5, z: 3}. Give prob of picking 2 r and 1 t.", "unit": "dimensionless", "value": "0.164835", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-12"}}
{"id": "dm-probability__swr_p_level_set-hard-12", "pool": "math", "split": "train", "question": "Two letters picked without replacement from rkkkkkrkkkkkkkkkrk. Give prob of picking 2 r.", "unit": "dimensionless", "value": "0.0196078", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-13"}}
{"id": "dm-probability__swr_p_level_set-hard-13", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {p: 8, q: 5, g: 7}. What is prob of picking 2 g?", "unit": "dimensionless", "value": "0.110526", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-14"}}
{"id": "dm-probability__swr_p_level_set-hard-14", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {s: 2, e: 2, j: 6, o: 3, n: 2}. What is prob of picking 2 n, 1 j and 1 o?", "unit": "dimensionless", "value": "0.0131868", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-15"}}
{"id": "dm-probability__swr_p_level_set-hard-15", "pool": "math", "split": "train", "question": "Four letters picked without replacement from iiii. What is prob of picking 4 i?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-16"}}
{"id": "dm-probability__swr_p_level_set-hard-16", "pool": "math", "split": "train", "question": "Four letters picked without replacement from kmuxjmq. Give prob of picking 1 k, 1 u and 2 m.", "unit": "dimensionless", "value": "0.0285714", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-17"}}
{"id": "dm-probability__swr_p_level_set-hard-17", "pool": "math", "split": "train", "question": "What is prob of picking 1 n, 1 c, 1 z and 1 j when four letters picked without replacement from nnjcjnnjonncjnjznj?", "unit": "dimensionless", "value": "0.0313725", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-18"}}
{"id": "dm-probability__swr_p_level_set-hard-18", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 c and 2 k when four letters picked without replacement from xkkttccqttktcc.", "unit": "dimensionless", "value": "0.0179820", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-19"}}
{"id": "dm-probability__swr_p_level_set-hard-19", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {n: 1, p: 6, s: 8, j: 3}. What is prob of picking 1 s and 1 j?", "unit": "dimensionless", "value": "0.156863", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-20"}}
{"id": "dm-probability__swr_p_level_set-hard-20", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {h: 2, c: 1, j: 1, x: 5, f: 1}. What is prob of picking 1 h, 1 x and 1 c?", "unit": "dimensionless", "value": "0.0833333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-21"}}
{"id": "dm-probability__swr_p_level_set-hard-21", "pool": "math", "split": "train", "question": "Two letters picked without replacement from agsamgsgwgsx. Give prob of picking 1 s and 1 m.", "unit": "dimensionless", "value": "0.0454545", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-22"}}
{"id": "dm-probability__swr_p_level_set-hard-22", "pool": "math", "split": "train", "question": "What is prob of picking 1 d and 1 g when two letters picked without replacement from zdg?", "unit": "dimensionless", "value": "0.333333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-23"}}
{"id": "dm-probability__swr_p_level_set-hard-23", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {l: 2, g: 2}. What is prob of picking 2 g and 1 l?", "unit": "dimensionless", "value": "0.5", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-24"}}
{"id": "dm-probability__swr_p_level_set-hard-24", "pool": "math", "split": "train", "question": "Three letters picked without replacement from mpmmpmppmpmppmmmppp. What is prob of picking 3 p?", "unit": "dimensionless", "value": "0.123839", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-25"}}
{"id": "dm-probability__swr_p_level_set-hard-25", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {r: 1, s: 4, b: 1, k: 2}. What is prob of picking 1 s and 1 r?", "unit": "dimensionless", "value": "0.142857", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-26"}}
{"id": "dm-probability__swr_p_level_set-hard-26", "pool": "math", "split": "train", "question": "Calculate prob of picking 4 n when four letters picked without replacement from nnlnnnlnnln.", "unit": "dimensionless", "value": "0.212121", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-27"}}
{"id": "dm-probability__swr_p_level_set-hard-27", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 a when two letters picked without replacement from {a: 15, y: 5}.", "unit": "dimensionless", "value": "0.552632", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-28"}}
{"id": "dm-probability__swr_p_level_set-hard-28", "pool": "math", "split": "train", "question": "Two letters picked without replacement from hykhkaajkkkhahchkka. Give prob of picking 1 h and 1 y.", "unit": "dimensionless", "value": "0.0292398", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-29"}}
{"id": "dm-probability__swr_p_level_set-hard-29", "pool": "math", "split": "train", "question": "Two letters picked without replacement from llee. What is prob of picking 2 l?", "unit": "dimensionless", "value": "0.166667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-30"}}
{"id": "dm-probability__swr_p_level_set-hard-30", "pool": "math", "split": "train", "question": "What is prob of picking 1 l, 1 q and 1 x when three letters picked without replacement from qlxpw?", "unit": "dimensionless", "value": "0.1", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-31"}}
{"id": "dm-probability__swr_p_level_set-hard-31", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 s when two letters picked without replacement from {o: 4, s: 2, r: 6}.", "unit": "dimensionless", "value": "0.0151515", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-32"}}
{"id": "dm-probability__swr_p_level_set-hard-32", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 a when two letters picked without replacement from zazaazz.", "unit": "dimensionless", "value": "0.142857", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-33"}}
{"id": "dm-probability__swr_p_level_set-hard-33", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {w: 6, b: 13}. What is prob of picking 1 w and 2 b?", "unit": "dimensionless", "value": "0.482972", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-34"}}
{"id": "dm-probability__swr_p_level_set-hard-34", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {f: 9, g: 8, r: 2}. Give prob of picking 3 g.", "unit": "dimensionless", "value": "0.0577915", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-35"}}
{"id": "dm-probability__swr_p_level_set-hard-35", "pool": "math", "split": "train", "question": "Two letters picked without replacement from ddss. What is prob of picking 2 s?", "unit": "dimensionless", "value": "0.166667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-36"}}
{"id": "dm-probability__swr_p_level_set-hard-36", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {r: 1, v: 2, c: 5, b: 4, t: 2}. What is prob of picking 1 b and 2 t?", "unit": "dimensionless", "value": "0.0109890", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-37"}}
{"id": "dm-probability__swr_p_level_set-hard-37", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {b: 2, f: 2, k: 1, g: 1, q: 1}. Give prob of picking 1 g, 1 q and 1 b.", "unit": "dimensionless", "value": "0.0571429", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-38"}}
{"id": "dm-probability__swr_p_level_set-hard-38", "pool": "math", "split": "train", "question": "Three letters picked without replacement from uhuhhhhuuhuuh. What is prob of picking 3 h?", "unit": "dimensionless", "value": "0.122378", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-39"}}
{"id": "dm-probability__swr_p_level_set-hard-39", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 n and 1 g when two letters picked without replacement from {q: 5, g: 2, z: 3, u: 3, r: 1, n: 1}.", "unit": "dimensionless", "value": "0.0190476", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-40"}}
{"id": "dm-probability__swr_p_level_set-hard-40", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 i and 2 u when three letters picked without replacement from xouuijxouoxojjaojjj.", "unit": "dimensionless", "value": "0.00309598", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-41"}}
{"id": "dm-probability__swr_p_level_set-hard-41", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 o and 1 t when two letters picked without replacement from iomtiti.", "unit": "dimensionless", "value": "0.0952381", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-42"}}
{"id": "dm-probability__swr_p_level_set-hard-42", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {h: 2, x: 3}. What is prob of picking 1 h and 1 x?", "unit": "dimensionless", "value": "0.6", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-43"}}
{"id": "dm-probability__swr_p_level_set-hard-43", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 g when two letters picked without replacement from dgog.", "unit": "dimensionless", "value": "0.166667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-44"}}
{"id": "dm-probability__swr_p_level_set-hard-44", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {i: 6, v: 4, j: 5}. What is prob of picking 3 i and 1 j?", "unit": "dimensionless", "value": "0.0732601", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-45"}}
{"id": "dm-probability__swr_p_level_set-hard-45", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 f and 1 r when two letters picked without replacement from hhhrmhhmrhhhrrhfhmh.", "unit": "dimensionless", "value": "0.0233918", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-46"}}
{"id": "dm-probability__swr_p_level_set-hard-46", "pool": "math", "split": "train", "question": "What is prob of picking 2 k and 1 h when three letters picked without replacement from fkkhtkkkkkkk?", "unit": "dimensionless", "value": "0.163636", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-47"}}
{"id": "dm-probability__swr_p_level_set-hard-47", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {z: 11, n: 3}. Give prob of picking 4 z.", "unit": "dimensionless", "value": "0.329670", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-48"}}
{"id": "dm-probability__swr_p_level_set-hard-48", "pool": "math", "split": "train", "question": "What is prob of picking 2 y and 2 v when four letters picked without replacement from vyyddwdwdywvvydwdwd?", "unit": "dimensionless", "value": "0.00464396", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-49"}}
{"id": "dm-probability__swr_p_level_set-hard-49", "pool": "math", "split": "train", "question": "What is prob of picking 1 f and 3 m when four letters picked without replacement from {m: 3, f: 9}?", "unit": "dimensionless", "value": "0.0181818", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-50"}}
{"id": "dm-probability__swr_p_level_set-hard-50", "pool": "math", "split": "train", "question": "Calculate prob of picking 4 v when four letters picked without replacement from vvvyvvvvyyyvyv.", "unit": "dimensionless", "value": "0.125874", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-51"}}
{"id": "dm-probability__swr_p_level_set-hard-51", "pool": "math", "split": "train", "question": "Calculate prob of picking 4 k when four letters picked without replacement from kbbhkhkkhkhkkkbh.", "unit": "dimensionless", "value": "0.0384615", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-52"}}
{"id": "dm-probability__swr_p_level_set-hard-52", "pool": "math", "split": "train", "question": "Calculate prob of picking 3 j and 1 t when four letters picked without replacement from jjjjjjjtjjjjt.", "unit": "dimensionless", "value": "0.461538", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-53"}}
{"id": "dm-probability__swr_p_level_set-hard-53", "pool": "math", "split": "train", "question": "What is prob of picking 2 n when two letters picked without replacement from {n: 5}?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-54"}}
{"id": "dm-probability__swr_p_level_set-hard-54", "pool": "math", "split": "train", "question": "What is prob of picking 1 n and 2 d when three letters picked without replacement from sddsnnssddhdh?", "unit": "dimensionless", "value": "0.0699301", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-55"}}
{"id": "dm-probability__swr_p_level_set-hard-55", "pool": "math", "split": "train", "question": "What is prob of picking 1 d and 1 i when two letters picked without replacement from {d: 5, i: 5, a: 1, x: 1, y: 1, u: 4}?", "unit": "dimensionless", "value": "0.183824", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-56"}}
{"id": "dm-probability__swr_p_level_set-hard-56", "pool": "math", "split": "train", "question": "Two letters picked without replacement from vxyxxvm. Give prob of picking 1 v and 1 m.", "unit": "dimensionless", "value": "0.0952381", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-57"}}
{"id": "dm-probability__swr_p_level_set-hard-57", "pool": "math", "split": "train", "question": "Three letters picked without replacement from zwzmmzmmwwwwwmm. What is prob of picking 2 z and 1 m?", "unit": "dimensionless", "value": "0.0395604", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-58"}}
{"id": "dm-probability__swr_p_level_set-hard-58", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 f and 1 e when two letters picked without replacement from eefifiiiiieffeieiiei.", "unit": "dimensionless", "value": "0.126316", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-59"}}
{"id": "dm-probability__swr_p_level_set-hard-59", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 b and 1 h when two letters picked without replacement from bhhbbbb.", "unit": "dimensionless", "value": "0.476190", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-60"}}
{"id": "dm-probability__swr_p_level_set-hard-60", "pool": "math", "split": "train", "question": "Four letters picked without replacement from sjsssjjjssssjssjsjs. Give prob of picking 1 j and 3 s.", "unit": "dimensionless", "value": "0.397317", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-61"}}
{"id": "dm-probability__swr_p_level_set-hard-61", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {z: 1, j: 3}. Give prob of picking 2 j.", "unit": "dimensionless", "value": "0.5", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-62"}}
{"id": "dm-probability__swr_p_level_set-hard-62", "pool": "math", "split": "train", "question": "What is prob of picking 1 r and 1 n when two letters picked without replacement from rrrrrrrrnrrrr?", "unit": "dimensionless", "value": "0.153846", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-63"}}
{"id": "dm-probability__swr_p_level_set-hard-63", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 g, 1 d and 1 a when three letters picked without replacement from zdazygndaznd.", "unit": "dimensionless", "value": "0.0272727", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-64"}}
{"id": "dm-probability__swr_p_level_set-hard-64", "pool": "math", "split": "train", "question": "What is prob of picking 3 a and 1 s when four letters picked without replacement from {g: 3, a: 9, s: 2, i: 2}?", "unit": "dimensionless", "value": "0.0923077", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-65"}}
{"id": "dm-probability__swr_p_level_set-hard-65", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 p and 2 x when three letters picked without replacement from {p: 3, x: 15}.", "unit": "dimensionless", "value": "0.386029", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-66"}}
{"id": "dm-probability__swr_p_level_set-hard-66", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 k, 1 o and 1 f when three letters picked without replacement from mfmko.", "unit": "dimensionless", "value": "0.1", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-67"}}
{"id": "dm-probability__swr_p_level_set-hard-67", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {c: 2, f: 1, g: 1, e: 1, u: 2}. Give prob of picking 1 u and 1 f.", "unit": "dimensionless", "value": "0.0952381", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-68"}}
{"id": "dm-probability__swr_p_level_set-hard-68", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 y and 2 s when four letters picked without replacement from kkkysysskrsyyys.", "unit": "dimensionless", "value": "0.0732601", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-69"}}
{"id": "dm-probability__swr_p_level_set-hard-69", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 u when two letters picked without replacement from ktttuut.", "unit": "dimensionless", "value": "0.0476190", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-70"}}
{"id": "dm-probability__swr_p_level_set-hard-70", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {d: 2, p: 1, u: 2, m: 2, x: 1}. Give prob of picking 1 m, 2 d and 1 p.", "unit": "dimensionless", "value": "0.0285714", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-71"}}
{"id": "dm-probability__swr_p_level_set-hard-71", "pool": "math", "split": "train", "question": "Calculate prob of picking 3 e when three letters picked without replacement from eeffweweeee.", "unit": "dimensionless", "value": "0.212121", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-72"}}
{"id": "dm-probability__swr_p_level_set-hard-72", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 t and 2 p when three letters picked without replacement from {t: 2, p: 3}.", "unit": "dimensionless", "value": "0.6", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-73"}}
{"id": "dm-probability__swr_p_level_set-hard-73", "pool": "math", "split": "train", "question": "Three letters picked without replacement from bbvbvbbbvv. What is prob of picking 1 v and 2 b?", "unit": "dimensionless", "value": "0.5", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-74"}}
{"id": "dm-probability__swr_p_level_set-hard-74", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 v and 1 i when two letters picked without replacement from vvnnvninnuviniunnnv.", "unit": "dimensionless", "value": "0.0877193", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-75"}}
{"id": "dm-probability__swr_p_level_set-hard-75", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {v: 2, t: 3, r: 1, b: 1}. What is prob of picking 1 b and 1 t?", "unit": "dimensionless", "value": "0.142857", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-76"}}
{"id": "dm-probability__swr_p_level_set-hard-76", "pool": "math", "split": "train", "question": "Two letters picked without replacement from lohlc. What is prob of picking 1 o and 1 c?", "unit": "dimensionless", "value": "0.1", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-77"}}
{"id": "dm-probability__swr_p_level_set-hard-77", "pool": "math", "split": "train", "question": "What is prob of picking 2 t, 1 r and 1 h when four letters picked without replacement from nnnnfnttnnnttthtnrn?", "unit": "dimensionless", "value": "0.00386997", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-78"}}
{"id": "dm-probability__swr_p_level_set-hard-78", "pool": "math", "split": "train", "question": "What is prob of picking 1 n and 1 a when two letters picked without replacement from vqqqnqqnqqaa?", "unit": "dimensionless", "value": "0.0606061", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-79"}}
{"id": "dm-probability__swr_p_level_set-hard-79", "pool": "math", "split": "train", "question": "What is prob of picking 2 y when two letters picked without replacement from paavyay?", "unit": "dimensionless", "value": "0.0476190", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-80"}}
{"id": "dm-probability__swr_p_level_set-hard-80", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {s: 1, e: 3}. What is prob of picking 2 e?", "unit": "dimensionless", "value": "0.5", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-81"}}
{"id": "dm-probability__swr_p_level_set-hard-81", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {j: 1, m: 1, f: 1, a: 3, e: 2, p: 5}. What is prob of picking 2 a and 1 m?", "unit": "dimensionless", "value": "0.0104895", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-82"}}
{"id": "dm-probability__swr_p_level_set-hard-82", "pool": "math", "split": "train", "question": "What is prob of picking 1 p and 2 j when three letters picked without replacement from jjjpjpjp?", "unit": "dimensionless", "value": "0.535714", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-83"}}
{"id": "dm-probability__swr_p_level_set-hard-83", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {z: 1, j: 4, p: 2}. What is prob of picking 1 p and 1 z?", "unit": "dimensionless", "value": "0.0952381", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-84"}}
{"id": "dm-probability__swr_p_level_set-hard-84", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {v: 1, d: 1, x: 2}. What is prob of picking 1 v and 1 d?", "unit": "dimensionless", "value": "0.166667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-85"}}
{"id": "dm-probability__swr_p_level_set-hard-85", "pool": "math", "split": "train", "question": "Two letters picked without replacement from bwgwgwbwgwwgww. Give prob of picking 2 b.", "unit": "dimensionless", "value": "0.0109890", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-86"}}
{"id": "dm-probability__swr_p_level_set-hard-86", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {s: 3, d: 4, i: 6, f: 1}. Give prob of picking 1 d and 1 f.", "unit": "dimensionless", "value": "0.0439560", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-87"}}
{"id": "dm-probability__swr_p_level_set-hard-87", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {h: 1, g: 1, b: 2, k: 2}. Give prob of picking 2 h.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-88"}}
{"id": "dm-probability__swr_p_level_set-hard-88", "pool": "math", "split": "train", "question": "Two letters picked without replacement from ppcecpc. What is prob of picking 1 c and 1 p?", "unit": "dimensionless", "value": "0.428571", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-89"}}
{"id": "dm-probability__swr_p_level_set-hard-89", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 n, 1 a and 1 f when four letters picked without replacement from afneffonafto.", "unit": "dimensionless", "value": "0.0161616", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-90"}}
{"id": "dm-probability__swr_p_level_set-hard-90", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 d when two letters picked without replacement from yddyyy.", "unit": "dimensionless", "value": "0.0666667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-91"}}
{"id": "dm-probability__swr_p_level_set-hard-91", "pool": "math", "split": "train", "question": "Two letters picked without replacement from rerrrrererrr. What is prob of picking 1 r and 1 e?", "unit": "dimensionless", "value": "0.409091", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-92"}}
{"id": "dm-probability__swr_p_level_set-hard-92", "pool": "math", "split": "train", "question": "What is prob of picking 4 n when four letters picked without replacement from snsngywksgwkynwswns?", "unit": "dimensionless", "value": "0.000257998", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-93"}}
{"id": "dm-probability__swr_p_level_set-hard-93", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 b when two letters picked without replacement from vvvvvbvbbvbb.", "unit": "dimensionless", "value": "0.151515", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-94"}}
{"id": "dm-probability__swr_p_level_set-hard-94", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 m and 2 k when four letters picked without replacement from {k: 11, m: 5}.", "unit": "dimensionless", "value": "0.302198", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-95"}}
{"id": "dm-probability__swr_p_level_set-hard-95", "pool": "math", "split": "train", "question": "What is prob of picking 1 r and 3 m when four letters picked without replacement from rrmmmmmm?", "unit": "dimensionless", "value": "0.571429", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-96"}}
{"id": "dm-probability__swr_p_level_set-hard-96", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {d: 3, x: 2}. Give prob of picking 2 x and 1 d.", "unit": "dimensionless", "value": "0.3", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-97"}}
{"id": "dm-probability__swr_p_level_set-hard-97", "pool": "math", "split": "train", "question": "What is prob of picking 1 c and 1 f when two letters picked without replacement from ufuucoucocxuxu?", "unit": "dimensionless", "value": "0.0329670", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-98"}}
{"id": "dm-probability__swr_p_level_set-hard-98", "pool": "math", "split": "train", "question": "Four letters picked without replacement from cwtwnwnittwswswswc. What is prob of picking 1 w, 1 i and 2 t?", "unit": "dimensionless", "value": "0.00686275", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-99"}}
{"id": "dm-probability__swr_p_level_set-hard-99", "pool": "math", "split": "train", "question": "What is prob of picking 1 c and 1 t when two letters picked without replacement from tttttttttctt?", "unit": "dimensionless", "value": "0.166667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-100"}}
{"id": "dm-probability__swr_p_level_set-hard-100", "pool": "math", "split": "train", "question": "Three letters picked without replacement from paapiaupapppupp. Give prob of picking 1 a and 2 u.", "unit": "dimensionless", "value": "0.00879121", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-101"}}
{"id": "dm-probability__swr_p_level_set-hard-101", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 s when two letters picked without replacement from yyyyyyyssyyyyysyyy.", "unit": "dimensionless", "value": "0.0196078", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-102"}}
{"id": "dm-probability__swr_p_level_set-hard-102", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {u: 2, b: 4}. What is prob of picking 2 b and 2 u?", "unit": "dimensionless", "value": "0.4", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-103"}}
{"id": "dm-probability__swr_p_level_set-hard-103", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {j: 2, g: 1, f: 2, e: 4, l: 1}. What is prob of picking 1 g, 1 f and 1 j?", "unit": "dimensionless", "value": "0.0333333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-104"}}
{"id": "dm-probability__swr_p_level_set-hard-104", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 b and 1 x when two letters picked without replacement from {x: 1, z: 1, b: 1, w: 2}.", "unit": "dimensionless", "value": "0.1", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-105"}}
{"id": "dm-probability__swr_p_level_set-hard-105", "pool": "math", "split": "train", "question": "Two letters picked without replacement from yfhukhe. What is prob of picking 1 k and 1 h?", "unit": "dimensionless", "value": "0.0952381", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-106"}}
{"id": "dm-probability__swr_p_level_set-hard-106", "pool": "math", "split": "train", "question": "Three letters picked without replacement from aammaaaaamaaaa. Give prob of picking 2 a and 1 m.", "unit": "dimensionless", "value": "0.453297", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-107"}}
{"id": "dm-probability__swr_p_level_set-hard-107", "pool": "math", "split": "train", "question": "Two letters picked without replacement from fyooboofoojyoy. Give prob of picking 1 j and 1 b.", "unit": "dimensionless", "value": "0.0109890", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-108"}}
{"id": "dm-probability__swr_p_level_set-hard-108", "pool": "math", "split": "train", "question": "Two letters picked without replacement from wwwwooowwow. What is prob of picking 2 o?", "unit": "dimensionless", "value": "0.109091", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-109"}}
{"id": "dm-probability__swr_p_level_set-hard-109", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 y and 1 o when two letters picked without replacement from {y: 1, c: 1, k: 1, n: 1, o: 1}.", "unit": "dimensionless", "value": "0.1", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-110"}}
{"id": "dm-probability__swr_p_level_set-hard-110", "pool": "math", "split": "train", "question": "What is prob of picking 1 z and 2 r when three letters picked without replacement from ttrltltrtzllzltllztt?", "unit": "dimensionless", "value": "0.00263158", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-111"}}
{"id": "dm-probability__swr_p_level_set-hard-111", "pool": "math", "split": "train", "question": "Two letters picked without replacement from qdabhbahhah. What is prob of picking 1 q and 1 a?", "unit": "dimensionless", "value": "0.0545455", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-112"}}
{"id": "dm-probability__swr_p_level_set-hard-112", "pool": "math", "split": "train", "question": "Three letters picked without replacement from zccuzbuzzcunuzzzbc. Give prob of picking 1 c and 2 u.", "unit": "dimensionless", "value": "0.0294118", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-113"}}
{"id": "dm-probability__swr_p_level_set-hard-113", "pool": "math", "split": "train", "question": "Two letters picked without replacement from babadbdaabbbaabbb. Give prob of picking 2 a.", "unit": "dimensionless", "value": "0.110294", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-114"}}
{"id": "dm-probability__swr_p_level_set-hard-114", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {a: 1, c: 5, k: 14}. Give prob of picking 2 c and 1 a.", "unit": "dimensionless", "value": "0.00877193", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-115"}}
{"id": "dm-probability__swr_p_level_set-hard-115", "pool": "math", "split": "train", "question": "What is prob of picking 4 b when four letters picked without replacement from {b: 4}?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-116"}}
{"id": "dm-probability__swr_p_level_set-hard-116", "pool": "math", "split": "train", "question": "What is prob of picking 2 g and 2 e when four letters picked without replacement from ggzegzgeeggegzggzeg?", "unit": "dimensionless", "value": "0.116099", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-117"}}
{"id": "dm-probability__swr_p_level_set-hard-117", "pool": "math", "split": "train", "question": "Three letters picked without replacement from lltlllllxblallhxhlll. What is prob of picking 2 l and 1 b?", "unit": "dimensionless", "value": "0.0684211", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-118"}}
{"id": "dm-probability__swr_p_level_set-hard-118", "pool": "math", "split": "train", "question": "What is prob of picking 3 n when three letters picked without replacement from {n: 6, z: 12}?", "unit": "dimensionless", "value": "0.0245098", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-119"}}
{"id": "dm-probability__swr_p_level_set-hard-119", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {e: 3, z: 3, s: 6, c: 1}. What is prob of picking 3 z?", "unit": "dimensionless", "value": "0.00349650", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-120"}}
{"id": "dm-probability__swr_p_level_set-hard-120", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {n: 5, p: 7, i: 1, z: 3, c: 3}. Give prob of picking 1 c and 1 i.", "unit": "dimensionless", "value": "0.0175439", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-121"}}
{"id": "dm-probability__swr_p_level_set-hard-121", "pool": "math", "split": "train", "question": "What is prob of picking 2 x and 2 b when four letters picked without replacement from {b: 5, x: 7, e: 2}?", "unit": "dimensionless", "value": "0.209790", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-122"}}
{"id": "dm-probability__swr_p_level_set-hard-122", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {k: 7, o: 4, q: 3}. Give prob of picking 3 k and 1 o.", "unit": "dimensionless", "value": "0.139860", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-123"}}
{"id": "dm-probability__swr_p_level_set-hard-123", "pool": "math", "split": "train", "question": "Three letters picked without replacement from hrhhrhhrhhhhrhhrhhr. What is prob of picking 3 h?", "unit": "dimensionless", "value": "0.295150", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-124"}}
{"id": "dm-probability__swr_p_level_set-hard-124", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {a: 3, v: 3, s: 1, e: 5, g: 7}. Give prob of picking 1 s and 2 g.", "unit": "dimensionless", "value": "0.0216718", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-125"}}
{"id": "dm-probability__swr_p_level_set-hard-125", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {h: 3, m: 1, i: 3, f: 1, c: 2, a: 1}. What is prob of picking 2 h?", "unit": "dimensionless", "value": "0.0545455", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-126"}}
{"id": "dm-probability__swr_p_level_set-hard-126", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 i and 3 l when four letters picked without replacement from {u: 2, i: 3, l: 5}.", "unit": "dimensionless", "value": "0.142857", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-127"}}
{"id": "dm-probability__swr_p_level_set-hard-127", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 j when two letters picked without replacement from kxkxxjjkkkijixij.", "unit": "dimensionless", "value": "0.05", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-128"}}
{"id": "dm-probability__swr_p_level_set-hard-128", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {s: 1, r: 3, m: 3}. What is prob of picking 2 m and 2 r?", "unit": "dimensionless", "value": "0.257143", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-129"}}
{"id": "dm-probability__swr_p_level_set-hard-129", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 x, 1 y and 2 n when four letters picked without replacement from xnyny.", "unit": "dimensionless", "value": "0.4", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-130"}}
{"id": "dm-probability__swr_p_level_set-hard-130", "pool": "math", "split": "train", "question": "What is prob of picking 1 c, 1 p and 1 y when three letters picked without replacement from {c: 5, p: 7, k: 2, y: 4}?", "unit": "dimensionless", "value": "0.171569", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-131"}}
{"id": "dm-probability__swr_p_level_set-hard-131", "pool": "math", "split": "train", "question": "Two letters picked without replacement from meevvttzvkkm. What is prob of picking 1 k and 1 z?", "unit": "dimensionless", "value": "0.0303030", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-132"}}
{"id": "dm-probability__swr_p_level_set-hard-132", "pool": "math", "split": "train", "question": "Two letters picked without replacement from cmeeccmmemccemc. Give prob of picking 2 m.", "unit": "dimensionless", "value": "0.0952381", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-133"}}
{"id": "dm-probability__swr_p_level_set-hard-133", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {w: 1, d: 1, p: 2, q: 1}. Give prob of picking 4 d.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-134"}}
{"id": "dm-probability__swr_p_level_set-hard-134", "pool": "math", "split": "train", "question": "Two letters picked without replacement from ptptccccjctjc. Give prob of picking 2 j.", "unit": "dimensionless", "value": "0.0128205", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-135"}}
{"id": "dm-probability__swr_p_level_set-hard-135", "pool": "math", "split": "train", "question": "Calculate prob of picking 3 u when three letters picked without replacement from uuuuuu.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-136"}}
{"id": "dm-probability__swr_p_level_set-hard-136", "pool": "math", "split": "train", "question": "What is prob of picking 3 q when three letters picked without replacement from {b: 4, k: 1, l: 2, q: 6, n: 7}?", "unit": "dimensionless", "value": "0.0175439", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-137"}}
{"id": "dm-probability__swr_p_level_set-hard-137", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {g: 7, b: 2}. What is prob of picking 1 b and 2 g?", "unit": "dimensionless", "value": "0.5", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-138"}}
{"id": "dm-probability__swr_p_level_set-hard-138", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {h: 2, q: 3, n: 1, v: 1}. Give prob of picking 1 n, 1 h, 1 q and 1 v.", "unit": "dimensionless", "value": "0.171429", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-139"}}
{"id": "dm-probability__swr_p_level_set-hard-139", "pool": "math", "split": "train", "question": "Four letters picked without replacement from tkqkqqtqttqtt. What is prob of picking 2 k, 1 t and 1 q?", "unit": "dimensionless", "value": "0.0419580", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-140"}}
{"id": "dm-probability__swr_p_level_set-hard-140", "pool": "math", "split": "train", "question": "Two letters picked without replacement from twjjjwtjjwjjjjjjj. What is prob of picking 2 j?", "unit": "dimensionless", "value": "0.485294", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-141"}}
{"id": "dm-probability__swr_p_level_set-hard-141", "pool": "math", "split": "train", "question": "Four letters picked without replacement from nhifpnnpifppnninhp. Give prob of picking 4 p.", "unit": "dimensionless", "value": "0.00163399", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-142"}}
{"id": "dm-probability__swr_p_level_set-hard-142", "pool": "math", "split": "train", "question": "What is prob of picking 2 y when two letters picked without replacement from xuuxuuyyu?", "unit": "dimensionless", "value": "0.0277778", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-143"}}
{"id": "dm-probability__swr_p_level_set-hard-143", "pool": "math", "split": "train", "question": "What is prob of picking 1 l and 2 w when three letters picked without replacement from wlwltwzlllrzl?", "unit": "dimensionless", "value": "0.0629371", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-144"}}
{"id": "dm-probability__swr_p_level_set-hard-144", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {q: 1, y: 2, e: 8, c: 5}. What is prob of picking 1 c and 1 y?", "unit": "dimensionless", "value": "0.0833333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-145"}}
{"id": "dm-probability__swr_p_level_set-hard-145", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {r: 7, m: 2}. What is prob of picking 3 r and 1 m?", "unit": "dimensionless", "value": "0.555556", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-146"}}
{"id": "dm-probability__swr_p_level_set-hard-146", "pool": "math", "split": "train", "question": "What is prob of picking 1 g and 1 p when two letters picked without replacement from {p: 1, g: 2, w: 1}?", "unit": "dimensionless", "value": "0.333333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-147"}}
{"id": "dm-probability__swr_p_level_set-hard-147", "pool": "math", "split": "train", "question": "What is prob of picking 1 l and 1 r when two letters picked without replacement from lrllllr?", "unit": "dimensionless", "value": "0.476190", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-148"}}
{"id": "dm-probability__swr_p_level_set-hard-148", "pool": "math", "split": "train", "question": "What is prob of picking 2 k, 1 u and 1 a when four letters picked without replacement from {u: 10, a: 6, k: 4}?", "unit": "dimensionless", "value": "0.0743034", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-149"}}
{"id": "dm-probability__swr_p_level_set-hard-149", "pool": "math", "split": "train", "question": "Two letters picked without replacement from ygppnnhyyyp. What is prob of picking 2 n?", "unit": "dimensionless", "value": "0.0181818", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-150"}}
{"id": "dm-probability__swr_p_level_set-hard-150", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {n: 7, f: 2, b: 3, p: 5, q: 1}. Give prob of picking 1 p and 2 n.", "unit": "dimensionless", "value": "0.128676", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-151"}}
{"id": "dm-probability__swr_p_level_set-hard-151", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {f: 6, j: 2, b: 4}. Give prob of picking 1 b and 1 j.", "unit": "dimensionless", "value": "0.121212", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-152"}}
{"id": "dm-probability__swr_p_level_set-hard-152", "pool": "math", "split": "train", "question": "What is prob of picking 1 y, 1 k and 1 r when three letters picked without replacement from ykglrlg?", "unit": "dimensionless", "value": "0.0285714", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-153"}}
{"id": "dm-probability__swr_p_level_set-hard-153", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {l: 1, e: 1, p: 2, i: 7, r: 2, b: 2}. What is prob of picking 2 b, 1 r and 1 p?", "unit": "dimensionless", "value": "0.00293040", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-154"}}
{"id": "dm-probability__swr_p_level_set-hard-154", "pool": "math", "split": "train", "question": "Three letters picked without replacement from ghhhghgghhhgh. What is prob of picking 3 g?", "unit": "dimensionless", "value": "0.0349650", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-155"}}
{"id": "dm-probability__swr_p_level_set-hard-155", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {p: 1, z: 1, w: 2, c: 4, m: 2}. Give prob of picking 1 z and 1 m.", "unit": "dimensionless", "value": "0.0444444", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-156"}}
{"id": "dm-probability__swr_p_level_set-hard-156", "pool": "math", "split": "train", "question": "What is prob of picking 1 z, 1 e, 1 t and 1 r when four letters picked without replacement from {x: 2, t: 7, r: 1, e: 6, z: 2, l: 1}?", "unit": "dimensionless", "value": "0.0216718", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-157"}}
{"id": "dm-probability__swr_p_level_set-hard-157", "pool": "math", "split": "train", "question": "What is prob of picking 2 w and 1 e when three letters picked without replacement from whchchwwwwcreccheehw?", "unit": "dimensionless", "value": "0.0394737", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-158"}}
{"id": "dm-probability__swr_p_level_set-hard-158", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 r, 1 b, 1 w and 1 k when four letters picked without replacement from bwrbrkrrbrrr.", "unit": "dimensionless", "value": "0.0424242", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-159"}}
{"id": "dm-probability__swr_p_level_set-hard-159", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {w: 5, h: 5, b: 3}. Give prob of picking 1 b and 1 w.", "unit": "dimensionless", "value": "0.192308", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-160"}}
{"id": "dm-probability__swr_p_level_set-hard-160", "pool": "math", "split": "train", "question": "What is prob of picking 1 b and 1 f when two letters picked without replacement from fppfffbffbbbpbbfbb?", "unit": "dimensionless", "value": "0.366013", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-161"}}
{"id": "dm-probability__swr_p_level_set-hard-161", "pool": "math", "split": "train", "question": "What is prob of picking 1 u and 1 q when two letters picked without replacement from {s: 1, z: 2, a: 1, u: 2, q: 1, k: 1}?", "unit": "dimensionless", "value": "0.0714286", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-162"}}
{"id": "dm-probability__swr_p_level_set-hard-162", "pool": "math", "split": "train", "question": "Three letters picked without replacement from sass. Give prob of picking 3 s.", "unit": "dimensionless", "value": "0.25", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-163"}}
{"id": "dm-probability__swr_p_level_set-hard-163", "pool": "math", "split": "train", "question": "Three letters picked without replacement from bonnxnnnoonxbnbnx. Give prob of picking 2 x and 1 n.", "unit": "dimensionless", "value": "0.0352941", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-164"}}
{"id": "dm-probability__swr_p_level_set-hard-164", "pool": "math", "split": "train", "question": "Four letters picked without replacement from hhkshskhsw. What is prob of picking 1 w and 3 s?", "unit": "dimensionless", "value": "0.00476190", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-165"}}
{"id": "dm-probability__swr_p_level_set-hard-165", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 o and 1 u when two letters picked without replacement from {u: 1, m: 1, g: 5, y: 3, o: 1, p: 2}.", "unit": "dimensionless", "value": "0.0128205", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-166"}}
{"id": "dm-probability__swr_p_level_set-hard-166", "pool": "math", "split": "train", "question": "Three letters picked without replacement from ctjcacj. Give prob of picking 2 j and 1 a.", "unit": "dimensionless", "value": "0.0285714", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-167"}}
{"id": "dm-probability__swr_p_level_set-hard-167", "pool": "math", "split": "train", "question": "Calculate prob of picking 3 v and 1 q when four letters picked without replacement from vzvqzzqvnznz.", "unit": "dimensionless", "value": "0.00404040", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-168"}}
{"id": "dm-probability__swr_p_level_set-hard-168", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {e: 2, q: 9, l: 2}. What is prob of picking 3 q?", "unit": "dimensionless", "value": "0.293706", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-169"}}
{"id": "dm-probability__swr_p_level_set-hard-169", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {h: 1, e: 3, i: 11}. Give prob of picking 1 i and 1 e.", "unit": "dimensionless", "value": "0.314286", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-170"}}
{"id": "dm-probability__swr_p_level_set-hard-170", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 c, 1 k and 2 y when four letters picked without replacement from cccckkcyctkkckckqyy.", "unit": "dimensionless", "value": "0.0371517", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-171"}}
{"id": "dm-probability__swr_p_level_set-hard-171", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 v and 1 h when two letters picked without replacement from {b: 1, d: 1, h: 1, v: 2, a: 1, o: 1}.", "unit": "dimensionless", "value": "0.0952381", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-172"}}
{"id": "dm-probability__swr_p_level_set-hard-172", "pool": "math", "split": "train", "question": "What is prob of picking 3 w when three letters picked without replacement from nnvwnqwnnnnnwnvw?", "unit": "dimensionless", "value": "0.00714286", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-173"}}
{"id": "dm-probability__swr_p_level_set-hard-173", "pool": "math", "split": "train", "question": "What is prob of picking 1 e and 1 o when two letters picked without replacement from yyjyyejjogjjgeeeeaye?", "unit": "dimensionless", "value": "0.0315789", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-174"}}
{"id": "dm-probability__swr_p_level_set-hard-174", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 t and 1 l when two letters picked without replacement from {l: 1, t: 1, h: 1, z: 3, q: 2, e: 3}.", "unit": "dimensionless", "value": "0.0181818", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-175"}}
{"id": "dm-probability__swr_p_level_set-hard-175", "pool": "math", "split": "train", "question": "What is prob of picking 3 h when three letters picked without replacement from {h: 15, b: 4}?", "unit": "dimensionless", "value": "0.469556", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-176"}}
{"id": "dm-probability__swr_p_level_set-hard-176", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 t when two letters picked without replacement from vvvtvvvvvvvtvvt.", "unit": "dimensionless", "value": "0.0285714", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-177"}}
{"id": "dm-probability__swr_p_level_set-hard-177", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 s when two letters picked without replacement from ossoopsxxpxooxsppo.", "unit": "dimensionless", "value": "0.0392157", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-178"}}
{"id": "dm-probability__swr_p_level_set-hard-178", "pool": "math", "split": "train", "question": "Three letters picked without replacement from ssssssvsvsssssssvvvs. What is prob of picking 3 v?", "unit": "dimensionless", "value": "0.00877193", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-179"}}
{"id": "dm-probability__swr_p_level_set-hard-179", "pool": "math", "split": "train", "question": "What is prob of picking 2 u when two letters picked without replacement from {y: 2, u: 11}?", "unit": "dimensionless", "value": "0.705128", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-180"}}
{"id": "dm-probability__swr_p_level_set-hard-180", "pool": "math", "split": "train", "question": "What is prob of picking 1 q and 1 b when two letters picked without replacement from sbsqt?", "unit": "dimensionless", "value": "0.1", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-181"}}
{"id": "dm-probability__swr_p_level_set-hard-181", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {c: 1, k: 2, g: 7, l: 2}. What is prob of picking 1 k, 1 c, 1 l and 1 g?", "unit": "dimensionless", "value": "0.0565657", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-182"}}
{"id": "dm-probability__swr_p_level_set-hard-182", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 s, 1 n and 2 r when four letters picked without replacement from srnnnrsrr.", "unit": "dimensionless", "value": "0.285714", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-183"}}
{"id": "dm-probability__swr_p_level_set-hard-183", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {l: 4, y: 12, e: 2, j: 2}. What is prob of picking 1 e and 1 y?", "unit": "dimensionless", "value": "0.126316", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-184"}}
{"id": "dm-probability__swr_p_level_set-hard-184", "pool": "math", "split": "train", "question": "Two letters picked without replacement from ngobgngnnng. Give prob of picking 1 g and 1 b.", "unit": "dimensionless", "value": "0.0727273", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-185"}}
{"id": "dm-probability__swr_p_level_set-hard-185", "pool": "math", "split": "train", "question": "What is prob of picking 1 q and 1 e when two letters picked without replacement from equuwwewequuueuqe?", "unit": "dimensionless", "value": "0.110294", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-186"}}
{"id": "dm-probability__swr_p_level_set-hard-186", "pool": "math", "split": "train", "question": "Two letters picked without replacement from paiaiaiviian. Give prob of picking 1 a and 1 p.", "unit": "dimensionless", "value": "0.0606061", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-187"}}
{"id": "dm-probability__swr_p_level_set-hard-187", "pool": "math", "split": "train", "question": "Two letters picked without replacement from snsssnbsnsbnsbss. What is prob of picking 2 s?", "unit": "dimensionless", "value": "0.3", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-188"}}
{"id": "dm-probability__swr_p_level_set-hard-188", "pool": "math", "split": "train", "question": "Two letters picked without replacement from wnnwmtwwwwmzmhz. Give prob of picking 1 w and 1 m.", "unit": "dimensionless", "value": "0.171429", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-189"}}
{"id": "dm-probability__swr_p_level_set-hard-189", "pool": "math", "split": "train", "question": "Four letters picked without replacement from llummmimuuuicm. Give prob of picking 1 c, 1 u, 1 m and 1 l.", "unit": "dimensionless", "value": "0.0399600", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-190"}}
{"id": "dm-probability__swr_p_level_set-hard-190", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {t: 3, s: 5}. Give prob of picking 2 t.", "unit": "dimensionless", "value": "0.107143", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-191"}}
{"id": "dm-probability__swr_p_level_set-hard-191", "pool": "math", "split": "train", "question": "Four letters picked without replacement from gogddgggvddgddg. What is prob of picking 3 d and 1 o?", "unit": "dimensionless", "value": "0.0146520", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-192"}}
{"id": "dm-probability__swr_p_level_set-hard-192", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {n: 16, e: 4}. What is prob of picking 2 e?", "unit": "dimensionless", "value": "0.0315789", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-193"}}
{"id": "dm-probability__swr_p_level_set-hard-193", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 p and 1 t when two letters picked without replacement from ztpzttipyztytpcyz.", "unit": "dimensionless", "value": "0.110294", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-194"}}
{"id": "dm-probability__swr_p_level_set-hard-194", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {w: 2, c: 5, y: 6, o: 1, r: 3, l: 3}. Give prob of picking 2 l and 1 o.", "unit": "dimensionless", "value": "0.00263158", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-195"}}
{"id": "dm-probability__swr_p_level_set-hard-195", "pool": "math", "split": "train", "question": "What is prob of picking 2 u when two letters picked without replacement from {u: 2, n: 1}?", "unit": "dimensionless", "value": "0.333333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-196"}}
{"id": "dm-probability__swr_p_level_set-hard-196", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {m: 3, i: 2, f: 4, x: 4, v: 1, a: 1}. Give prob of picking 1 i and 1 x.", "unit": "dimensionless", "value": "0.0761905", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-197"}}
{"id": "dm-probability__swr_p_level_set-hard-197", "pool": "math", "split": "train", "question": "What is prob of picking 2 w when two letters picked without replacement from uruwwwwruuwwuuu?", "unit": "dimensionless", "value": "0.142857", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-198"}}
{"id": "dm-probability__swr_p_level_set-hard-198", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 o when two letters picked without replacement from {p: 1, o: 2}.", "unit": "dimensionless", "value": "0.333333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-199"}}
{"id": "dm-probability__swr_p_level_set-hard-199", "pool": "math", "split": "train", "question": "What is prob of picking 2 x when two letters picked without replacement from tttxxx?", "unit": "dimensionless", "value": "0.2", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-200"}}
{"id": "dm-probability__swr_p_level_set-hard-200", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 i and 2 s when four letters picked without replacement from issssssssis.", "unit": "dimensionless", "value": "0.109091", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-201"}}
{"id": "dm-probability__swr_p_level_set-hard-201", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {i: 5, f: 5, b: 1}. What is prob of picking 2 f and 2 i?", "unit": "dimensionless", "value": "0.303030", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-202"}}
{"id": "dm-probability__swr_p_level_set-hard-202", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {f: 18, i: 1}. Give prob of picking 1 i and 1 f.", "unit": "dimensionless", "value": "0.105263", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-203"}}
{"id": "dm-probability__swr_p_level_set-hard-203", "pool": "math", "split": "train", "question": "Two letters picked without replacement from liilili. What is prob of picking 2 i?", "unit": "dimensionless", "value": "0.285714", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-204"}}
{"id": "dm-probability__swr_p_level_set-hard-204", "pool": "math", "split": "train", "question": "Calculate prob of picking 3 e and 1 a when four letters picked without replacement from {a: 1, e: 7, d: 2, z: 6, f: 4}.", "unit": "dimensionless", "value": "0.00722394", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-205"}}
{"id": "dm-probability__swr_p_level_set-hard-205", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 e and 1 q when two letters picked without replacement from {p: 1, g: 1, q: 5, f: 3, e: 4}.", "unit": "dimensionless", "value": "0.219780", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-206"}}
{"id": "dm-probability__swr_p_level_set-hard-206", "pool": "math", "split": "train", "question": "What is prob of picking 2 e when two letters picked without replacement from yjjjjejjenjjjyej?", "unit": "dimensionless", "value": "0.025", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-207"}}
{"id": "dm-probability__swr_p_level_set-hard-207", "pool": "math", "split": "train", "question": "What is prob of picking 1 y and 1 z when two letters picked without replacement from {x: 3, y: 4, z: 4, r: 8}?", "unit": "dimensionless", "value": "0.0935673", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-208"}}
{"id": "dm-probability__swr_p_level_set-hard-208", "pool": "math", "split": "train", "question": "Two letters picked without replacement from ccuuuuuuuucuuuucuucu. What is prob of picking 2 u?", "unit": "dimensionless", "value": "0.552632", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-209"}}
{"id": "dm-probability__swr_p_level_set-hard-209", "pool": "math", "split": "train", "question": "What is prob of picking 4 y when four letters picked without replacement from byybbbbbybbhyh?", "unit": "dimensionless", "value": "0.000999001", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-210"}}
{"id": "dm-probability__swr_p_level_set-hard-210", "pool": "math", "split": "train", "question": "Calculate prob of picking 3 r when three letters picked without replacement from {z: 4, r: 3}.", "unit": "dimensionless", "value": "0.0285714", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-211"}}
{"id": "dm-probability__swr_p_level_set-hard-211", "pool": "math", "split": "train", "question": "Three letters picked without replacement from zymziimymmzmzniyyyzz. What is prob of picking 3 i?", "unit": "dimensionless", "value": "0.000877193", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-212"}}
{"id": "dm-probability__swr_p_level_set-hard-212", "pool": "math", "split": "train", "question": "What is prob of picking 2 a when two letters picked without replacement from aajp?", "unit": "dimensionless", "value": "0.166667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-213"}}
{"id": "dm-probability__swr_p_level_set-hard-213", "pool": "math", "split": "train", "question": "Three letters picked without replacement from aabbaba. Give prob of picking 2 a and 1 b.", "unit": "dimensionless", "value": "0.514286", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-214"}}
{"id": "dm-probability__swr_p_level_set-hard-214", "pool": "math", "split": "train", "question": "What is prob of picking 1 i and 1 q when two letters picked without replacement from {p: 2, m: 1, o: 1, q: 1, i: 2}?", "unit": "dimensionless", "value": "0.0952381", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-215"}}
{"id": "dm-probability__swr_p_level_set-hard-215", "pool": "math", "split": "train", "question": "What is prob of picking 1 h and 1 t when two letters picked without replacement from {i: 1, y: 1, s: 2, h: 5, t: 9}?", "unit": "dimensionless", "value": "0.294118", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-216"}}
{"id": "dm-probability__swr_p_level_set-hard-216", "pool": "math", "split": "train", "question": "What is prob of picking 1 h and 1 t when two letters picked without replacement from {t: 2, h: 11}?", "unit": "dimensionless", "value": "0.282051", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-217"}}
{"id": "dm-probability__swr_p_level_set-hard-217", "pool": "math", "split": "train", "question": "What is prob of picking 2 q and 2 d when four letters picked without replacement from {q: 9, d: 10}?", "unit": "dimensionless", "value": "0.417957", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-218"}}
{"id": "dm-probability__swr_p_level_set-hard-218", "pool": "math", "split": "train", "question": "What is prob of picking 1 d, 1 j and 2 q when four letters picked without replacement from {j: 2, d: 5, q: 5}?", "unit": "dimensionless", "value": "0.202020", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-219"}}
{"id": "dm-probability__swr_p_level_set-hard-219", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {s: 3, x: 2, q: 1, d: 6}. Give prob of picking 2 d.", "unit": "dimensionless", "value": "0.227273", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-220"}}
{"id": "dm-probability__swr_p_level_set-hard-220", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {m: 1, q: 14}. What is prob of picking 2 q and 1 m?", "unit": "dimensionless", "value": "0.2", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-221"}}
{"id": "dm-probability__swr_p_level_set-hard-221", "pool": "math", "split": "train", "question": "What is prob of picking 1 c and 1 d when two letters picked without replacement from {c: 3, v: 1, i: 1, d: 4, u: 3, b: 3}?", "unit": "dimensionless", "value": "0.114286", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-222"}}
{"id": "dm-probability__swr_p_level_set-hard-222", "pool": "math", "split": "train", "question": "Four letters picked without replacement from vvbvfvvdvvvvvvv. Give prob of picking 2 v and 2 b.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-223"}}
{"id": "dm-probability__swr_p_level_set-hard-223", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {y: 2, a: 7}. What is prob of picking 2 y and 1 a?", "unit": "dimensionless", "value": "0.0833333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-224"}}
{"id": "dm-probability__swr_p_level_set-hard-224", "pool": "math", "split": "train", "question": "What is prob of picking 2 u and 1 f when three letters picked without replacement from fffufhthuffsss?", "unit": "dimensionless", "value": "0.0164835", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-225"}}
{"id": "dm-probability__swr_p_level_set-hard-225", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {f: 5, d: 2, w: 7, a: 1, i: 3}. Give prob of picking 2 w and 1 f.", "unit": "dimensionless", "value": "0.128676", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-226"}}
{"id": "dm-probability__swr_p_level_set-hard-226", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 w and 3 m when four letters picked without replacement from {m: 5, w: 7}.", "unit": "dimensionless", "value": "0.141414", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-227"}}
{"id": "dm-probability__swr_p_level_set-hard-227", "pool": "math", "split": "train", "question": "Two letters picked without replacement from mfmpmoppcc. What is prob of picking 1 c and 1 p?", "unit": "dimensionless", "value": "0.133333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-228"}}
{"id": "dm-probability__swr_p_level_set-hard-228", "pool": "math", "split": "train", "question": "What is prob of picking 2 v and 2 a when four letters picked without replacement from {a: 3, v: 5}?", "unit": "dimensionless", "value": "0.428571", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-229"}}
{"id": "dm-probability__swr_p_level_set-hard-229", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 s and 3 v when four letters picked without replacement from kvguvgvgvtguvgsktug.", "unit": "dimensionless", "value": "0.00257998", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-230"}}
{"id": "dm-probability__swr_p_level_set-hard-230", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {f: 4, q: 3, h: 1}. Give prob of picking 4 f.", "unit": "dimensionless", "value": "0.0142857", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-231"}}
{"id": "dm-probability__swr_p_level_set-hard-231", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {m: 1, c: 2, t: 3, j: 4, h: 3, y: 2}. Give prob of picking 1 c and 1 t.", "unit": "dimensionless", "value": "0.0571429", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-232"}}
{"id": "dm-probability__swr_p_level_set-hard-232", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 o when two letters picked without replacement from ooooooooo.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-233"}}
{"id": "dm-probability__swr_p_level_set-hard-233", "pool": "math", "split": "train", "question": "What is prob of picking 3 m when three letters picked without replacement from qjjmjjcmcm?", "unit": "dimensionless", "value": "0.00833333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-234"}}
{"id": "dm-probability__swr_p_level_set-hard-234", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {n: 8, m: 2}. Give prob of picking 2 n.", "unit": "dimensionless", "value": "0.622222", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-235"}}
{"id": "dm-probability__swr_p_level_set-hard-235", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {n: 5, m: 14}. Give prob of picking 3 n and 1 m.", "unit": "dimensionless", "value": "0.0361197", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-236"}}
{"id": "dm-probability__swr_p_level_set-hard-236", "pool": "math", "split": "train", "question": "What is prob of picking 1 s and 3 f when four letters picked without replacement from kforrfwffofrsso?", "unit": "dimensionless", "value": "0.0146520", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-237"}}
{"id": "dm-probability__swr_p_level_set-hard-237", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {j: 4, x: 3}. Give prob of picking 4 j.", "unit": "dimensionless", "value": "0.0285714", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-238"}}
{"id": "dm-probability__swr_p_level_set-hard-238", "pool": "math", "split": "train", "question": "What is prob of picking 3 w when three letters picked without replacement from wwwxxxxwwwwx?", "unit": "dimensionless", "value": "0.159091", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-239"}}
{"id": "dm-probability__swr_p_level_set-hard-239", "pool": "math", "split": "train", "question": "What is prob of picking 2 i and 2 v when four letters picked without replacement from {i: 3, n: 6, v: 2, k: 4}?", "unit": "dimensionless", "value": "0.00219780", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-240"}}
{"id": "dm-probability__swr_p_level_set-hard-240", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {g: 1, y: 2, j: 4, r: 5, x: 2}. What is prob of picking 1 y and 2 j?", "unit": "dimensionless", "value": "0.0329670", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-241"}}
{"id": "dm-probability__swr_p_level_set-hard-241", "pool": "math", "split": "train", "question": "Four letters picked without replacement from nnnnncjannnnnncxaxnn. Give prob of picking 1 j, 2 c and 1 x.", "unit": "dimensionless", "value": "0.000412797", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-242"}}
{"id": "dm-probability__swr_p_level_set-hard-242", "pool": "math", "split": "train", "question": "Two letters picked without replacement from gwqqpprrrrgq. Give prob of picking 1 p and 1 q.", "unit": "dimensionless", "value": "0.0909091", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-243"}}
{"id": "dm-probability__swr_p_level_set-hard-243", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {w: 5, s: 5, c: 1}. What is prob of picking 1 w and 1 c?", "unit": "dimensionless", "value": "0.0909091", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-244"}}
{"id": "dm-probability__swr_p_level_set-hard-244", "pool": "math", "split": "train", "question": "What is prob of picking 1 x and 1 e when two letters picked without replacement from {k: 1, x: 1, v: 2, m: 2, e: 1}?", "unit": "dimensionless", "value": "0.0476190", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-245"}}
{"id": "dm-probability__swr_p_level_set-hard-245", "pool": "math", "split": "train", "question": "Four letters picked without replacement from llwwtlhlhlwqltlwlll. Give prob of picking 2 h, 1 w and 1 q.", "unit": "dimensionless", "value": "0.00103199", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-246"}}
{"id": "dm-probability__swr_p_level_set-hard-246", "pool": "math", "split": "train", "question": "What is prob of picking 1 g, 2 q and 1 n when four letters picked without replacement from {g: 2, q: 4, n: 6}?", "unit": "dimensionless", "value": "0.145455", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-247"}}
{"id": "dm-probability__swr_p_level_set-hard-247", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {f: 1, a: 1, o: 8, l: 1, s: 1, h: 2}. What is prob of picking 1 l, 1 h and 1 a?", "unit": "dimensionless", "value": "0.00549451", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-248"}}
{"id": "dm-probability__swr_p_level_set-hard-248", "pool": "math", "split": "train", "question": "Calculate prob of picking 3 f and 1 q when four letters picked without replacement from {c: 2, o: 11, f: 3, q: 3}.", "unit": "dimensionless", "value": "0.000773994", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-249"}}
{"id": "dm-probability__swr_p_level_set-hard-249", "pool": "math", "split": "train", "question": "What is prob of picking 1 a and 1 j when two letters picked without replacement from {j: 1, t: 2, h: 3, p: 3, a: 1, u: 1}?", "unit": "dimensionless", "value": "0.0181818", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-250"}}
{"id": "dm-probability__swr_p_level_set-hard-250", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {y: 4, g: 2, k: 2}. What is prob of picking 1 g, 1 y and 2 k?", "unit": "dimensionless", "value": "0.114286", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-251"}}
{"id": "dm-probability__swr_p_level_set-hard-251", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {q: 1, b: 4, x: 3, f: 3}. Give prob of picking 3 b.", "unit": "dimensionless", "value": "0.0242424", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-252"}}
{"id": "dm-probability__swr_p_level_set-hard-252", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 w, 1 x and 1 t when three letters picked without replacement from {x: 1, w: 1, j: 1, d: 1, t: 1}.", "unit": "dimensionless", "value": "0.1", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-253"}}
{"id": "dm-probability__swr_p_level_set-hard-253", "pool": "math", "split": "train", "question": "What is prob of picking 1 w and 1 e when two letters picked without replacement from cywyyywyyyhhywyyeyye?", "unit": "dimensionless", "value": "0.0315789", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-254"}}
{"id": "dm-probability__swr_p_level_set-hard-254", "pool": "math", "split": "train", "question": "What is prob of picking 1 t and 2 a when three letters picked without replacement from {l: 1, a: 13, t: 3}?", "unit": "dimensionless", "value": "0.344118", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-255"}}
{"id": "dm-probability__swr_p_level_set-hard-255", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {t: 4, s: 4, x: 4, w: 3, v: 4}. What is prob of picking 2 t and 2 w?", "unit": "dimensionless", "value": "0.00464396", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-256"}}
{"id": "dm-probability__swr_p_level_set-hard-256", "pool": "math", "split": "train", "question": "What is prob of picking 3 h and 1 e when four letters picked without replacement from {e: 15, h: 5}?", "unit": "dimensionless", "value": "0.0309598", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-257"}}
{"id": "dm-probability__swr_p_level_set-hard-257", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {o: 3, b: 6, t: 1, e: 3}. Give prob of picking 1 o, 2 e and 1 t.", "unit": "dimensionless", "value": "0.0125874", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-258"}}
{"id": "dm-probability__swr_p_level_set-hard-258", "pool": "math", "split": "train", "question": "Four letters picked without replacement from cdcvudmcvdumvucv. Give prob of picking 2 v, 1 c and 1 d.", "unit": "dimensionless", "value": "0.0395604", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-259"}}
{"id": "dm-probability__swr_p_level_set-hard-259", "pool": "math", "split": "train", "question": "Two letters picked without replacement from srqsmrss. What is prob of picking 2 s?", "unit": "dimensionless", "value": "0.214286", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-260"}}
{"id": "dm-probability__swr_p_level_set-hard-260", "pool": "math", "split": "train", "question": "Four letters picked without replacement from osstjjyoojytooooopsj. What is prob of picking 1 p and 3 o?", "unit": "dimensionless", "value": "0.0115583", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-261"}}
{"id": "dm-probability__swr_p_level_set-hard-261", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {v: 6, i: 2, j: 2, h: 9}. What is prob of picking 2 j and 1 i?", "unit": "dimensionless", "value": "0.00206398", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-262"}}
{"id": "dm-probability__swr_p_level_set-hard-262", "pool": "math", "split": "train", "question": "Three letters picked without replacement from ffffoffodfoflff. What is prob of picking 2 f and 1 d?", "unit": "dimensionless", "value": "0.0989011", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-263"}}
{"id": "dm-probability__swr_p_level_set-hard-263", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 h and 2 n when three letters picked without replacement from {x: 2, h: 4, n: 5}.", "unit": "dimensionless", "value": "0.242424", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-264"}}
{"id": "dm-probability__swr_p_level_set-hard-264", "pool": "math", "split": "train", "question": "Two letters picked without replacement from nhvsnnh. Give prob of picking 1 v and 1 h.", "unit": "dimensionless", "value": "0.0952381", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-265"}}
{"id": "dm-probability__swr_p_level_set-hard-265", "pool": "math", "split": "train", "question": "Three letters picked without replacement from cszpr. Give prob of picking 1 s, 1 c and 1 p.", "unit": "dimensionless", "value": "0.1", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-266"}}
{"id": "dm-probability__swr_p_level_set-hard-266", "pool": "math", "split": "train", "question": "What is prob of picking 2 f and 1 u when three letters picked without replacement from mujuujffu?", "unit": "dimensionless", "value": "0.0476190", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-267"}}
{"id": "dm-probability__swr_p_level_set-hard-267", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 c when two letters picked without replacement from {w: 2, c: 6, s: 3, m: 2}.", "unit": "dimensionless", "value": "0.192308", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-268"}}
{"id": "dm-probability__swr_p_level_set-hard-268", "pool": "math", "split": "train", "question": "Three letters picked without replacement from xxxdxxdxxxd. Give prob of picking 3 x.", "unit": "dimensionless", "value": "0.339394", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-269"}}
{"id": "dm-probability__swr_p_level_set-hard-269", "pool": "math", "split": "train", "question": "Two letters picked without replacement from tdaddtadtadadaddt. Give prob of picking 2 d.", "unit": "dimensionless", "value": "0.205882", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-270"}}
{"id": "dm-probability__swr_p_level_set-hard-270", "pool": "math", "split": "train", "question": "What is prob of picking 1 e and 2 a when three letters picked without replacement from {i: 5, e: 4, a: 1, p: 6, l: 4}?", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-271"}}
{"id": "dm-probability__swr_p_level_set-hard-271", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 v and 1 i when two letters picked without replacement from {y: 1, b: 2, v: 6, i: 2}.", "unit": "dimensionless", "value": "0.218182", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-272"}}
{"id": "dm-probability__swr_p_level_set-hard-272", "pool": "math", "split": "train", "question": "What is prob of picking 2 y and 1 d when three letters picked without replacement from ddynynndnd?", "unit": "dimensionless", "value": "0.0333333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-273"}}
{"id": "dm-probability__swr_p_level_set-hard-273", "pool": "math", "split": "train", "question": "Two letters picked without replacement from zwwwwzzwwzwzzzwzzwzh. Give prob of picking 2 w.", "unit": "dimensionless", "value": "0.189474", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-274"}}
{"id": "dm-probability__swr_p_level_set-hard-274", "pool": "math", "split": "train", "question": "What is prob of picking 2 y and 1 w when three letters picked without replacement from dnydwydwdvyvyky?", "unit": "dimensionless", "value": "0.0439560", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-275"}}
{"id": "dm-probability__swr_p_level_set-hard-275", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {v: 3, p: 13}. What is prob of picking 1 v and 2 p?", "unit": "dimensionless", "value": "0.417857", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-276"}}
{"id": "dm-probability__swr_p_level_set-hard-276", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 f and 1 g when three letters picked without replacement from {g: 1, d: 1, f: 2, l: 2}.", "unit": "dimensionless", "value": "0.05", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-277"}}
{"id": "dm-probability__swr_p_level_set-hard-277", "pool": "math", "split": "train", "question": "What is prob of picking 1 c and 3 i when four letters picked without replacement from {c: 2, i: 7, k: 2}?", "unit": "dimensionless", "value": "0.212121", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-278"}}
{"id": "dm-probability__swr_p_level_set-hard-278", "pool": "math", "split": "train", "question": "Calculate prob of picking 3 i when three letters picked without replacement from {k: 10, i: 2}.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-279"}}
{"id": "dm-probability__swr_p_level_set-hard-279", "pool": "math", "split": "train", "question": "Two letters picked without replacement from hddhhdhhdddd. What is prob of picking 2 d?", "unit": "dimensionless", "value": "0.318182", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-280"}}
{"id": "dm-probability__swr_p_level_set-hard-280", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 e and 2 s when four letters picked without replacement from {e: 16, s: 2}.", "unit": "dimensionless", "value": "0.0392157", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-281"}}
{"id": "dm-probability__swr_p_level_set-hard-281", "pool": "math", "split": "train", "question": "Four letters picked without replacement from rrrkrqkqqhmkjmj. Give prob of picking 4 r.", "unit": "dimensionless", "value": "0.000732601", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-282"}}
{"id": "dm-probability__swr_p_level_set-hard-282", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {k: 7, y: 3}. What is prob of picking 2 y?", "unit": "dimensionless", "value": "0.0666667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-283"}}
{"id": "dm-probability__swr_p_level_set-hard-283", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {d: 1, r: 4, f: 1, b: 1, z: 4}. What is prob of picking 2 z?", "unit": "dimensionless", "value": "0.109091", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-284"}}
{"id": "dm-probability__swr_p_level_set-hard-284", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {u: 1, s: 1, p: 2, q: 5, z: 1}. What is prob of picking 1 z and 1 s?", "unit": "dimensionless", "value": "0.0222222", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-285"}}
{"id": "dm-probability__swr_p_level_set-hard-285", "pool": "math", "split": "train", "question": "Two letters picked without replacement from sjsssjsssssssisss. What is prob of picking 2 j?", "unit": "dimensionless", "value": "0.00735294", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-286"}}
{"id": "dm-probability__swr_p_level_set-hard-286", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {s: 5, u: 8, e: 5}. Give prob of picking 2 e.", "unit": "dimensionless", "value": "0.0653595", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-287"}}
{"id": "dm-probability__swr_p_level_set-hard-287", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 l, 1 w and 2 h when four letters picked without replacement from wlttrrhhzrtt.", "unit": "dimensionless", "value": "0.00202020", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-288"}}
{"id": "dm-probability__swr_p_level_set-hard-288", "pool": "math", "split": "train", "question": "Four letters picked without replacement from xxxxsxwwxxwwx. Give prob of picking 1 w and 3 x.", "unit": "dimensionless", "value": "0.313287", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-289"}}
{"id": "dm-probability__swr_p_level_set-hard-289", "pool": "math", "split": "train", "question": "What is prob of picking 1 s and 1 o when two letters picked without replacement from zozszdd?", "unit": "dimensionless", "value": "0.0476190", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-290"}}
{"id": "dm-probability__swr_p_level_set-hard-290", "pool": "math", "split": "train", "question": "Calculate prob of picking 3 f when three letters picked without replacement from {i: 4, f: 7}.", "unit": "dimensionless", "value": "0.212121", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-291"}}
{"id": "dm-probability__swr_p_level_set-hard-291", "pool": "math", "split": "train", "question": "Three letters picked without replacement from vvvxyxdvxdsdv. What is prob of picking 2 v and 1 x?", "unit": "dimensionless", "value": "0.104895", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-292"}}
{"id": "dm-probability__swr_p_level_set-hard-292", "pool": "math", "split": "train", "question": "Calculate prob of picking 3 s when three letters picked without replacement from {v: 6, w: 7, s: 4}.", "unit": "dimensionless", "value": "0.00588235", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-293"}}
{"id": "dm-probability__swr_p_level_set-hard-293", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {f: 6, g: 1, x: 10}. What is prob of picking 1 g and 3 f?", "unit": "dimensionless", "value": "0.00840336", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-294"}}
{"id": "dm-probability__swr_p_level_set-hard-294", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {v: 5}. Give prob of picking 2 v.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-295"}}
{"id": "dm-probability__swr_p_level_set-hard-295", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {z: 4, e: 7}. What is prob of picking 2 e?", "unit": "dimensionless", "value": "0.381818", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-296"}}
{"id": "dm-probability__swr_p_level_set-hard-296", "pool": "math", "split": "train", "question": "Three letters picked without replacement from uxxuxu. Give prob of picking 3 x.", "unit": "dimensionless", "value": "0.05", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-297"}}
{"id": "dm-probability__swr_p_level_set-hard-297", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {u: 13, z: 5}. What is prob of picking 3 z and 1 u?", "unit": "dimensionless", "value": "0.0424837", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-298"}}
{"id": "dm-probability__swr_p_level_set-hard-298", "pool": "math", "split": "train", "question": "What is prob of picking 1 m and 1 t when two letters picked without replacement from {t: 3, m: 9}?", "unit": "dimensionless", "value": "0.409091", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-299"}}
{"id": "dm-probability__swr_p_level_set-hard-299", "pool": "math", "split": "train", "question": "Three letters picked without replacement from ubbbgbbuggbgg. What is prob of picking 1 g, 1 u and 1 b?", "unit": "dimensionless", "value": "0.209790", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-300"}}
{"id": "dm-probability__swr_p_level_set-hard-300", "pool": "math", "split": "train", "question": "What is prob of picking 2 e when two letters picked without replacement from {g: 1, h: 3, q: 4, v: 6, e: 1}?", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-301"}}
{"id": "dm-probability__swr_p_level_set-hard-301", "pool": "math", "split": "train", "question": "Two letters picked without replacement from qxzxlzjs. What is prob of picking 1 j and 1 z?", "unit": "dimensionless", "value": "0.0714286", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-302"}}
{"id": "dm-probability__swr_p_level_set-hard-302", "pool": "math", "split": "train", "question": "Two letters picked without replacement from uaauaauuaaau. Give prob of picking 2 a.", "unit": "dimensionless", "value": "0.318182", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-303"}}
{"id": "dm-probability__swr_p_level_set-hard-303", "pool": "math", "split": "train", "question": "What is prob of picking 1 y and 1 i when two letters picked without replacement from iny?", "unit": "dimensionless", "value": "0.333333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-304"}}
{"id": "dm-probability__swr_p_level_set-hard-304", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {k: 4, i: 3, g: 3, d: 3, o: 5}. Give prob of picking 1 i, 1 d and 1 o.", "unit": "dimensionless", "value": "0.0551471", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-305"}}
{"id": "dm-probability__swr_p_level_set-hard-305", "pool": "math", "split": "train", "question": "Four letters picked without replacement from wmwmwwwwwwm. Give prob of picking 3 m and 1 w.", "unit": "dimensionless", "value": "0.0242424", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-306"}}
{"id": "dm-probability__swr_p_level_set-hard-306", "pool": "math", "split": "train", "question": "What is prob of picking 2 k when two letters picked without replacement from bkksbbsukb?", "unit": "dimensionless", "value": "0.0666667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-307"}}
{"id": "dm-probability__swr_p_level_set-hard-307", "pool": "math", "split": "train", "question": "Three letters picked without replacement from kkbbxbxbkfkbjbjkbj. What is prob of picking 1 b and 2 k?", "unit": "dimensionless", "value": "0.0857843", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-308"}}
{"id": "dm-probability__swr_p_level_set-hard-308", "pool": "math", "split": "train", "question": "Four letters picked without replacement from rhqzh. Give prob of picking 1 r, 1 q and 2 h.", "unit": "dimensionless", "value": "0.2", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-309"}}
{"id": "dm-probability__swr_p_level_set-hard-309", "pool": "math", "split": "train", "question": "Three letters picked without replacement from cwcwww. Give prob of picking 1 c and 2 w.", "unit": "dimensionless", "value": "0.6", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-310"}}
{"id": "dm-probability__swr_p_level_set-hard-310", "pool": "math", "split": "train", "question": "Three letters picked without replacement from bbqbbqb. Give prob of picking 2 q and 1 b.", "unit": "dimensionless", "value": "0.142857", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-311"}}
{"id": "dm-probability__swr_p_level_set-hard-311", "pool": "math", "split": "train", "question": "What is prob of picking 2 v and 1 k when three letters picked without replacement from vvvvhhhvhkkhk?", "unit": "dimensionless", "value": "0.104895", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-312"}}
{"id": "dm-probability__swr_p_level_set-hard-312", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 d and 1 u when two letters picked without replacement from {u: 1, d: 2, b: 1}.", "unit": "dimensionless", "value": "0.333333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-313"}}
{"id": "dm-probability__swr_p_level_set-hard-313", "pool": "math", "split": "train", "question": "Four letters picked without replacement from gggghhgghgg. Give prob of picking 3 g and 1 h.", "unit": "dimensionless", "value": "0.509091", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-314"}}
{"id": "dm-probability__swr_p_level_set-hard-314", "pool": "math", "split": "train", "question": "What is prob of picking 1 d and 1 z when two letters picked without replacement from {d: 7, z: 9}?", "unit": "dimensionless", "value": "0.525", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-315"}}
{"id": "dm-probability__swr_p_level_set-hard-315", "pool": "math", "split": "train", "question": "What is prob of picking 1 i, 1 f and 2 n when four letters picked without replacement from {n: 3, i: 4, f: 2}?", "unit": "dimensionless", "value": "0.190476", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-316"}}
{"id": "dm-probability__swr_p_level_set-hard-316", "pool": "math", "split": "train", "question": "What is prob of picking 1 k and 1 n when two letters picked without replacement from kknkknkn?", "unit": "dimensionless", "value": "0.535714", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-317"}}
{"id": "dm-probability__swr_p_level_set-hard-317", "pool": "math", "split": "train", "question": "Two letters picked without replacement from ttttjtrrj. Give prob of picking 2 r.", "unit": "dimensionless", "value": "0.0277778", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-318"}}
{"id": "dm-probability__swr_p_level_set-hard-318", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {l: 3, a: 6, s: 7, c: 2, f: 1}. Give prob of picking 1 s and 1 c.", "unit": "dimensionless", "value": "0.0818713", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-319"}}
{"id": "dm-probability__swr_p_level_set-hard-319", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 w and 1 j when two letters picked without replacement from wjw.", "unit": "dimensionless", "value": "0.666667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-320"}}
{"id": "dm-probability__swr_p_level_set-hard-320", "pool": "math", "split": "train", "question": "What is prob of picking 3 z when three letters picked without replacement from {z: 4}?", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-321"}}
{"id": "dm-probability__swr_p_level_set-hard-321", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 q and 1 d when two letters picked without replacement from {d: 1, t: 1, f: 1, q: 2}.", "unit": "dimensionless", "value": "0.2", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-322"}}
{"id": "dm-probability__swr_p_level_set-hard-322", "pool": "math", "split": "train", "question": "Three letters picked without replacement from lllmmllll. What is prob of picking 1 l and 2 m?", "unit": "dimensionless", "value": "0.0833333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-323"}}
{"id": "dm-probability__swr_p_level_set-hard-323", "pool": "math", "split": "train", "question": "What is prob of picking 1 b and 1 i when two letters picked without replacement from {h: 2, i: 1, s: 1, l: 1, q: 1, b: 1}?", "unit": "dimensionless", "value": "0.0476190", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-324"}}
{"id": "dm-probability__swr_p_level_set-hard-324", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {n: 2, s: 2, u: 1, e: 8}. Give prob of picking 2 n.", "unit": "dimensionless", "value": "0.0128205", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-325"}}
{"id": "dm-probability__swr_p_level_set-hard-325", "pool": "math", "split": "train", "question": "What is prob of picking 1 d, 1 m, 1 t and 1 y when four letters picked without replacement from gydmytdt?", "unit": "dimensionless", "value": "0.114286", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-326"}}
{"id": "dm-probability__swr_p_level_set-hard-326", "pool": "math", "split": "train", "question": "Two letters picked without replacement from wmmyjmmjm. What is prob of picking 1 y and 1 m?", "unit": "dimensionless", "value": "0.138889", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-327"}}
{"id": "dm-probability__swr_p_level_set-hard-327", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 f, 2 w and 1 d when four letters picked without replacement from dasdssfaswfsdsaf.", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-328"}}
{"id": "dm-probability__swr_p_level_set-hard-328", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 u when two letters picked without replacement from {l: 9, g: 6, u: 2, o: 1}.", "unit": "dimensionless", "value": "0.00653595", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-329"}}
{"id": "dm-probability__swr_p_level_set-hard-329", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 l, 2 w and 1 c when four letters picked without replacement from {r: 3, s: 1, w: 2, l: 11, c: 1}.", "unit": "dimensionless", "value": "0.00359477", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-330"}}
{"id": "dm-probability__swr_p_level_set-hard-330", "pool": "math", "split": "train", "question": "What is prob of picking 3 r and 1 q when four letters picked without replacement from rqqrsqrsr?", "unit": "dimensionless", "value": "0.0952381", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-331"}}
{"id": "dm-probability__swr_p_level_set-hard-331", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 d and 1 p when two letters picked without replacement from {e: 5, l: 2, f: 1, p: 1, d: 2, n: 4}.", "unit": "dimensionless", "value": "0.0190476", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-332"}}
{"id": "dm-probability__swr_p_level_set-hard-332", "pool": "math", "split": "train", "question": "What is prob of picking 1 t and 1 g when two letters picked without replacement from {t: 3, g: 2, b: 9, z: 5}?", "unit": "dimensionless", "value": "0.0350877", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-333"}}
{"id": "dm-probability__swr_p_level_set-hard-333", "pool": "math", "split": "train", "question": "Two letters picked without replacement from nnzhzlolll. Give prob of picking 1 z and 1 o.", "unit": "dimensionless", "value": "0.0444444", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-334"}}
{"id": "dm-probability__swr_p_level_set-hard-334", "pool": "math", "split": "train", "question": "What is prob of picking 1 g and 1 h when two letters picked without replacement from hrrhghhhhhghh?", "unit": "dimensionless", "value": "0.230769", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-335"}}
{"id": "dm-probability__swr_p_level_set-hard-335", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 e and 1 r when three letters picked without replacement from rrvevevvrrr.", "unit": "dimensionless", "value": "0.0303030", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-336"}}
{"id": "dm-probability__swr_p_level_set-hard-336", "pool": "math", "split": "train", "question": "Three letters picked without replacement from gpopppgpoopopggo. What is prob of picking 3 o?", "unit": "dimensionless", "value": "0.0178571", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-337"}}
{"id": "dm-probability__swr_p_level_set-hard-337", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {n: 6, l: 3, y: 1, i: 1, z: 3, u: 3}. What is prob of picking 1 y and 1 n?", "unit": "dimensionless", "value": "0.0441176", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-338"}}
{"id": "dm-probability__swr_p_level_set-hard-338", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {j: 2, k: 5, g: 5}. Give prob of picking 1 k, 1 g and 1 j.", "unit": "dimensionless", "value": "0.227273", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-339"}}
{"id": "dm-probability__swr_p_level_set-hard-339", "pool": "math", "split": "train", "question": "Two letters picked without replacement from sdrs. Give prob of picking 1 d and 1 s.", "unit": "dimensionless", "value": "0.333333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-340"}}
{"id": "dm-probability__swr_p_level_set-hard-340", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 g, 1 l and 1 o when three letters picked without replacement from gwwhwolwwwhgh.", "unit": "dimensionless", "value": "0.00699301", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-341"}}
{"id": "dm-probability__swr_p_level_set-hard-341", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {q: 1, d: 2, z: 1}. What is prob of picking 2 d?", "unit": "dimensionless", "value": "0.166667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-342"}}
{"id": "dm-probability__swr_p_level_set-hard-342", "pool": "math", "split": "train", "question": "Two letters picked without replacement from lgzggglggggprrrlgzg. Give prob of picking 1 p and 1 l.", "unit": "dimensionless", "value": "0.0175439", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-343"}}
{"id": "dm-probability__swr_p_level_set-hard-343", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 m and 2 r when three letters picked without replacement from rmrmrmrrrrmrrrrrrr.", "unit": "dimensionless", "value": "0.446078", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-344"}}
{"id": "dm-probability__swr_p_level_set-hard-344", "pool": "math", "split": "train", "question": "Two letters picked without replacement from obbbooooooo. What is prob of picking 2 b?", "unit": "dimensionless", "value": "0.0545455", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-345"}}
{"id": "dm-probability__swr_p_level_set-hard-345", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 q and 1 f when two letters picked without replacement from fqqqfqqqfqqfqqqqqfq.", "unit": "dimensionless", "value": "0.409357", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-346"}}
{"id": "dm-probability__swr_p_level_set-hard-346", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {x: 3, w: 4, g: 5, p: 1, y: 1}. Give prob of picking 2 x.", "unit": "dimensionless", "value": "0.0329670", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-347"}}
{"id": "dm-probability__swr_p_level_set-hard-347", "pool": "math", "split": "train", "question": "What is prob of picking 2 l when two letters picked without replacement from ovllovlloxlvvlvsoov?", "unit": "dimensionless", "value": "0.0877193", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-348"}}
{"id": "dm-probability__swr_p_level_set-hard-348", "pool": "math", "split": "train", "question": "What is prob of picking 1 q and 1 y when two letters picked without replacement from qrrzqrzzzyq?", "unit": "dimensionless", "value": "0.0545455", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-349"}}
{"id": "dm-probability__swr_p_level_set-hard-349", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 t and 1 i when two letters picked without replacement from uiouudtuiujddjddu.", "unit": "dimensionless", "value": "0.0147059", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-350"}}
{"id": "dm-probability__swr_p_level_set-hard-350", "pool": "math", "split": "train", "question": "Calculate prob of picking 3 q when three letters picked without replacement from aafqqmzwfazwwqf.", "unit": "dimensionless", "value": "0.00219780", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-351"}}
{"id": "dm-probability__swr_p_level_set-hard-351", "pool": "math", "split": "train", "question": "What is prob of picking 1 w, 1 t and 1 c when three letters picked without replacement from {x: 1, w: 2, c: 1, z: 1, i: 1, t: 1}?", "unit": "dimensionless", "value": "0.0571429", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-352"}}
{"id": "dm-probability__swr_p_level_set-hard-352", "pool": "math", "split": "train", "question": "What is prob of picking 1 r, 1 b and 1 z when three letters picked without replacement from znnxbnrrrrnrbnn?", "unit": "dimensionless", "value": "0.0219780", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-353"}}
{"id": "dm-probability__swr_p_level_set-hard-353", "pool": "math", "split": "train", "question": "Three letters picked without replacement from ksvvssxwkvkskxzwss. What is prob of picking 2 k and 1 v?", "unit": "dimensionless", "value": "0.0220588", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-354"}}
{"id": "dm-probability__swr_p_level_set-hard-354", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {x: 1, c: 5, o: 6, j: 2, a: 2}. Give prob of picking 1 a, 1 x and 1 j.", "unit": "dimensionless", "value": "0.00714286", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-355"}}
{"id": "dm-probability__swr_p_level_set-hard-355", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 t and 2 j when four letters picked without replacement from ttjjt.", "unit": "dimensionless", "value": "0.6", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-356"}}
{"id": "dm-probability__swr_p_level_set-hard-356", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {o: 17, r: 3}. What is prob of picking 2 r and 2 o?", "unit": "dimensionless", "value": "0.0842105", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-357"}}
{"id": "dm-probability__swr_p_level_set-hard-357", "pool": "math", "split": "train", "question": "Three letters picked without replacement from kyykyybbyyykykbb. What is prob of picking 2 y and 1 b?", "unit": "dimensionless", "value": "0.2", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-358"}}
{"id": "dm-probability__swr_p_level_set-hard-358", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {v: 1, y: 1, i: 9}. What is prob of picking 2 i?", "unit": "dimensionless", "value": "0.654545", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-359"}}
{"id": "dm-probability__swr_p_level_set-hard-359", "pool": "math", "split": "train", "question": "Four letters picked without replacement from kbhmbbkkbhbbm. Give prob of picking 1 k, 1 h and 2 m.", "unit": "dimensionless", "value": "0.00839161", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-360"}}
{"id": "dm-probability__swr_p_level_set-hard-360", "pool": "math", "split": "train", "question": "Two letters picked without replacement from jijjikjof. What is prob of picking 2 i?", "unit": "dimensionless", "value": "0.0277778", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-361"}}
{"id": "dm-probability__swr_p_level_set-hard-361", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {c: 1, k: 3, f: 3, z: 2, s: 1}. What is prob of picking 2 z?", "unit": "dimensionless", "value": "0.0222222", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-362"}}
{"id": "dm-probability__swr_p_level_set-hard-362", "pool": "math", "split": "train", "question": "Four letters picked without replacement from gggtggqgg. Give prob of picking 2 g, 1 t and 1 q.", "unit": "dimensionless", "value": "0.166667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-363"}}
{"id": "dm-probability__swr_p_level_set-hard-363", "pool": "math", "split": "train", "question": "Four letters picked without replacement from yccuyyyopoonpypoyc. What is prob of picking 1 o, 1 y, 1 u and 1 n?", "unit": "dimensionless", "value": "0.00784314", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-364"}}
{"id": "dm-probability__swr_p_level_set-hard-364", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {v: 2, o: 1, i: 6, p: 3, g: 6}. What is prob of picking 2 g and 1 i?", "unit": "dimensionless", "value": "0.110294", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-365"}}
{"id": "dm-probability__swr_p_level_set-hard-365", "pool": "math", "split": "train", "question": "Two letters picked without replacement from qfuruuuufrfuuuuf. What is prob of picking 1 r and 1 f?", "unit": "dimensionless", "value": "0.0666667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-366"}}
{"id": "dm-probability__swr_p_level_set-hard-366", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {a: 10, f: 2}. Give prob of picking 2 f and 2 a.", "unit": "dimensionless", "value": "0.0909091", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-367"}}
{"id": "dm-probability__swr_p_level_set-hard-367", "pool": "math", "split": "train", "question": "Three letters picked without replacement from dxuxpxxpxxapxpaxxxa. Give prob of picking 2 p and 1 a.", "unit": "dimensionless", "value": "0.0185759", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-368"}}
{"id": "dm-probability__swr_p_level_set-hard-368", "pool": "math", "split": "train", "question": "Four letters picked without replacement from zpmmsozzgms. Give prob of picking 1 g and 3 z.", "unit": "dimensionless", "value": "0.00303030", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-369"}}
{"id": "dm-probability__swr_p_level_set-hard-369", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 x and 2 w when three letters picked without replacement from {j: 4, o: 1, w: 2, x: 2}.", "unit": "dimensionless", "value": "0.0238095", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-370"}}
{"id": "dm-probability__swr_p_level_set-hard-370", "pool": "math", "split": "train", "question": "Three letters picked without replacement from vvvee. Give prob of picking 3 v.", "unit": "dimensionless", "value": "0.1", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-371"}}
{"id": "dm-probability__swr_p_level_set-hard-371", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 a and 1 r when two letters picked without replacement from erfrafffra.", "unit": "dimensionless", "value": "0.133333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-372"}}
{"id": "dm-probability__swr_p_level_set-hard-372", "pool": "math", "split": "train", "question": "Four letters picked without replacement from aajaaaaaaaaajj. What is prob of picking 1 a and 3 j?", "unit": "dimensionless", "value": "0.0109890", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-373"}}
{"id": "dm-probability__swr_p_level_set-hard-373", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 e, 1 r and 1 s when four letters picked without replacement from {e: 4, c: 9, r: 1, s: 2, y: 1}.", "unit": "dimensionless", "value": "0.00504202", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-374"}}
{"id": "dm-probability__swr_p_level_set-hard-374", "pool": "math", "split": "train", "question": "Four letters picked without replacement from lnilniniinlliiiil. What is prob of picking 3 l and 1 n?", "unit": "dimensionless", "value": "0.0168067", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-375"}}
{"id": "dm-probability__swr_p_level_set-hard-375", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {d: 13, b: 3}. What is prob of picking 1 d and 1 b?", "unit": "dimensionless", "value": "0.325", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-376"}}
{"id": "dm-probability__swr_p_level_set-hard-376", "pool": "math", "split": "train", "question": "Two letters picked without replacement from owowwwooooow. What is prob of picking 2 o?", "unit": "dimensionless", "value": "0.318182", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-377"}}
{"id": "dm-probability__swr_p_level_set-hard-377", "pool": "math", "split": "train", "question": "Two letters picked without replacement from wspnppspswpp. Give prob of picking 2 p.", "unit": "dimensionless", "value": "0.227273", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-378"}}
{"id": "dm-probability__swr_p_level_set-hard-378", "pool": "math", "split": "train", "question": "Two letters picked without replacement from lpwwpllwplplpwllp. Give prob of picking 2 l.", "unit": "dimensionless", "value": "0.154412", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-379"}}
{"id": "dm-probability__swr_p_level_set-hard-379", "pool": "math", "split": "train", "question": "Two letters picked without replacement from mmfmmmmmmsm. Give prob of picking 1 s and 1 m.", "unit": "dimensionless", "value": "0.163636", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-380"}}
{"id": "dm-probability__swr_p_level_set-hard-380", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {c: 2, j: 7}. What is prob of picking 2 c?", "unit": "dimensionless", "value": "0.0277778", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-381"}}
{"id": "dm-probability__swr_p_level_set-hard-381", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 p, 1 o and 1 d when four letters picked without replacement from qodhoojqqpqooqjpqdjq.", "unit": "dimensionless", "value": "0.00206398", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-382"}}
{"id": "dm-probability__swr_p_level_set-hard-382", "pool": "math", "split": "train", "question": "Four letters picked without replacement from hhhhhhhhh. Give prob of picking 4 h.", "unit": "dimensionless", "value": "1", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-383"}}
{"id": "dm-probability__swr_p_level_set-hard-383", "pool": "math", "split": "train", "question": "Four letters picked without replacement from vwwwvwwqwvqwqwvw. Give prob of picking 4 v.", "unit": "dimensionless", "value": "0.000549451", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-384"}}
{"id": "dm-probability__swr_p_level_set-hard-384", "pool": "math", "split": "train", "question": "Calculate prob of picking 3 s and 1 i when four letters picked without replacement from {s: 3, r: 5, i: 5}.", "unit": "dimensionless", "value": "0.00699301", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-385"}}
{"id": "dm-probability__swr_p_level_set-hard-385", "pool": "math", "split": "train", "question": "What is prob of picking 2 a when two letters picked without replacement from waafwfffa?", "unit": "dimensionless", "value": "0.0833333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-386"}}
{"id": "dm-probability__swr_p_level_set-hard-386", "pool": "math", "split": "train", "question": "Two letters picked without replacement from kkffkffftkffk. What is prob of picking 1 f and 1 k?", "unit": "dimensionless", "value": "0.448718", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-387"}}
{"id": "dm-probability__swr_p_level_set-hard-387", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {d: 3, p: 1, f: 6, b: 1, k: 3, z: 3}. Give prob of picking 1 b, 1 k and 2 d.", "unit": "dimensionless", "value": "0.00378151", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-388"}}
{"id": "dm-probability__swr_p_level_set-hard-388", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {w: 3, a: 6, p: 1, b: 5, x: 1, d: 3}. Give prob of picking 1 d and 1 b.", "unit": "dimensionless", "value": "0.0877193", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-389"}}
{"id": "dm-probability__swr_p_level_set-hard-389", "pool": "math", "split": "train", "question": "What is prob of picking 1 h, 2 z and 1 f when four letters picked without replacement from {f: 5, z: 1, p: 5, h: 8}?", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-390"}}
{"id": "dm-probability__swr_p_level_set-hard-390", "pool": "math", "split": "train", "question": "Two letters picked without replacement from tab. Give prob of picking 1 a and 1 b.", "unit": "dimensionless", "value": "0.333333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-391"}}
{"id": "dm-probability__swr_p_level_set-hard-391", "pool": "math", "split": "train", "question": "Three letters picked without replacement from {u: 1, v: 2, j: 1, k: 2, c: 2}. What is prob of picking 2 c and 1 v?", "unit": "dimensionless", "value": "0.0357143", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-392"}}
{"id": "dm-probability__swr_p_level_set-hard-392", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {v: 1, m: 1, g: 2, i: 2, n: 1, p: 2}. Give prob of picking 1 n and 1 v.", "unit": "dimensionless", "value": "0.0277778", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-393"}}
{"id": "dm-probability__swr_p_level_set-hard-393", "pool": "math", "split": "train", "question": "Two letters picked without replacement from gyyxyygyyyyx. What is prob of picking 2 y?", "unit": "dimensionless", "value": "0.424242", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-394"}}
{"id": "dm-probability__swr_p_level_set-hard-394", "pool": "math", "split": "train", "question": "Four letters picked without replacement from gzqrrzgtzr. What is prob of picking 1 r, 2 z and 1 g?", "unit": "dimensionless", "value": "0.0857143", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-395"}}
{"id": "dm-probability__swr_p_level_set-hard-395", "pool": "math", "split": "train", "question": "What is prob of picking 2 l when two letters picked without replacement from {l: 2, q: 2, s: 2}?", "unit": "dimensionless", "value": "0.0666667", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-396"}}
{"id": "dm-probability__swr_p_level_set-hard-396", "pool": "math", "split": "train", "question": "Two letters picked without replacement from wwy. What is prob of picking 2 w?", "unit": "dimensionless", "value": "0.333333", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-397"}}
{"id": "dm-probability__swr_p_level_set-hard-397", "pool": "math", "split": "train", "question": "Four letters picked without replacement from ozaaoxono. What is prob of picking 3 x and 1 o?", "unit": "dimensionless", "value": "0", "precision": {"kind": "decimals", "n": 0}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-398"}}
{"id": "dm-probability__swr_p_level_set-hard-398", "pool": "math", "split": "train", "question": "Two letters picked without replacement from {d: 4, e: 9, a: 1, x: 1}. Give prob of picking 2 e.", "unit": "dimensionless", "value": "0.342857", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-399"}}
{"id": "dm-probability__swr_p_level_set-hard-399", "pool": "math", "split": "train", "question": "What is prob of picking 1 g and 1 p when two letters picked without replacement from npwpgwfg?", "unit": "dimensionless", "value": "0.142857", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-400"}}
{"id": "dm-probability__swr_p_level_set-hard-400", "pool": "math", "split": "train", "question": "What is prob of picking 1 r and 1 y when two letters picked without replacement from yryrrpr?", "unit": "dimensionless", "value": "0.380952", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-401"}}
{"id": "dm-probability__swr_p_level_set-hard-401", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 f and 1 x when two letters picked without replacement from xfqxfxwqfwfqqw.", "unit": "dimensionless", "value": "0.131868", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-402"}}
{"id": "dm-probability__swr_p_level_set-hard-402", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 t and 2 h when four letters picked without replacement from ththhht.", "unit": "dimensionless", "value": "0.514286", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-403"}}
{"id": "dm-probability__swr_p_level_set-hard-403", "pool": "math", "split": "train", "question": "Three letters picked without replacement from uuuuuueeueeuuuue. Give prob of picking 3 e.", "unit": "dimensionless", "value": "0.0178571", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-404"}}
{"id": "dm-probability__swr_p_level_set-hard-404", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 k and 1 b when two letters picked without replacement from {k: 2, e: 3, b: 1, i: 1, j: 4, t: 1}.", "unit": "dimensionless", "value": "0.0303030", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-405"}}
{"id": "dm-probability__swr_p_level_set-hard-405", "pool": "math", "split": "train", "question": "Calculate prob of picking 1 e and 2 x when three letters picked without replacement from xnmmexxxx.", "unit": "dimensionless", "value": "0.119048", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-406"}}
{"id": "dm-probability__swr_p_level_set-hard-406", "pool": "math", "split": "train", "question": "Four letters picked without replacement from {z: 2, f: 3, b: 1, x: 9, s: 3}. What is prob of picking 1 b, 1 s and 2 x?", "unit": "dimensionless", "value": "0.0352941", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-407"}}
{"id": "dm-probability__swr_p_level_set-hard-407", "pool": "math", "split": "train", "question": "Calculate prob of picking 2 s when two letters picked without replacement from mmsmsmmmmm.", "unit": "dimensionless", "value": "0.0222222", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-408"}}
{"id": "dm-probability__swr_p_level_set-hard-408", "pool": "math", "split": "train", "question": "What is prob of picking 2 w and 2 i when four letters picked without replacement from {i: 2, w: 4}?", "unit": "dimensionless", "value": "0.4", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-409"}}
{"id": "dm-probability__swr_p_level_set-hard-409", "pool": "math", "split": "train", "question": "Three letters picked without replacement from lgldk. Give prob of picking 2 l and 1 k.", "unit": "dimensionless", "value": "0.1", "precision": {"kind": "sigfigs", "n": 4}, "relative_tolerance": "0", "category": "probability__swr_p_level_set", "difficulty": "hard", "source": {"generator": "deepmind/mathematics_dataset 1.0.1 (Apache-2.0)", "module": "probability__swr_p_level_set", "level": "hard", "seed": "probability__swr_p_level_set-hard-410"}}