id stringlengths 25 25 | question stringlengths 45 1.01k | chain stringlengths 75 4.11k | result stringclasses 5 values | result_float float64 -4,212 100B | question_without_options stringlengths 6 962 | options dict | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | rationale stringlengths 1 2.74k | category stringclasses 6 values |
|---|---|---|---|---|---|---|---|---|---|---|
math_qa__y9wglefaU0ZVjHjE | On dividing a number by 5, we get 3 as remainder. What will be the remainder when the square of this number is divided by 5 ? Choices
A) 0 B) 1 C) 3 D) 4 E) 2 | <gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">9 / 5</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">floor(9/5)</gadget>
<output>1</output>
<gadget id="calculator">(9/5) - 1</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 5</gadget>
<output>4</output>
<result>D</result> | D | 4 | On dividing a number by 5, we get 3 as remainder. What will be the remainder when the square of this number is divided by 5 ? | {
"A": "0",
"B": "1",
"C": "3",
"D": "4",
"E": "2"
} | multiply(subtract(divide(power(3, const_2), 5), floor(divide(power(3, const_2), 5))), 5) | power(n1,const_2)|divide(#0,n0)|floor(#1)|subtract(#1,#2)|multiply(n0,#3) | let the number be x and on dividing x by 5 , we get k as quotient and 3 as remainder . x = 5 k + 3 x ^ 2 = ( 5 k + 3 ) ^ 2 = ( 25 k ^ 2 + 30 k + 9 ) = 5 ( 5 k ^ 2 + 6 k + 1 ) + 4 on dividing x ^ 2 by 5 , we get 4 as remainder . answer is d | geometry |
math_qa__C3MuubzRTVB7Bwzg | A certain car uses one gallon of gasoline every 38 miles when it travels on highway, and one gallon of gasoline every 20 miles when it travels in the city. When a car travels 4 miles on highway and 4 additional miles in the city, it uses what percent more gasoline than if it travels 8 miles on the highway?
Choose the correct choice from the following answers
A) 15 %
B) 20 %
C) 22.5 %
D) 45 %
E) 50 % | <gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 4</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 38</gadget>
<output>1/38 = around 0.026316</output>
<gadget id="calculator">4 * (1/38)</gadget>
<output>2/19 = around 0.105263</output>
<gadget id="calculator">(1/5) + (2/19)</gadget>
<output>29/95 = around 0.305263</output>
<gadget id="calculator">8 * (1/38)</gadget>
<output>4/19 = around 0.210526</output>
<gadget id="calculator">(29/95) - (4/19)</gadget>
<output>9/95 = around 0.094737</output>
<gadget id="calculator">(9/95) / (4/19)</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(9/20) * 100</gadget>
<output>45</output>
<result>D</result> | D | 45 | A certain car uses one gallon of gasoline every 38 miles when it travels on highway, and one gallon of gasoline every 20 miles when it travels in the city. When a car travels 4 miles on highway and 4 additional miles in the city, it uses what percent more gasoline than if it travels 8 miles on the highway? | {
"A": "15 %",
"B": "20 %",
"C": "22.5 %",
"D": "45 %",
"E": "50 %"
} | multiply(divide(subtract(add(multiply(divide(const_1, 20), 4), multiply(4, divide(const_1, 38))), multiply(8, divide(const_1, 38))), multiply(8, divide(const_1, 38))), const_100) | divide(const_1,n1)|divide(const_1,n0)|multiply(n2,#0)|multiply(n2,#1)|multiply(n4,#1)|add(#2,#3)|subtract(#5,#4)|divide(#6,#4)|multiply(#7,const_100)| | "4 miles on the highway = 4 / 38 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 38 + 4 / 20 = 29 / 95 gallons . 8 miles on the highway = 8 / 38 gallons . the % change = ( 29 / 95 - 8 / 38 ) / ( 8 / 38 ) = 0.45 . answer : d ." | general |
math_qa__1m4v8OM0DalWmpZd | A man can row upstream at 45 kmph and downstream at 55 kmph, and then find the speed of the man in still water? Choose the correct choice from the following:
A) 32 kmph
B) 34 kmph
C) 30 kmph
D) 50 kmph
E) 65 kmph | <gadget id="calculator">45 + 55</gadget>
<output>100</output>
<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<result>D</result> | D | 50 | A man can row upstream at 45 kmph and downstream at 55 kmph, and then find the speed of the man in still water? | {
"A": "32 kmph",
"B": "34 kmph",
"C": "30 kmph",
"D": "50 kmph",
"E": "65 kmph"
} | divide(add(45, 55), const_2) | add(n0,n1)|divide(#0,const_2)| | "us = 45 ds = 55 m = ( 45 + 55 ) / 2 = 50 answer : d" | physics |
math_qa__QyXWXNWRIranyzI3 | The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 8 cm each. The radius of the sphere is Choices:
A) 3 cm B) 4 cm C) 6 cm D) 8 cm E) none | <gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">8 * 4</gadget>
<output>32</output>
<gadget id="calculator">pi * 32</gadget>
<output>32*pi = around 100.530965</output>
<gadget id="calculator">(32*pi) * 2</gadget>
<output>64*pi = around 201.06193</output>
<gadget id="calculator">pi * 4</gadget>
<output>4*pi = around 12.566371</output>
<gadget id="calculator">(64*pi) / (4*pi)</gadget>
<output>16</output>
<gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>
<result>B</result> | B | 4 | The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 8 cm each. The radius of the sphere is | {
"A": "3 cm",
"B": "4 cm",
"C": "6 cm",
"D": "8 cm",
"E": "none"
} | sqrt(divide(multiply(multiply(const_pi, multiply(8, divide(8, const_2))), const_2), multiply(const_pi, const_4))) | divide(n0,const_2)|multiply(const_4,const_pi)|multiply(n0,#0)|multiply(#2,const_pi)|multiply(#3,const_2)|divide(#4,#1)|sqrt(#5) | solution 4 î r 2 = 2 î 4 x 8 â ‡ ’ r 2 = ( 4 x 8 / 2 ) â ‡ ’ 16 â ‡ ’ r = 4 cm . answer b | geometry |
math_qa__vaEiUi1hzwH8d9Ke | The sum of the non-prime numbers between 30 and 40, non-inclusive, is Choose the correct choice from the following options.
A) 202 B) 217 C) 232 D) 247 E) 262 | <gadget id="calculator">30 + 1</gadget>
<output>31</output>
<gadget id="calculator">31 + 1</gadget>
<output>32</output>
<gadget id="calculator">31 + 32</gadget>
<output>63</output>
<gadget id="calculator">32 + 2</gadget>
<output>34</output>
<gadget id="calculator">63 + 34</gadget>
<output>97</output>
<gadget id="calculator">34 + 1</gadget>
<output>35</output>
<gadget id="calculator">97 + 35</gadget>
<output>132</output>
<gadget id="calculator">35 + 1</gadget>
<output>36</output>
<gadget id="calculator">132 + 36</gadget>
<output>168</output>
<gadget id="calculator">36 + 1</gadget>
<output>37</output>
<gadget id="calculator">168 + 37</gadget>
<output>205</output>
<gadget id="calculator">37 + 1</gadget>
<output>38</output>
<gadget id="calculator">205 + 38</gadget>
<output>243</output>
<result>D</result> | D | 247 | The sum of the non-prime numbers between 30 and 40, non-inclusive, is | {
"A": "202",
"B": "217",
"C": "232",
"D": "247",
"E": "262"
} | add(add(add(add(add(add(add(30, const_1), add(add(30, const_1), const_1)), add(add(add(30, const_1), const_1), const_2)), add(add(add(add(30, const_1), const_1), const_2), const_1)), add(add(add(add(add(30, const_1), const_1), const_2), const_1), const_1)), add(add(add(add(add(add(30, const_1), const_1), const_2), const_1), const_1), const_1)), add(add(add(add(add(add(add(30, const_1), const_1), const_2), const_1), const_1), const_1), const_1)) | add(n0,const_1)|add(#0,const_1)|add(#0,#1)|add(#1,const_2)|add(#2,#3)|add(#3,const_1)|add(#4,#5)|add(#5,const_1)|add(#6,#7)|add(#7,const_1)|add(#8,#9)|add(#9,const_1)|add(#10,#11)| | "sum of consecutive integers from 31 to 39 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 31 + 39 ) / 2 * 9 = 35 * 9 = 315 sum of non - prime numbers b / w 30 and 40 , non inclusive = = = > 315 - 68 ( i . e . , 31 + 37 , being the prime # s in the range ) = 247 answer : d" | general |
math_qa__UgMYjjOG0XOGfGm6 | 6 wires are by average 80 cm long each. If the average length of one third of the wires is 70 cm, what is the average of the other wires?
Pick: A) 75 . B) 85 . C) 90 . D) 94 . E) 100 . | <gadget id="calculator">6 * 80</gadget>
<output>480</output>
<gadget id="calculator">2 * 70</gadget>
<output>140</output>
<gadget id="calculator">480 - 140</gadget>
<output>340</output>
<gadget id="calculator">340 / 4</gadget>
<output>85</output>
<result>B</result> | B | 85 | 6 wires are by average 80 cm long each. If the average length of one third of the wires is 70 cm, what is the average of the other wires? | {
"A": "75 .",
"B": "85 .",
"C": "90 .",
"D": "94 .",
"E": "100 ."
} | divide(subtract(multiply(6, 80), multiply(const_2, 70)), const_4) | multiply(n0,n1)|multiply(n2,const_2)|subtract(#0,#1)|divide(#2,const_4) | edit : given ( x 1 + x 2 . . . + x 6 ) / 6 = 80 ( x 1 + x 2 . . . + x 6 ) = 480 - - > eq 1 . now given avg length of one third wires is 70 . that means out 6 / 3 = 2 wires . let the avg length of two wires be ( x 1 + x 2 ) / 2 = 70 . ( x 1 + x 2 ) = 140 . - - > eq 2 . now we are asked to find the average of the remaining i . e . ( x 3 + x 4 + x 5 + x 6 ) substitute eq 2 in eq 1 then we get 140 + x 3 + x 4 + x 5 + x 6 = 480 = > x 3 + x 4 + x 5 + x 6 = 340 now divide 340 by 4 we get 85 . = > ( x 3 + x 4 + x 5 + x 6 ) / 4 = 85 = avg length of remaining wires . imo correct option is b . | general |
math_qa__qqAjeaPmhZZgwPjY | When 15 is divided by integer u, the remainder is 4. For how many values of u is this be true? Choose one:
A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">15 - 4</gadget>
<output>11</output>
<gadget id="calculator">11 + 4</gadget>
<output>15</output>
<gadget id="calculator">15 / 15</gadget>
<output>1</output>
<result>A</result> | A | 1 | When 15 is divided by integer u, the remainder is 4. For how many values of u is this be true? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | divide(add(subtract(15, 4), 4), 15) | subtract(n0,n1)|add(n1,#0)|divide(#1,n0) | when 15 is divided by u , the remainder is 4 i . e . 4 mangoes left over after grouping , so u must be greater than 4 . it also means that 11 is completely divisible by u . factors of 11 are 1 and 11 . out of these , u could be 11 . answer ( a ) | general |
math_qa__or7u2jRG9wKnNYJM | The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 7 seconds than it was moving after 4 seconds? Choices.
A) 4 B) 9 C) 39 D) 48 E) 63 | <gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">49 + 14</gadget>
<output>63</output>
<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">16 + 8</gadget>
<output>24</output>
<gadget id="calculator">63 - 24</gadget>
<output>39</output>
<result>C</result> | C | 39 | The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 7 seconds than it was moving after 4 seconds? | {
"A": "4",
"B": "9",
"C": "39",
"D": "48",
"E": "63"
} | subtract(add(power(7, 2), multiply(7, 2)), add(power(4, 2), multiply(4, 2))) | multiply(n0,n4)|multiply(n0,n5)|power(n4,n0)|power(n5,n0)|add(#0,#2)|add(#1,#3)|subtract(#4,#5)| | "given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 4 ) = 4 ^ 2 + 2 * 4 = 24 z ( 7 ) = 7 ^ 2 + 2 * 7 = 63 therefore z ( 7 ) - z ( 3 ) = 63 - 24 = 39 km / hr option c" | physics |
math_qa__hi0OlDgQTwjib7QT | If p#q denotes the least common multiple of p and q, then W=((12#16)#(18#24)) = ? Choose the correct choice:
A) 216 B) 180 C) 144 D) 108 E) 72 | <gadget id="calculator">18 * 24</gadget>
<output>432</output>
<gadget id="calculator">12 * 16</gadget>
<output>192</output>
<gadget id="calculator">432 - 192</gadget>
<output>240</output>
<gadget id="calculator">240 / 2</gadget>
<output>120</output>
<gadget id="calculator">120 + 24</gadget>
<output>144</output>
<result>C</result> | C | 144 | If p#q denotes the least common multiple of p and q, then W=((12#16)#(18#24)) = ? | {
"A": "216",
"B": "180",
"C": "144",
"D": "108",
"E": "72"
} | add(divide(subtract(multiply(18, 24), multiply(12, 16)), const_2), 24) | multiply(n2,n3)|multiply(n0,n1)|subtract(#0,#1)|divide(#2,const_2)|add(n3,#3)| | "there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , w = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c ." | general |
math_qa__ZHMzMDr7fLThhs10 | A car travels from point A to point B. The average speed of the car is 60 km/hr and it travels the first half of the trip at a speed of 75 km/hr. What is the speed of the car in the second half of the trip? Pick one.
A) 40
B) 45
C) 48
D) 50
E) 55 | <gadget id="calculator">75 * 60</gadget>
<output>4_500</output>
<gadget id="calculator">75 - 60</gadget>
<output>15</output>
<gadget id="calculator">15 * 60</gadget>
<output>900</output>
<gadget id="calculator">4_500 / 900</gadget>
<output>5</output>
<gadget id="calculator">60 * 5</gadget>
<output>300</output>
<gadget id="calculator">60 / 10</gadget>
<output>6</output>
<gadget id="calculator">300 / 6</gadget>
<output>50</output>
<result>D</result> | D | 50 | A car travels from point A to point B. The average speed of the car is 60 km/hr and it travels the first half of the trip at a speed of 75 km/hr. What is the speed of the car in the second half of the trip? | {
"A": "40",
"B": "45",
"C": "48",
"D": "50",
"E": "55"
} | divide(multiply(60, divide(multiply(75, 60), multiply(subtract(75, 60), 60))), divide(60, const_10)) | divide(n0,const_10)|multiply(n0,n1)|subtract(n1,n0)|multiply(n0,#2)|divide(#1,#3)|multiply(n0,#4)|divide(#5,#0) | let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 150 + ( d / 2 ) / v d / 100 = d / 2 v and so v = 50 km / hr the answer is d . | general |
math_qa__zgXOFScz11OUmq6I | A rectangular table, kept against a wall has a three sides free and the wall along the fourth side. The side opposite the wall is twice the length of each of the other two free sides. If the area of the rectangular table is 128 square feet, what is the total length of the table free sides, in feet? Choose the correct option:
A) 4
B) 8
C) 16
D) 32
E) 64 | <gadget id="calculator">128 / 2</gadget>
<output>64</output>
<gadget id="calculator">64 ** (1/2)</gadget>
<output>8</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">8 + 16</gadget>
<output>24</output>
<gadget id="calculator">24 + 8</gadget>
<output>32</output>
<result>D</result> | D | 32 | A rectangular table, kept against a wall has a three sides free and the wall along the fourth side. The side opposite the wall is twice the length of each of the other two free sides. If the area of the rectangular table is 128 square feet, what is the total length of the table free sides, in feet? | {
"A": "4",
"B": "8",
"C": "16",
"D": "32",
"E": "64"
} | add(add(sqrt(divide(128, const_2)), multiply(sqrt(divide(128, const_2)), const_2)), sqrt(divide(128, const_2))) | divide(n0,const_2)|sqrt(#0)|multiply(#1,const_2)|add(#2,#1)|add(#3,#1) | two sides each = x the third = 2 x and the wall side is thus 2 x too x * 2 x = 2 x ^ 2 = 128 ie x ^ 2 = 64 ie x = 8 l = 16 w = 8 total lenght of table ' s free sides = 2 * 8 + 16 = 32 my answer is d | geometry |
math_qa__KhYkeaGzATVoKX73 | A boat having a length 8 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is: Select:
A) 100 kg B) 120 kg C) 89 kg D) 80 kg E) 240 kg | <gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">24 * (1/100)</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">(6/25) * 1_000</gadget>
<output>240</output>
<result>E</result> | E | 240 | A boat having a length 8 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is: | {
"A": "100 kg",
"B": "120 kg",
"C": "89 kg",
"D": "80 kg",
"E": "240 kg"
} | multiply(multiply(multiply(8, 3), divide(1, const_100)), const_1000) | divide(n2,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(#2,const_1000)| | "volume of water displaced = ( 8 x 3 x 0.01 ) m 3 = 0.24 m 3 . mass of man = volume of water displaced x density of water = ( 0.24 x 1000 ) kg = 240 kg . answer : e" | physics |
math_qa__vLCuO1pWDLTKcOjB | Excluding stoppages, the speed of a bus is 86 kmph and including stoppages, it is 76 kmph. For how many minutes does the bus stop per hour? Choose the correct choice from the following answers.
A) 7.5 min B) 16 min C) 20 min D) 7 min E) 40 min | <gadget id="calculator">86 - 76</gadget>
<output>10</output>
<gadget id="calculator">10 / 86</gadget>
<output>5/43 = around 0.116279</output>
<gadget id="calculator">60 * (5/43)</gadget>
<output>300/43 = around 6.976744</output>
<result>D</result> | D | 7 | Excluding stoppages, the speed of a bus is 86 kmph and including stoppages, it is 76 kmph. For how many minutes does the bus stop per hour? | {
"A": "7.5 min",
"B": "16 min",
"C": "20 min",
"D": "7 min",
"E": "40 min"
} | multiply(const_60, divide(subtract(86, 76), 86)) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_60)| | "d 7 min due to stoppages , it covers 10 km less . time taken to cover 10 km = ( 10 / 86 x 60 ) min = 7 min" | physics |
math_qa__HogNoGnpcHTrNeD8 | The perimeter of a square is equal to the perimeter of a rectangle of length 15 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places) Choices
A) 22.78 B) 23.54 C) 24.5 D) 25.55 E) 23.51 | <gadget id="calculator">14 + 15</gadget>
<output>29</output>
<gadget id="calculator">2 * 29</gadget>
<output>58</output>
<gadget id="calculator">58 / 4</gadget>
<output>29/2 = around 14.5</output>
<gadget id="calculator">(29/2) / 2</gadget>
<output>29/4 = around 7.25</output>
<gadget id="calculator">2 * pi * (29/4)</gadget>
<output>29*pi/2 = around 45.553093</output>
<gadget id="calculator">(29*pi/2) / 2</gadget>
<output>29*pi/4 = around 22.776547</output>
<gadget id="calculator">floor(29*pi/4)</gadget>
<output>22</output>
<result>A</result> | A | 22.78 | The perimeter of a square is equal to the perimeter of a rectangle of length 15 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places) | {
"A": "22.78",
"B": "23.54",
"C": "24.5",
"D": "25.55",
"E": "23.51"
} | floor(divide(circumface(divide(divide(multiply(const_2, add(14, 15)), const_4), const_2)), const_2)) | add(n0,n1)|multiply(#0,const_2)|divide(#1,const_4)|divide(#2,const_2)|circumface(#3)|divide(#4,const_2)|floor(#5) | let the side of the square be a cm . perimeter of the rectangle = 2 ( 15 + 14 ) = 58 cm perimeter of the square = 58 cm i . e . 4 a = 58 a = 14.5 diameter of the semicircle = 14.5 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 14.5 ) = 1 / 2 ( 22 / 7 ) ( 14.5 ) = 22.78 cm to two decimal places answer : a | geometry |
math_qa__phGkyfp7mdmJXBRw | The ratio of numbers is 3:4 and their H.C.F is 4. Their L.C.M is? Choose the correct choice from the following: A) 23 B) 77 C) 88 D) 48 E) 11 | <gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">lcm(12, 16)</gadget>
<output>48</output>
<result>D</result> | D | 48 | The ratio of numbers is 3:4 and their H.C.F is 4. Their L.C.M is? | {
"A": "23",
"B": "77",
"C": "88",
"D": "48",
"E": "11"
} | lcm(multiply(3, 4), multiply(4, 4)) | multiply(n0,n2)|multiply(n1,n2)|lcm(#0,#1)| | "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 4 . so , the numbers are 12 and 16 . l . c . m of 12 and 16 = 48 . answer : d" | other |
math_qa__0KKmajSHt1aLjI1D | John makes $60 a week from his job. He earns a raise and now makes $120 a week. What is the % increase? Choose one
A) 16 % B) 100 % C) 17 % D) 17.61 % E) 17.56 % | <gadget id="calculator">120 - 60</gadget>
<output>60</output>
<gadget id="calculator">60 / 60</gadget>
<output>1</output>
<gadget id="calculator">1 * 100</gadget>
<output>100</output>
<result>B</result> | B | 100 | John makes $60 a week from his job. He earns a raise and now makes $120 a week. What is the % increase? | {
"A": "16 %",
"B": "100 %",
"C": "17 %",
"D": "17.61 %",
"E": "17.56 %"
} | multiply(divide(subtract(120, 60), 60), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | "increase = ( 60 / 60 ) * 100 = ( 6 / 6 ) * 100 = 100 % . b" | gain |
math_qa__bRytGB9oQAn90VQd | A can finish a work in 12 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
Choose the correct choice.
A) 4
B) 5 1 / 2
C) 6
D) 8
E) none of these | <gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/15) * 10</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 12</gadget>
<output>8</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<result>A</result> | A | 4 | A can finish a work in 12 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work? | {
"A": "4",
"B": "5 1 / 2",
"C": "6",
"D": "8",
"E": "none of these"
} | divide(multiply(multiply(divide(const_1, 15), 10), 12), const_2) | divide(const_1,n1)|multiply(n2,#0)|multiply(n0,#1)|divide(#2,const_2)| | "b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 12 * 1 / 3 ) = 4 days . correct option : a" | physics |
math_qa__tyKfpfsnB00RG8Kr | Two trains are moving in opposite directions with speed of 90 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds Choose the correct choice from the following.
A) 56 B) 40 C) 47 D) 26 E) 25 | <gadget id="calculator">1.1 + 0.9</gadget>
<output>2</output>
<gadget id="calculator">90 + 90</gadget>
<output>180</output>
<gadget id="calculator">2 / 180</gadget>
<output>1/90 = around 0.011111</output>
<gadget id="calculator">(1/90) * 3_600</gadget>
<output>40</output>
<result>B</result> | B | 40 | Two trains are moving in opposite directions with speed of 90 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds | {
"A": "56",
"B": "40",
"C": "47",
"D": "26",
"E": "25"
} | multiply(divide(add(1.10, 0.9), add(90, 90)), const_3600) | add(n2,n3)|add(n0,n1)|divide(#0,#1)|multiply(#2,const_3600)| | "explanation : relative speed = 90 + 90 = 180 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 180 hr = 1 / 90 hr = 3600 / 90 seconds = 40 seconds answer : option b" | physics |
math_qa__Up2gxMsdB3PQhPjD | For any number s, s* is defined as the greatest positive even integer less than or equal to s. What is the value of 5.2 – 5.2*?
Pick.
A) 0.2 B) 1.2 C) 1.8 D) 2.2 E) 4.0 | <gadget id="calculator">5.2 - 4</gadget>
<output>1.2</output>
<result>B</result> | B | 1.2 | For any number s, s* is defined as the greatest positive even integer less than or equal to s. What is the value of 5.2 – 5.2*? | {
"A": "0.2",
"B": "1.2",
"C": "1.8",
"D": "2.2",
"E": "4.0"
} | subtract(5.2, const_4) | subtract(n0,const_4) | since s * is defined as the greatest positive even integer less than or equal to s , then 5.2 * = 4 ( the greatest positive even integer less than or equal to 5.2 is 4 ) . hence , 5.2 – 5.2 * = 5.2 - 4 = 1.2 answer : b . | general |
math_qa__gUNtFiSlRYfmsv0j | The present ages of A,B & C are in the ratio of 5:7:8. 7years ago, the sum oftheir ages was 59. What is the present age of eldest one? Choices:
A) 30
B) 31
C) 32
D) 35
E) 36 | <gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">21 + 59</gadget>
<output>80</output>
<gadget id="calculator">5 + 7</gadget>
<output>12</output>
<gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">80 / 20</gadget>
<output>4</output>
<gadget id="calculator">4 * 8</gadget>
<output>32</output>
<result>C</result> | C | 32 | The present ages of A,B & C are in the ratio of 5:7:8. 7years ago, the sum oftheir ages was 59. What is the present age of eldest one? | {
"A": "30",
"B": "31",
"C": "32",
"D": "35",
"E": "36"
} | multiply(divide(add(multiply(7, const_3), 59), add(add(5, 7), 8)), 8) | add(n0,n1)|multiply(n1,const_3)|add(n4,#1)|add(n2,#0)|divide(#2,#3)|multiply(n2,#4) | let their present ages be 5 x , 7 x and 8 x . 7 years ago , sum of their ages was 59 . sum of their present ages = 59 + ( 3 x 7 ) = 80 sum of their present ages given is 5 x + 7 x + 8 x = 20 x 20 x = 80 = > x = 80 20 = 4 age of the eldest one = 8 x = 8 x 4 = 32 years . c | general |
math_qa__fWNfF0bfi0P6BsFK | ?% of 360 = 129.6 Choose the correct answer: A) 277 B) 36 C) 64 D) 72 E) none of these | <gadget id="calculator">129.6 * 100</gadget>
<output>12_960</output>
<gadget id="calculator">12_960 / 360</gadget>
<output>36</output>
<result>B</result> | B | 36 | ?% of 360 = 129.6 | {
"A": "277",
"B": "36",
"C": "64",
"D": "72",
"E": "none of these"
} | divide(multiply(129.6, const_100), 360) | multiply(n1,const_100)|divide(#0,n0)| | "? % of 360 = 129.6 or , ? = 129.6 × 100 / 360 = 36 answer b" | gain |
math_qa__qZSCk8QcFqLPbzN9 | If the average (arithmetic mean) of 16 consecutive odd integers is 414, then the least of these integers is
Choose the correct choice from the following answers: A) 399 B) 418 C) 519 D) 521 E) 525 | <gadget id="calculator">414 - 16</gadget>
<output>398</output>
<gadget id="calculator">398 + 1</gadget>
<output>399</output>
<result>A</result> | A | 399 | If the average (arithmetic mean) of 16 consecutive odd integers is 414, then the least of these integers is | {
"A": "399",
"B": "418",
"C": "519",
"D": "521",
"E": "525"
} | add(subtract(414, 16), const_1) | subtract(n1,n0)|add(#0,const_1)| | "a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 414 . there are 16 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 7 th and 8 th numbers in the set ) . this means that numbers 7 and 8 in this set are 413 and 415 . because we know that number 7 is 413 , we know that the smallest number is 7 odd numbers below this , which means that it is 7 * 2 = 14 below this ( every odd number is every other number ) . therefore 413 - 14 = 399 , answer choice a ." | general |
math_qa__HmNrst4THfTfg4M9 | A car gets 30 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 200 kilometers? Choose one:
A) 3.5 gallons B) 2.7 gallons C) 6.7 gallons D) 4.5 gallons E) 7.5 gallons | <gadget id="calculator">200 / 30</gadget>
<output>20/3 = around 6.666667</output>
<result>C</result> | C | 6.7 | A car gets 30 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 200 kilometers? | {
"A": "3.5 gallons",
"B": "2.7 gallons",
"C": "6.7 gallons",
"D": "4.5 gallons",
"E": "7.5 gallons"
} | divide(200, 30) | divide(n1,n0)| | "each 30 kilometers , 1 gallon is needed . we need to know how many 30 kilometers are there in 200 kilometers ? 200 ã · 30 = 6.7 ã — 1 gallon = 6.7 gallons correct answer is c ) 6.7 gallons" | physics |
math_qa__SoHmlJ4BmocTlvBC | Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability W, that a book selected at random is either a hard cover book or a chemistry book?
Choose one
A) 1 / 10 B) 3 / 20 C) 1 / 5 D) 1 / 4 E) 9 / 20 | <gadget id="calculator">2 + 4</gadget>
<output>6</output>
<gadget id="calculator">2 + 6</gadget>
<output>8</output>
<gadget id="calculator">8 + 12</gadget>
<output>20</output>
<gadget id="calculator">2 / 20</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">8 / 20</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(1/10) + (2/5)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/10) * (2/5)</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/2) - (1/25)</gadget>
<output>23/50 = around 0.46</output>
<result>E</result> | E | 0.45 | Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability W, that a book selected at random is either a hard cover book or a chemistry book? | {
"A": "1 / 10",
"B": "3 / 20",
"C": "1 / 5",
"D": "1 / 4",
"E": "9 / 20"
} | subtract(add(divide(const_2, add(add(const_2, add(const_2, 4)), 12)), divide(add(const_2, add(const_2, 4)), add(add(const_2, add(const_2, 4)), 12))), multiply(divide(const_2, add(add(const_2, add(const_2, 4)), 12)), divide(add(const_2, add(const_2, 4)), add(add(const_2, add(const_2, 4)), 12)))) | add(n2,const_2)|add(#0,const_2)|add(n3,#1)|divide(const_2,#2)|divide(#1,#2)|add(#3,#4)|multiply(#3,#4)|subtract(#5,#6)| | "first phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf . to do so , you have the equations : m + p + c = 20 ( since 4 / 5 of the 25 spots are full of books ) m = 2 p p = 4 + c from that , you can use substitution to get everything down to one variable . c = p - 4 m = 2 p p = p then ( p - 4 ) + 2 p + p = 20 , so 4 p = 24 and p = 6 . that means that there are 12 math , 6 physics , and 2 chemistry books on the shelf . with those numbers , you also know that there are 8 total hardcovers , 1 of which is chemistry . so if your goal is to get either a hardcover or a chemistry , there are 9 ways towin - either one of the 7 hardcovers that are n ' t chemistry or the two chemistry books . so out of the 20 total , w = 9 provide the desired outcome , making the answer e ." | general |
math_qa__RbnahJVuHiqBGw9I | This year, MBB Consulting fired 10% of its employees and left remaining employee salaries unchanged. Sally, a first-year post-MBA consultant, noticed that that the average (arithmetic mean) of employee salaries at MBB was 10% more after the employee headcount reduction than before. The total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction? Pick
A) 99 %
B) 100.0 %
C) 102.8 %
D) 104.5 %
E) 105.0 % | <gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">100 + 1_000</gadget>
<output>1_100</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 + 4</gadget>
<output>94</output>
<gadget id="calculator">1_100 * 94</gadget>
<output>103_400</output>
<gadget id="calculator">103_400 / 1_000</gadget>
<output>517/5 = around 103.4</output>
<result>A</result> | A | 99 | This year, MBB Consulting fired 10% of its employees and left remaining employee salaries unchanged. Sally, a first-year post-MBA consultant, noticed that that the average (arithmetic mean) of employee salaries at MBB was 10% more after the employee headcount reduction than before. The total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction? | {
"A": "99 %",
"B": "100.0 %",
"C": "102.8 %",
"D": "104.5 %",
"E": "105.0 %"
} | divide(multiply(add(const_100, multiply(const_100, 10)), add(subtract(const_100, 10), const_4)), multiply(const_100, 10)) | multiply(n1,const_100)|subtract(const_100,n0)|add(#0,const_100)|add(#1,const_4)|multiply(#2,#3)|divide(#4,#0)| | "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 10 % reduction in employees lead to 90 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 90 employees is 90 * 1100 = 99000 now the new salary is more than previous salary by x % . x = ( 99000 / 100000 ) * 100 = 99 % so the answer is a" | general |
math_qa__IQmXcesawn7IX2iG | Real-estate salesman Z is selling a house at a 30 percent discount from its retail price. Real-estate salesman X vows to match this price, and then offers an additional 15 percent discount. Real-estate salesman Y decides to average the prices of salesmen Z and X, then offer an additional 40 percent discount. Salesman Y's final price is what fraction of salesman X's final price? Answers: A) 39 / 6 B) 62 / 11 C) 11 / 61 D) 21 / 61 E) 20 / 61 | <gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">70 * (17/20)</gadget>
<output>119/2 = around 59.5</output>
<gadget id="calculator">70 + (119/2)</gadget>
<output>259/2 = around 129.5</output>
<gadget id="calculator">(259/2) / 2</gadget>
<output>259/4 = around 64.75</output>
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">(259/4) * 60</gadget>
<output>3_885</output>
<gadget id="calculator">3_885 / 100</gadget>
<output>777/20 = around 38.85</output>
<gadget id="calculator">(777/20) / (119/2)</gadget>
<output>111/170 = around 0.652941</output>
<gadget id="calculator">(111/170) * 10</gadget>
<output>111/17 = around 6.529412</output>
<result>A</result> | A | 6.5 | Real-estate salesman Z is selling a house at a 30 percent discount from its retail price. Real-estate salesman X vows to match this price, and then offers an additional 15 percent discount. Real-estate salesman Y decides to average the prices of salesmen Z and X, then offer an additional 40 percent discount. Salesman Y's final price is what fraction of salesman X's final price? | {
"A": "39 / 6",
"B": "62 / 11",
"C": "11 / 61",
"D": "21 / 61",
"E": "20 / 61"
} | multiply(divide(divide(multiply(divide(add(subtract(const_100, 30), multiply(subtract(const_100, 30), divide(subtract(const_100, 15), const_100))), const_2), subtract(const_100, 40)), const_100), multiply(subtract(const_100, 30), divide(subtract(const_100, 15), const_100))), const_10) | subtract(const_100,n1)|subtract(const_100,n0)|subtract(const_100,n2)|divide(#0,const_100)|multiply(#3,#1)|add(#4,#1)|divide(#5,const_2)|multiply(#6,#2)|divide(#7,const_100)|divide(#8,#4)|multiply(#9,const_10) | let the retail price be = x selling price of z = 0.7 x selling price of x = 0.85 * 0.7 x = 0.60 x selling price of y = ( ( 0.7 x + 0.6 x ) / 2 ) * 0.60 = 0.65 x * 0.60 = 0.39 x 0.39 x = k * 0.60 x k = 0.39 / 0.6 = 39 / 6 answer : a | general |
math_qa__xv2PEG087N8ylyYh | In a certain alphabet, 11 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line? Choose the correct choice from the following
A) 5 B) 8 C) 14 D) 20 E) 28 | <gadget id="calculator">11 + 24</gadget>
<output>35</output>
<gadget id="calculator">40 - 35</gadget>
<output>5</output>
<result>A</result> | A | 5 | In a certain alphabet, 11 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line? | {
"A": "5",
"B": "8",
"C": "14",
"D": "20",
"E": "28"
} | subtract(40, add(11, 24)) | add(n0,n1)|subtract(n2,#0)| | "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 11 + 24 = 35 ; next , we find the total # of letters without line : 40 - 35 = 5 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 5 - 0 = 5 . a" | other |
math_qa__oypivIlJgBlVAVYs | The average weight of 30 boys sitting in a bus had some value. A new person added to them whose weight was 40 kg only. Due to his arrival, the average weight of all the boys decreased by 2 kg. Find the average weight of first 30 boys? Choose the most appropriate option
A) 150 B) 122 C) 30 D) 120 E) 102 | <gadget id="calculator">30 + 30</gadget>
<output>60</output>
<gadget id="calculator">40 + 60</gadget>
<output>100</output>
<gadget id="calculator">100 + 2</gadget>
<output>102</output>
<result>E</result> | E | 102 | The average weight of 30 boys sitting in a bus had some value. A new person added to them whose weight was 40 kg only. Due to his arrival, the average weight of all the boys decreased by 2 kg. Find the average weight of first 30 boys? | {
"A": "150",
"B": "122",
"C": "30",
"D": "120",
"E": "102"
} | add(add(40, add(30, 30)), 2) | add(n0,n0)|add(n1,#0)|add(n2,#1) | 30 x + 40 = 31 ( x â € “ 2 ) x = 102 e | general |
math_qa__6bzmbawu3608jmrx | The original price of a suit is $200. The price increased 25%, and after this increase, the store published a 25% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 25% off the increased price, how much did these consumers pay for the suit? Choose the correct choice from the following answers: A) $ 178.50 B) $ 182.50 C) $ 185.50 D) $ 187.50 E) $ 200 | <gadget id="calculator">200 * 25</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 / 100</gadget>
<output>50</output>
<gadget id="calculator">200 + 50</gadget>
<output>250</output>
<gadget id="calculator">250 * 25</gadget>
<output>6_250</output>
<gadget id="calculator">6_250 / 100</gadget>
<output>125/2 = around 62.5</output>
<gadget id="calculator">250 - (125/2)</gadget>
<output>375/2 = around 187.5</output>
<result>D</result> | D | 187.5 | The original price of a suit is $200. The price increased 25%, and after this increase, the store published a 25% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 25% off the increased price, how much did these consumers pay for the suit? | {
"A": "$ 178.50",
"B": "$ 182.50",
"C": "$ 185.50",
"D": "$ 187.50",
"E": "$ 200"
} | subtract(add(200, divide(multiply(200, 25), const_100)), divide(multiply(add(200, divide(multiply(200, 25), const_100)), 25), const_100)) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)|multiply(n1,#2)|divide(#3,const_100)|subtract(#2,#4)| | "0.75 * ( 1.25 * 200 ) = $ 187.50 the answer is d ." | general |
math_qa__NWp5CWpCow26hce4 | What is the maximum number R of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
Choose one:
A) 36
B) 32
C) 24
D) 21
E) 15 | <gadget id="calculator">9 / 3</gadget>
<output>3</output>
<gadget id="calculator">27 ** (1/3)</gadget>
<output>3</output>
<gadget id="calculator">12 / 3</gadget>
<output>4</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">8 / 3</gadget>
<output>8/3 = around 2.666667</output>
<gadget id="calculator">floor(8/3)</gadget>
<output>2</output>
<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<result>C</result> | C | 24 | What is the maximum number R of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ? | {
"A": "36",
"B": "32",
"C": "24",
"D": "21",
"E": "15"
} | multiply(multiply(divide(9, const_3), divide(12, cube_edge_by_volume(27))), floor(divide(8, cube_edge_by_volume(27)))) | cube_edge_by_volume(n0)|divide(n2,const_3)|divide(n1,#0)|divide(n3,#0)|floor(#2)|multiply(#1,#3)|multiply(#4,#5) | 27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get r = 24 cubes . ans . c | geometry |
math_qa__w8ZsHKTyABzJeQeD | if x/4-x-3/6=1,then find the value of x.
Choices:
A) 6
B) 4
C) 5
D) 1
E) 2 | <gadget id="calculator">3 / 6</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) + 1</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 4</gadget>
<output>6</output>
<result>A</result> | A | 6 | if x/4-x-3/6=1,then find the value of x. | {
"A": "6",
"B": "4",
"C": "5",
"D": "1",
"E": "2"
} | multiply(add(divide(3, 6), 1), 4) | divide(n1,n2)|add(n3,#0)|multiply(n0,#1) | ( x / 4 ) - ( ( x - 3 ) / 6 ) = 1 = > ( 3 x - 2 ( x - 3 ) ) / 12 = 1 = > 3 x - 2 x + 6 = 12 = > x = 6 . answer is a | general |
math_qa__MwXGafodYJp7VJyu | Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 42 more. What was his original selling price? Select.
A) $ 480 B) $ 570 C) $ 660 D) $ 720 E) $ 850 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">(9/10) * (13/10)</gadget>
<output>117/100 = around 1.17</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(117/100) - (11/10)</gadget>
<output>7/100 = around 0.07</output>
<gadget id="calculator">42 / (7/100)</gadget>
<output>600</output>
<gadget id="calculator">600 * (11/10)</gadget>
<output>660</output>
<result>C</result> | C | 660 | Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 42 more. What was his original selling price? | {
"A": "$ 480",
"B": "$ 570",
"C": "$ 660",
"D": "$ 720",
"E": "$ 850"
} | multiply(divide(42, subtract(multiply(subtract(const_1, divide(10, const_100)), add(const_1, divide(30, const_100))), add(const_1, divide(10, const_100)))), add(const_1, divide(10, const_100))) | divide(n0,const_100)|divide(n2,const_100)|add(#0,const_1)|add(#1,const_1)|subtract(const_1,#0)|multiply(#3,#4)|subtract(#5,#2)|divide(n3,#6)|multiply(#2,#7)| | "let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 42 0.07 = 42 p = 600 the original selling price was 600 * 1.1 = 660 . the correct answer is c ." | general |
math_qa__RH7jwuoW7CWU5CLB | X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.14300 ? Pick one: A) 3200 B) 4000 C) 3250 D) 4160 E) 3985 | <gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">48_000 * 8</gadget>
<output>384_000</output>
<gadget id="calculator">36_000 * 12</gadget>
<output>432_000</output>
<gadget id="calculator">42_000 * 12</gadget>
<output>504_000</output>
<gadget id="calculator">432_000 + 504_000</gadget>
<output>936_000</output>
<gadget id="calculator">936_000 + 384_000</gadget>
<output>1_320_000</output>
<gadget id="calculator">14_300 / 1_320_000</gadget>
<output>13/1_200 = around 0.010833</output>
<gadget id="calculator">384_000 * (13/1_200)</gadget>
<output>4_160</output>
<result>D</result> | D | 4,160 | X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.14300 ? | {
"A": "3200",
"B": "4000",
"C": "3250",
"D": "4160",
"E": "3985"
} | multiply(multiply(48000, subtract(multiply(const_3, 4), 4)), divide(14300, add(add(multiply(36000, multiply(const_3, 4)), multiply(42000, multiply(const_3, 4))), multiply(48000, subtract(multiply(const_3, 4), 4))))) | multiply(const_3,n2)|multiply(n0,#0)|multiply(n1,#0)|subtract(#0,n2)|add(#1,#2)|multiply(n3,#3)|add(#4,#5)|divide(n4,#6)|multiply(#7,#5)| | "ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 14300 ã — 16 / 55 = rs . 4160 . share of z in the profit is rs . 4160 . option d" | gain |
math_qa__QYEvTMMeTH6wEImc | In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (10, 0), (0, -3.5), (-10, 0)?
Choose the most appropriate option:
A) 56 B) 88 C) 70 D) 116 E) 120 | <gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">3.5 * 2</gadget>
<output>7</output>
<gadget id="calculator">(20 * 7) / 2</gadget>
<output>70</output>
<result>C</result> | C | 70 | In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (10, 0), (0, -3.5), (-10, 0)? | {
"A": "56",
"B": "88",
"C": "70",
"D": "116",
"E": "120"
} | rhombus_area(multiply(10, const_2), multiply(3.5, const_2)) | multiply(n2,const_2)|multiply(n1,const_2)|rhombus_area(#0,#1)| | "area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 10 + 10 = 20 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 20 * 7 = 70 c is the answer" | geometry |
math_qa__EKelXIbz0rjNRYyA | In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 10 overs to reach the target of 282 runs?
Choices:
A) 6.25 B) 5.5 C) 25 D) 15 E) 6 | <gadget id="calculator">10 * 3.2</gadget>
<output>32</output>
<gadget id="calculator">282 - 32</gadget>
<output>250</output>
<gadget id="calculator">250 / 10</gadget>
<output>25</output>
<result>C</result> | C | 25 | In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 10 overs to reach the target of 282 runs? | {
"A": "6.25",
"B": "5.5",
"C": "25",
"D": "15",
"E": "6"
} | divide(subtract(282, multiply(10, 3.2)), 10) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 10 run rate needed = 250 / 10 = 25 answer : option c" | gain |
math_qa__x1mbzF8Zjeg5MJ0e | If the cost price of 50 articles is equal to the selling price of 25 articles, then the gain or loss percent is? Pick.
A) 16 B) 127 C) 12 D) 18 E) 100 | <gadget id="calculator">100 * 25</gadget>
<output>2_500</output>
<gadget id="calculator">2_500 / 50</gadget>
<output>50</output>
<gadget id="calculator">100 - 50</gadget>
<output>50</output>
<gadget id="calculator">50 / 50</gadget>
<output>1</output>
<gadget id="calculator">100 * 1</gadget>
<output>100</output>
<result>E</result> | E | 100 | If the cost price of 50 articles is equal to the selling price of 25 articles, then the gain or loss percent is? | {
"A": "16",
"B": "127",
"C": "12",
"D": "18",
"E": "100"
} | multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 25), 50)), divide(multiply(const_100, 25), 50))) | multiply(n1,const_100)|divide(#0,n0)|subtract(const_100,#1)|divide(#2,#1)|multiply(#3,const_100)| | "percentage of profit = 25 / 25 * 100 = 100 % answer : e" | gain |
math_qa__xNAM6Z11064mnoO3 | Jake can dig a well in 16 days. Paul can dig the same well in 24 days. Jake, Paul and Hari together dig the well in 8 days. Hari alone can dig the well in
Choose the correct answer:
A) 96 days B) 48 days C) 32 days D) 24 days E) 28 days | <gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(1/16) + (1/24)</gadget>
<output>5/48 = around 0.104167</output>
<gadget id="calculator">(1/8) - (5/48)</gadget>
<output>1/48 = around 0.020833</output>
<gadget id="calculator">1 / (1/48)</gadget>
<output>48</output>
<result>B</result> | B | 48 | Jake can dig a well in 16 days. Paul can dig the same well in 24 days. Jake, Paul and Hari together dig the well in 8 days. Hari alone can dig the well in | {
"A": "96 days",
"B": "48 days",
"C": "32 days",
"D": "24 days",
"E": "28 days"
} | inverse(subtract(divide(const_1, 8), add(divide(const_1, 16), divide(const_1, 24)))) | divide(const_1,n2)|divide(const_1,n0)|divide(const_1,n1)|add(#1,#2)|subtract(#0,#3)|inverse(#4) | jake 1 day work = 1 / 16 paul 1 day work = 1 / 24 j + p + h 1 ady work = 1 / 8 1 / 16 + 1 / 24 + 1 / x = 1 / 8 1 / x = 1 / 48 x = 48 so , hari alone can dig the well in 48 days answer : b | physics |
math_qa__BIOpvfKf1QIfgj7g | 3 numbers are in the ratio 4 : 5 : 6 and their average is 20 . the largest number is :
Select the correct option:
A) 24 B) 32 C) 36 D) 42 E) 45 | <gadget id="calculator">4 + 5</gadget>
<output>9</output>
<gadget id="calculator">9 + 6</gadget>
<output>15</output>
<gadget id="calculator">15 / 3</gadget>
<output>5</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">4 * 6</gadget>
<output>24</output>
<result>A</result> | A | 24 | 3 numbers are in the ratio 4 : 5 : 6 and their average is 20 . the largest number is : | {
"A": "24",
"B": "32",
"C": "36",
"D": "42",
"E": "45"
} | multiply(divide(20, divide(add(add(4, 5), 6), 3)), 6) | add(n1,n2)|add(n3,#0)|divide(#1,n0)|divide(n4,#2)|multiply(n3,#3) | explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 20 15 x = 60 x = 4 largest number = 6 x = 24 . answer a | general |
math_qa__w3Joz9BlvFYHwgpJ | a father told his son ` ` i was as old as you are at present , at the time of your birth ' ' . if the father is 38 years old now , then what was the son ' s age 5 years ago in years ? Select.
A) 14 B) 19 C) 38 D) 33 E) 35 | <gadget id="calculator">38 / 2</gadget>
<output>19</output>
<gadget id="calculator">19 - 5</gadget>
<output>14</output>
<result>A</result> | A | 14 | a father told his son ` ` i was as old as you are at present , at the time of your birth ' ' . if the father is 38 years old now , then what was the son ' s age 5 years ago in years ? | {
"A": "14",
"B": "19",
"C": "38",
"D": "33",
"E": "35"
} | subtract(divide(38, const_2), 5) | divide(n0,const_2)|subtract(#0,n1) | et son ' s present age is = x then 38 - x = x x = 19 son ' s age 5 years back is 19 - 5 = 14 years . answer : a | general |
math_qa__qlVZ8Lj7iihUwh5e | The owner of a furniture shop charges his customer 25% more than the cost price. If a customer paid Rs. 5600 for a computer table, then what was the cost price of the computer table? Choose the correct choice from the following choices.
A) rs . 4480
B) rs . 5275
C) rs . 6275
D) rs . 6725
E) none of these | <gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 + (1/4)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">5_600 / (5/4)</gadget>
<output>4_480</output>
<result>A</result> | A | 4,480 | The owner of a furniture shop charges his customer 25% more than the cost price. If a customer paid Rs. 5600 for a computer table, then what was the cost price of the computer table? | {
"A": "rs . 4480",
"B": "rs . 5275",
"C": "rs . 6275",
"D": "rs . 6725",
"E": "none of these"
} | divide(5600, add(const_1, divide(25, const_100))) | divide(n0,const_100)|add(#0,const_1)|divide(n1,#1)| | "cp = sp * ( 100 / ( 100 + profit % ) ) = 5600 ( 100 / 125 ) = rs . 4480 . answer : a" | gain |
math_qa__EVMcON46hCAtmvwV | The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio o
Options.
A) 6 : 5 B) 4 : 7 C) 3 : 5 D) 5 : 7 E) 8 : 9 | <gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">12 / 10</gadget>
<output>6/5 = around 1.2</output>
<result>A</result> | A | 1.2 | The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio o | {
"A": "6 : 5",
"B": "4 : 7",
"C": "3 : 5",
"D": "5 : 7",
"E": "8 : 9"
} | divide(multiply(4, 3), multiply(5, 2)) | multiply(n0,n2)|multiply(n1,n3)|divide(#0,#1)| | "4 : 5 3 : 2 - - - - - - - 12 : 15 : 10 12 : 10 = = > 6.5 answer a" | other |
math_qa__x2eruYcb8vB3F60T | Last year, for every 100 million vehicles that traveled on a certain highway, 96 vehicles were involved in accidents. If 3 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000) Choose the correct choice from the following: A) 288 B) 320 C) 2,880 D) 3,200 E) 28,800 | <gadget id="calculator">3 * 10</gadget>
<output>30</output>
<gadget id="calculator">96 * 30</gadget>
<output>2_880</output>
<result>C</result> | C | 2,880 | Last year, for every 100 million vehicles that traveled on a certain highway, 96 vehicles were involved in accidents. If 3 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000) | {
"A": "288",
"B": "320",
"C": "2,880",
"D": "3,200",
"E": "28,800"
} | multiply(96, multiply(3, const_10)) | multiply(n2,const_10)|multiply(n1,#0) | to solve we will set up a proportion . we know that “ 100 million vehicles is to 96 accidents as 3 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 3,000 million rather than 3 billion . creating a proportion we have : 100 / 96 = 3,000 / x cross multiplying gives us : 100 x = 3,000 * 96 x = 30 * 96 = 2,880 correct answer is c . | general |
math_qa__btApo2MzHPMGk2Gl | 108. Triangle A’s base is 20% greater than the base of triangle B, and A’s height is 20% less than the height of triangle B. The area of triangle A is what percent less or more than the area of triangle B? Pick:
A) 0.25 % less
B) 1 % less
C) equal to each other
D) 1 % more
E) 9 % more | <gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">120 * 80</gadget>
<output>9_600</output>
<gadget id="calculator">10_000 - 9_600</gadget>
<output>400</output>
<gadget id="calculator">100 / 400</gadget>
<output>1/4 = around 0.25</output>
<result>A</result> | A | 0.25 | 108. Triangle A’s base is 20% greater than the base of triangle B, and A’s height is 20% less than the height of triangle B. The area of triangle A is what percent less or more than the area of triangle B? | {
"A": "0.25 % less",
"B": "1 % less",
"C": "equal to each other",
"D": "1 % more",
"E": "9 % more"
} | divide(const_100, subtract(multiply(const_100, const_100), multiply(add(const_100, 20), subtract(const_100, 20)))) | add(n1,const_100)|multiply(const_100,const_100)|subtract(const_100,n1)|multiply(#0,#2)|subtract(#1,#3)|divide(const_100,#4) | wish the question specified that we are talking about corresponding height . base of a = 21 / 20 * base of b height of a = 19 / 20 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 21 / 20 * 19 / 20 * area of b = 399 / 400 * area of b area of a is 0.25 % less than the area of b . answer ( a ) | geometry |
math_qa__cXt6NXJPRBaTOrSE | If N = 2^0.25 and N^b = 16, b must equal Pick one
A) 3 / 80 B) 3 / 5 C) 4 D) 16 E) 80 / 3 | <gadget id="calculator">log(16)</gadget>
<output>log(16) = around 2.772589</output>
<gadget id="calculator">2 ** 0.25</gadget>
<output>1.189207</output>
<gadget id="calculator">log(1.189207)</gadget>
<output>0.173287</output>
<gadget id="calculator">log(16) / 0.173287</gadget>
<output>5.77077334133547*log(16) = around 15.999981</output>
<result>D</result> | D | 16 | If N = 2^0.25 and N^b = 16, b must equal | {
"A": "3 / 80",
"B": "3 / 5",
"C": "4",
"D": "16",
"E": "80 / 3"
} | divide(log(16), log(power(2, 0.25))) | log(n2)|power(n0,n1)|log(#1)|divide(#0,#2)| | "25 / 100 = 1 / 4 n = 2 ^ 1 / 4 n ^ b = 2 ^ 4 ( 2 ^ 1 / 4 ) ^ b = 2 ^ 4 b = 16 answer : d" | general |
math_qa__ADpYPNaRpVk5NQD6 | in how many q ways can a 4 - letter password be chosen , using the letters a , b , c , d , e , and / or f , such that at least one letter is repeated within the password ?
Choose the correct choice from the following choices.
A) 720
B) 864
C) 900
D) 936
E) 1296 | <gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">36 * 25</gadget>
<output>900</output>
<result>D</result> | D | 936 | in how many q ways can a 4 - letter password be chosen , using the letters a , b , c , d , e , and / or f , such that at least one letter is repeated within the password ? | {
"A": "720",
"B": "864",
"C": "900",
"D": "936",
"E": "1296"
} | multiply(multiply(divide(divide(factorial(4), factorial(const_2)), factorial(const_2)), divide(divide(factorial(4), factorial(const_2)), factorial(const_2))), multiply(subtract(multiply(const_2, const_3), const_1), subtract(multiply(const_2, const_3), const_1))) | factorial(n0)|factorial(const_2)|multiply(const_2,const_3)|divide(#0,#1)|subtract(#2,const_1)|divide(#3,#1)|multiply(#4,#4)|multiply(#5,#5)|multiply(#7,#6) | total number of four letter passwords = 6 * 6 * 6 * 6 = 1296 - - - - - - ( 1 ) total number of passwords in which no letter repeats = 6 c 4 * 4 ! = 15 * 24 = 360 - - - - - - ( 2 ) therefore required value q = ( 1 ) - ( 2 ) = 1296 - 360 = 936 . d | general |
math_qa__T4Ud8wMd6bZF4Lgc | The distance between Delhi and Mathura is 150 kms. A starts from Delhi with a speed of 25 kmph at 5 a.m. for Mathura and B starts from Mathura with a speed of 40 kmph at 6 p.m. from Delhi. When will they meet?
Pick:
A) 11
B) 77
C) 8
D) 10
E) 12 | <gadget id="calculator">25 + 40</gadget>
<output>65</output>
<gadget id="calculator">150 / 65</gadget>
<output>30/13 = around 2.307692</output>
<gadget id="calculator">6 + (30/13)</gadget>
<output>108/13 = around 8.307692</output>
<result>C</result> | C | 8 | The distance between Delhi and Mathura is 150 kms. A starts from Delhi with a speed of 25 kmph at 5 a.m. for Mathura and B starts from Mathura with a speed of 40 kmph at 6 p.m. from Delhi. When will they meet? | {
"A": "11",
"B": "77",
"C": "8",
"D": "10",
"E": "12"
} | add(6, divide(150, add(25, 40))) | add(n1,n3)|divide(n0,#0)|add(n4,#1) | d = 150 – 25 = 125 rs = 40 + 25 = 65 t = 125 / 65 = 2 hours 6 a . m . + 2 = 8 a . m . . answer : c | physics |
math_qa__IW9AaBIfE2VSFKIn | Water boils at 212°F or 100°C and melts at 32°F or 0°C . If the temperature of the particular day is 35°C , it is equal to Choose the correct choice from the following options:
A) 50 ° f B) 76 ° f C) 95 ° f D) 110 ° f E) 120 ° f | <gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">212 - 32</gadget>
<output>180</output>
<gadget id="calculator">(7/20) * 180</gadget>
<output>63</output>
<gadget id="calculator">63 + 32</gadget>
<output>95</output>
<result>C</result> | C | 95 | Water boils at 212°F or 100°C and melts at 32°F or 0°C . If the temperature of the particular day is 35°C , it is equal to | {
"A": "50 ° f",
"B": "76 ° f",
"C": "95 ° f",
"D": "110 ° f",
"E": "120 ° f"
} | add(multiply(divide(35, 100), subtract(212, 32)), 32) | divide(n4,n1)|subtract(n0,n2)|multiply(#0,#1)|add(n2,#2) | let f and c denotes the temparature in fahrenheit anid celcsius respectively . then , ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) , if c = 35 , then f = 95 . c | physics |
math_qa__9Wckxt4zfvJqU5w0 | A man distributed Rs. 100 equally among his friends. If there had been 5 more friends, each would have received one rupee less. How many friends had he ?
Choose the correct choice.
A) 20
B) 25
C) 30
D) 35
E) 40 | <gadget id="calculator">100 / 5</gadget>
<output>20</output>
<gadget id="calculator">20 + 5</gadget>
<output>25</output>
<result>B</result> | B | 25 | A man distributed Rs. 100 equally among his friends. If there had been 5 more friends, each would have received one rupee less. How many friends had he ? | {
"A": "20",
"B": "25",
"C": "30",
"D": "35",
"E": "40"
} | add(divide(100, 5), 5) | divide(n0,n1)|add(n1,#0) | firstly we have 20 friends and money wiill be distribute each of them 5 rupee then 5 more friends it means total no frnd = 25 each recv 4 rupee which means all recv 1 less rupee answer : b | general |
math_qa__W6x56OBSwjhknONe | The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.6270.What was his original salary? Choose the correct choice from the following options
A) 6000
B) 2999
C) 1000
D) 2651
E) 1971 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 - (1/20)</gadget>
<output>19/20 = around 0.95</output>
<gadget id="calculator">(11/10) * (19/20)</gadget>
<output>209/200 = around 1.045</output>
<gadget id="calculator">6_270 / (209/200)</gadget>
<output>6_000</output>
<result>A</result> | A | 6,000 | The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.6270.What was his original salary? | {
"A": "6000",
"B": "2999",
"C": "1000",
"D": "2651",
"E": "1971"
} | divide(6270, multiply(add(const_1, divide(10, const_100)), subtract(const_1, divide(5, const_100)))) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|divide(n2,#4) | x * ( 110 / 100 ) * ( 95 / 100 ) = 6270 x * ( 11 / 10 ) * ( 1 / 100 ) = 66 x = 6000 answer : a | gain |
math_qa__KN10OYZ5FKs1EObw | The perimeter of one face of a cube is 28 cm. Its volume will be:
Choose the correct choice
A) 125 cm 3 B) 343 cm 3 C) 250 cm 3 D) 625 cm 3 E) none of these | <gadget id="calculator">28 / 4</gadget>
<output>7</output>
<gadget id="calculator">7 ** 3</gadget>
<output>343</output>
<result>B</result> | B | 343 | The perimeter of one face of a cube is 28 cm. Its volume will be: | {
"A": "125 cm 3",
"B": "343 cm 3",
"C": "250 cm 3",
"D": "625 cm 3",
"E": "none of these"
} | volume_cube(square_edge_by_perimeter(28)) | square_edge_by_perimeter(n0)|volume_cube(#0)| | "explanation : edge of cude = 28 / 4 = 7 cm volume = a * a * a = 7 * 7 * 7 = 343 cm cube option b" | geometry |
math_qa__OMRcCKNcQf3Et0Pa | The true discount on a bill of Rs.270 is Rs.45.The banker's discount is Choose the correct choice from the following answers.
A) 54 B) 55 C) 56 D) 57 E) none of these | <gadget id="calculator">270 - 45</gadget>
<output>225</output>
<gadget id="calculator">45 / 225</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 270</gadget>
<output>54</output>
<result>A</result> | A | 54 | The true discount on a bill of Rs.270 is Rs.45.The banker's discount is | {
"A": "54",
"B": "55",
"C": "56",
"D": "57",
"E": "none of these"
} | multiply(divide(45, subtract(270, 45)), 270) | subtract(n0,n1)|divide(n1,#0)|multiply(n0,#1) | solution p . w = rs . ( 270 - 45 ) = rs . 225 s . i on rs . 270 = rs . ( 45 / 225 x 270 ) = rs . 54 . answer a | gain |
math_qa__uxyzXdCvlEj6oq4v | A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter made instead a sandbox which was twice as long, twice as wide and twice as high as the original, what would the capacity be of the new larger sandbox?
Pick one.
A) 20 B) 40 C) 60 D) 80 E) 100 | <gadget id="calculator">2 ** 3</gadget>
<output>8</output>
<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<result>D</result> | D | 80 | A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter made instead a sandbox which was twice as long, twice as wide and twice as high as the original, what would the capacity be of the new larger sandbox? | {
"A": "20",
"B": "40",
"C": "60",
"D": "80",
"E": "100"
} | multiply(power(const_2, const_3), 10) | power(const_2,const_3)|multiply(n0,#0) | explanation : when all the dimensions of a three dimensional object are in fact doubled , then the capacity increases by a factor of 2 x 2 x 2 = 2 ^ 3 = 8 . thus the capacity of the new sandbox is 8 x 10 = 80 cubic feet . answer : option d | geometry |
math_qa__QH10Ym0Iq9Mm6UpD | A pipe can empty 2/3rd of a cistern in 12 mins. In 8 mins, what part of the cistern will be empty? Options
A) 2 / 3 B) 2 / 5 C) 4 / 9 D) 5 / 7 E) 4 / 11 | <gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 8</gadget>
<output>16/3 = around 5.333333</output>
<gadget id="calculator">(16/3) / 12</gadget>
<output>4/9 = around 0.444444</output>
<result>C</result> | C | 0.444444 | A pipe can empty 2/3rd of a cistern in 12 mins. In 8 mins, what part of the cistern will be empty? | {
"A": "2 / 3",
"B": "2 / 5",
"C": "4 / 9",
"D": "5 / 7",
"E": "4 / 11"
} | divide(multiply(divide(2, 3), 8), 12) | divide(n0,n1)|multiply(n3,#0)|divide(#1,n2)| | "2 / 3 - - - - 12 ? - - - - - 8 = = > 4 / 9 c" | physics |
math_qa__UOEmyzvRZzGDPOmF | If 20% of A is the same as 25% of B, then A : B is : Choose the correct option
A) 3 : 4 B) 4 : 3 C) 5 : 4 D) 6 : 7 E) 5 : 7 | <gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/4) / (1/5)</gadget>
<output>5/4 = around 1.25</output>
<result>C</result> | C | 1.25 | If 20% of A is the same as 25% of B, then A : B is : | {
"A": "3 : 4",
"B": "4 : 3",
"C": "5 : 4",
"D": "6 : 7",
"E": "5 : 7"
} | divide(divide(25, const_100), divide(20, const_100)) | divide(n1,const_100)|divide(n0,const_100)|divide(#0,#1)| | "expl : 20 % of a i = 25 % of b = 20 a / 100 = 25 b / 100 = 5 / 4 = 5 : 4 answer : c" | gain |
math_qa__ABQ1uI2HozsTciYG | A man buys an article for $100. and sells it for $120. Find the gain percent? Select
A) 10 % B) 15 % C) 25 % D) 20 % E) 30 % | <gadget id="calculator">100 / 100</gadget>
<output>1</output>
<gadget id="calculator">120 / 1</gadget>
<output>120</output>
<gadget id="calculator">120 - 100</gadget>
<output>20</output>
<result>D</result> | D | 20 | A man buys an article for $100. and sells it for $120. Find the gain percent? | {
"A": "10 %",
"B": "15 %",
"C": "25 %",
"D": "20 %",
"E": "30 %"
} | subtract(divide(120, divide(100, const_100)), const_100) | divide(n0,const_100)|divide(n1,#0)|subtract(#1,const_100)| | "c . p . = $ 100 s . p . = $ 120 gain = $ 20 gain % = 20 / 100 * 100 = 20 % answer is d" | gain |
math_qa__7AZvlB02gb5GRIYS | The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is Answers.
A) 45 kg B) 50 kg C) 53 kg D) 55 kg E) none of these | <gadget id="calculator">400 / 1_000</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">35 + (2/5)</gadget>
<output>177/5 = around 35.4</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<gadget id="calculator">(177/5) * 25</gadget>
<output>885</output>
<gadget id="calculator">24 * 35</gadget>
<output>840</output>
<gadget id="calculator">885 - 840</gadget>
<output>45</output>
<result>A</result> | A | 45 | The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is | {
"A": "45 kg",
"B": "50 kg",
"C": "53 kg",
"D": "55 kg",
"E": "none of these"
} | subtract(multiply(add(35, divide(400, const_1000)), add(24, const_1)), multiply(24, 35)) | add(n0,const_1)|divide(n2,const_1000)|multiply(n0,n1)|add(n1,#1)|multiply(#3,#0)|subtract(#4,#2)| | "solution weight of the teacher = ( 35.4 × 25 - 35 × 24 ) kg = 45 kg . answer a" | general |
math_qa__2eHAqav9ilkn2Tia | A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 25%? Choose the correct choice
A) 600 B) 887 C) 625 D) 654 E) 712 | <gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">500 * (1/4)</gadget>
<output>125</output>
<gadget id="calculator">500 + 125</gadget>
<output>625</output>
<result>C</result> | C | 625 | A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 25%? | {
"A": "600",
"B": "887",
"C": "625",
"D": "654",
"E": "712"
} | add(500, multiply(500, divide(25, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | "cost price = rs . 500 profit = 25 % of 500 = rs . 125 selling price = cost price + profit = 500 + 125 = 625 answer : c" | gain |
math_qa__uaWlB0f33NXDjpcE | If 28a+30b+31c=545.
then a+b+c=?.a,b,c are natural numbers
Choose the correct choice from the following options: A) 12 B) 14 C) 8 D) 25 E) 18 | <gadget id="calculator">545 / 31</gadget>
<output>545/31 = around 17.580645</output>
<result>E</result> | E | 18 | If 28a+30b+31c=545.
then a+b+c=?.a,b,c are natural numbers | {
"A": "12",
"B": "14",
"C": "8",
"D": "25",
"E": "18"
} | divide(545, 31) | divide(n3,n2) | have a look on your calender since , we all knw a year consist of 365 days february is d only month which has 28 days 4 months in a year has 30 days and , rest 7 months has 31 days . . so , following d given eq . we can write 28 * 1 + 30 * 10 + 31 * 7 . . hence values of a , b and c are 1 , 10 and 7 respectively . . a + b + c = 18 answer : e | general |
math_qa__6XLGHtGcYyZGXmDu | How many different ways can 2 students be seated in a row of 3 desks, so that there is always at least one empty desk between the students?
Choose the correct choice from the following answers.
A) 2 B) 3 C) 4 D) 6 E) 12 | <gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">factorial(2) / factorial(2 - 2)</gadget>
<output>2</output>
<result>A</result> | A | 2 | How many different ways can 2 students be seated in a row of 3 desks, so that there is always at least one empty desk between the students? | {
"A": "2",
"B": "3",
"C": "4",
"D": "6",
"E": "12"
} | permutation(subtract(3, const_1), 2) | subtract(n1,const_1)|permutation(#0,n0)| | "1 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 1 x 2 = 2 a" | probability |
math_qa__xD6OaX8ZbuvcbEMb | P and Q started a business investing Rs 75000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.
Options
A) 5 : 1
B) 17 : 3
C) 5 : 6
D) 17 : 7
E) 3 : 8 | <gadget id="calculator">75_000 / 15_000</gadget>
<output>5</output>
<result>A</result> | A | 5 | P and Q started a business investing Rs 75000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively. | {
"A": "5 : 1",
"B": "17 : 3",
"C": "5 : 6",
"D": "17 : 7",
"E": "3 : 8"
} | divide(75000, 15000) | divide(n0,n1)| | "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 75000 : 15000 = 75 : 15 = 5 : 1 option a" | gain |
math_qa__sSAVE5qpq3TjeT1L | The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is? Choose the correct choice: A) 56.8 m 2 B) 82.9 m 2 C) 52.8 m 2 D) 17.9 m 2 E) 72.9 m 2 | <gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 2</gadget>
<output>22</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>
<gadget id="calculator">144 * (22/7)</gadget>
<output>3_168/7 = around 452.571429</output>
<gadget id="calculator">3_600 / 10</gadget>
<output>360</output>
<gadget id="calculator">42 / 360</gadget>
<output>7/60 = around 0.116667</output>
<gadget id="calculator">(3_168/7) * (7/60)</gadget>
<output>264/5 = around 52.8</output>
<result>C</result> | C | 52.8 | The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is? | {
"A": "56.8 m 2",
"B": "82.9 m 2",
"C": "52.8 m 2",
"D": "17.9 m 2",
"E": "72.9 m 2"
} | multiply(multiply(power(12, const_2), divide(add(multiply(const_2, const_10), const_2), add(const_4, const_3))), divide(42, divide(const_3600, const_10))) | add(const_3,const_4)|divide(const_3600,const_10)|multiply(const_10,const_2)|power(n0,const_2)|add(#2,const_2)|divide(n1,#1)|divide(#4,#0)|multiply(#6,#3)|multiply(#5,#7)| | "42 / 360 * 22 / 7 * 12 * 12 = 52.8 m 2 answer : c" | geometry |
math_qa__VitK23FdgOwViPHv | The average weight of a group of boys is 35 kg. After a boy of weight 40 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? Answers:
A) 4 B) 5 C) 6 D) 7 E) 8 | <gadget id="calculator">35 + 1</gadget>
<output>36</output>
<gadget id="calculator">40 - 36</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<result>B</result> | B | 5 | The average weight of a group of boys is 35 kg. After a boy of weight 40 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? | {
"A": "4",
"B": "5",
"C": "6",
"D": "7",
"E": "8"
} | add(subtract(40, add(35, 1)), const_1) | add(n0,n2)|subtract(n1,#0)|add(#1,const_1) | let the number off boys in the group originally be x . total weight of the boys = 35 x after the boy weighing 40 kg joins the group , total weight of boys = 35 x + 40 so 35 x + 40 = 36 ( x + 1 ) = > x = 5 . answer : b | general |
math_qa__6SDsDqqXUsCak4qc | Points X, Y, and Z lie, in that order, on a straight railroad track. The distance from point X to point Y is twice the distance from point Y to point Z. A train traveled from point X to point Z without stopping. The train's average speed when traveling from point X to point Y was 100 miles per hour and the train's average speed when traveling from point Y to point Z was 75 miles per hour. What was the train's average speed, in miles per hour, when traveling from point X to point Z? Pick one: A) 90 B) 85 C) 85.5 D) 70 E) 90 | <gadget id="calculator">100 / 75</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">2 / (4/3)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) + 1</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">3 / (5/2)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) * 75</gadget>
<output>90</output>
<result>A</result> | A | 90 | Points X, Y, and Z lie, in that order, on a straight railroad track. The distance from point X to point Y is twice the distance from point Y to point Z. A train traveled from point X to point Z without stopping. The train's average speed when traveling from point X to point Y was 100 miles per hour and the train's average speed when traveling from point Y to point Z was 75 miles per hour. What was the train's average speed, in miles per hour, when traveling from point X to point Z? | {
"A": "90",
"B": "85",
"C": "85.5",
"D": "70",
"E": "90"
} | multiply(divide(const_3, add(divide(const_2, divide(100, 75)), const_1)), 75) | divide(n0,n1)|divide(const_2,#0)|add(#1,const_1)|divide(const_3,#2)|multiply(n1,#3)| | "average speed = distance / time because we are looking for average speed we can pick a distance for the variable d . speed x - y = 100 speed y - z = 75 average speed = total distance / total rate rate = distance / time x = = = = = = = = = = = = = = = = = = = = y = = = = = = = = = = z if x - y is twice the length of y - z then let x - y = 2 d and let y - z = d average speed = 3 d / ( 2 d / 100 ) + ( d / 75 ) 3 d / ( 6 d / 300 ) + ( 4 d / 300 ) 3 d / ( 10 d / 300 ) 900 d / 10 d average speed = 90 answer : a" | physics |
math_qa__ey6u6SiEVwzToAuW | If there are 200 questions in a 3 hr examination. Among these questions are 20 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? Options.
A) 72 min B) 62 min C) 70 min D) 32.72727 min E) 76 min | <gadget id="calculator">3 * 60</gadget>
<output>180</output>
<gadget id="calculator">200 - 20</gadget>
<output>180</output>
<gadget id="calculator">2 * 20</gadget>
<output>40</output>
<gadget id="calculator">180 + 40</gadget>
<output>220</output>
<gadget id="calculator">180 / 220</gadget>
<output>9/11 = around 0.818182</output>
<gadget id="calculator">2 * (9/11)</gadget>
<output>18/11 = around 1.636364</output>
<gadget id="calculator">(18/11) * 20</gadget>
<output>360/11 = around 32.727273</output>
<result>D</result> | D | 32.72727 | If there are 200 questions in a 3 hr examination. Among these questions are 20 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? | {
"A": "72 min",
"B": "62 min",
"C": "70 min",
"D": "32.72727 min",
"E": "76 min"
} | multiply(multiply(const_2, divide(multiply(3, const_60), add(subtract(200, 20), multiply(const_2, 20)))), 20) | multiply(n1,const_60)|multiply(n2,const_2)|subtract(n0,n2)|add(#1,#2)|divide(#0,#3)|multiply(#4,const_2)|multiply(n2,#5)| | "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 180 x + 20 * 2 x = 180 x = 180 / 220 x = 0.818182 time taken for type a problem = 20 * 2 * 0.818182 = 32.72727 min answer : d" | general |
math_qa__yeAlMvWCysifI0Rs | A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 36 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
Select:
A) 16 %
B) 32 %
C) 68 %
D) 84 %
E) 92 % | <gadget id="calculator">100 - 36</gadget>
<output>64</output>
<gadget id="calculator">64 / 2</gadget>
<output>32</output>
<gadget id="calculator">100 - 32</gadget>
<output>68</output>
<result>C</result> | C | 68 | A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 36 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ? | {
"A": "16 %",
"B": "32 %",
"C": "68 %",
"D": "84 %",
"E": "92 %"
} | subtract(const_100, divide(subtract(const_100, 36), const_2)) | subtract(const_100,n0)|divide(#0,const_2)|subtract(const_100,#1)| | "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 36 % is one st . dev , then on either side of m we have 36 / 2 = 18 % . so , 18 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 18 = 68 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 68 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it c" | general |
math_qa__dDEy7Xx6zJYGsOHO | Every student in a room is either a junior or a senior. There is at least one junior and at least one senior in the room. If 4/5 of the juniors is equal to 1/2 of the seniors, what fraction of the students in the room are juniors?
Pick one: A) 13 / 20 B) 11 / 3 C) 5 / 13 D) 12 / 17 E) 17 / 20 | <gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">2 + 25</gadget>
<output>27</output>
<gadget id="calculator">10 / 27</gadget>
<output>10/27 = around 0.37037</output>
<result>C</result> | C | 0.384615 | Every student in a room is either a junior or a senior. There is at least one junior and at least one senior in the room. If 4/5 of the juniors is equal to 1/2 of the seniors, what fraction of the students in the room are juniors? | {
"A": "13 / 20",
"B": "11 / 3",
"C": "5 / 13",
"D": "12 / 17",
"E": "17 / 20"
} | divide(multiply(5, const_2.0), add(2, multiply(5, 5))) | multiply(n2,n2)|add(n3,#0)|divide(#0,#1)| | "let total number of juniors = j total number of seniors = s ( 4 / 5 ) j = ( 1 / 2 ) s = > s = 8 / 5 j total number of students = j + s = ( 13 / 5 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 13 / 5 ) j ] = 5 / 13 answer c" | general |
math_qa__NRlTyIkDkyKwi55O | If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 40, what is the compound interest on the same sum at the rate and for the same time? Choose one.
A) s . 41.00
B) s . 51.22
C) s . 51.219
D) s . 41.18
E) s . 51.11 | <gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 2</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">40 / (1/10)</gadget>
<output>400</output>
<gadget id="calculator">400 * 5</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<gadget id="calculator">20 + 400</gadget>
<output>420</output>
<gadget id="calculator">420 * 5</gadget>
<output>2_100</output>
<gadget id="calculator">2_100 / 100</gadget>
<output>21</output>
<gadget id="calculator">420 + 21</gadget>
<output>441</output>
<gadget id="calculator">441 - 400</gadget>
<output>41</output>
<result>A</result> | A | 41 | If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 40, what is the compound interest on the same sum at the rate and for the same time? | {
"A": "s . 41.00",
"B": "s . 51.22",
"C": "s . 51.219",
"D": "s . 41.18",
"E": "s . 51.11"
} | subtract(add(add(divide(multiply(divide(40, multiply(divide(5, const_100), 2)), 5), const_100), divide(40, multiply(divide(5, const_100), 2))), divide(multiply(add(divide(multiply(divide(40, multiply(divide(5, const_100), 2)), 5), const_100), divide(40, multiply(divide(5, const_100), 2))), 5), const_100)), divide(40, multiply(divide(5, const_100), 2))) | divide(n1,const_100)|multiply(n0,#0)|divide(n2,#1)|multiply(n1,#2)|divide(#3,const_100)|add(#4,#2)|multiply(n1,#5)|divide(#6,const_100)|add(#5,#7)|subtract(#8,#2)| | "explanation : sum = ( 40 * 100 ) / ( 2 * 5 ) = rs . 400 amount = [ 400 * ( 1 + 5 / 100 ) 2 ] = rs . 441 c . i . = ( 441 - 400 ) = rs . 41 answer : a" | gain |
math_qa__5fbYxUzhU88POFgJ | Income and expenditure of a person are in the ratio 5:4. If the income of the person is Rs.18000, then find his savings? Choose one.
A) rs . 3600 B) rs . 3629 C) rs . 3279 D) rs . 3629 E) rs . 3283 | <gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 18_000</gadget>
<output>14_400</output>
<gadget id="calculator">18_000 - 14_400</gadget>
<output>3_600</output>
<result>A</result> | A | 3,600 | Income and expenditure of a person are in the ratio 5:4. If the income of the person is Rs.18000, then find his savings? | {
"A": "rs . 3600",
"B": "rs . 3629",
"C": "rs . 3279",
"D": "rs . 3629",
"E": "rs . 3283"
} | subtract(18000, multiply(divide(4, 5), 18000)) | divide(n1,n0)|multiply(n2,#0)|subtract(n2,#1)| | "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 18000 = > x = 3600 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3600 . answer : a" | other |
math_qa__pK3NjCdLkBmX6Jm7 | In a certain diving competition, 5 judges score each dive on a scale from 1 to 10. The point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty. If a dive with a degree of difficulty of 3.2 received scores of 7.5, 8.8, 9.0, 6.0, and 8.5, what was the point value of the dive? Choose the correct answer
A) 68.8 B) 73.6 C) 75.2 D) 76.8 E) 79.36 | <gadget id="calculator">7.5 + 8.8</gadget>
<output>16.3</output>
<gadget id="calculator">16.3 + 8.5</gadget>
<output>24.8</output>
<gadget id="calculator">24.8 * 3.2</gadget>
<output>79.36</output>
<result>E</result> | E | 79.36 | In a certain diving competition, 5 judges score each dive on a scale from 1 to 10. The point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty. If a dive with a degree of difficulty of 3.2 received scores of 7.5, 8.8, 9.0, 6.0, and 8.5, what was the point value of the dive? | {
"A": "68.8",
"B": "73.6",
"C": "75.2",
"D": "76.8",
"E": "79.36"
} | multiply(add(add(7.5, 8.8), 8.5), 3.2) | add(n4,n5)|add(n8,#0)|multiply(n3,#1)| | "degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.8 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8.8 + 8.5 ) = 24.8 point of value of the dive = 24 * 3.2 = 79.36 answer e" | general |
math_qa__4Cw0uq2au5PdHCdf | At the faculty of Aerospace Engineering, 310 students study Random-processing methods, 232 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering? Choose the correct choice:
A) 430 B) 432 C) 440 D) 442 E) 446 | <gadget id="calculator">112 / 2</gadget>
<output>56</output>
<gadget id="calculator">310 - 56</gadget>
<output>254</output>
<gadget id="calculator">232 - 56</gadget>
<output>176</output>
<gadget id="calculator">254 + 176</gadget>
<output>430</output>
<result>A</result> | A | 430 | At the faculty of Aerospace Engineering, 310 students study Random-processing methods, 232 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering? | {
"A": "430",
"B": "432",
"C": "440",
"D": "442",
"E": "446"
} | add(subtract(310, divide(112, const_2)), subtract(232, divide(112, const_2))) | divide(n2,const_2)|subtract(n0,#0)|subtract(n1,#0)|add(#1,#2)| | "310 + 232 - 112 ( since 112 is counted twice ) = 430 a is the answer" | other |
math_qa__ft5QB5XJ0Rho34kI | Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 12 times as heavy as water?
Pick one.
A) 1 : 2 B) 3 : 7 C) 4 : 1 D) 5 : 2 E) 6 : 5 | <gadget id="calculator">12 - 9</gadget>
<output>3</output>
<gadget id="calculator">19 - 12</gadget>
<output>7</output>
<gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>
<result>B</result> | B | 0.428571 | Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 12 times as heavy as water? | {
"A": "1 : 2",
"B": "3 : 7",
"C": "4 : 1",
"D": "5 : 2",
"E": "6 : 5"
} | divide(subtract(12, 9), subtract(19, 12)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)| | "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 12 w 19 + 9 x = 12 ( x + 1 ) x = 7 / 3 ratio of gold with copper = 1 : 7 / 3 = 3 : 7 answer is b" | general |
math_qa__bm3JPVhNc0mkEY5f | In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 14 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
Pick one:
A) 80 % B) 112 % C) 120 % D) 124.2 % E) 138 % | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">14 * (4/5)</gadget>
<output>56/5 = around 11.2</output>
<gadget id="calculator">(56/5) / 10</gadget>
<output>28/25 = around 1.12</output>
<gadget id="calculator">(28/25) * 100</gadget>
<output>112</output>
<result>B</result> | B | 112 | In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 14 percent of revenues. The profits in 2009 were what percent of the profits in 2008? | {
"A": "80 %",
"B": "112 %",
"C": "120 %",
"D": "124.2 %",
"E": "138 %"
} | multiply(divide(multiply(14, subtract(const_1, divide(20, const_100))), 10), const_100) | divide(n3,const_100)|subtract(const_1,#0)|multiply(n4,#1)|divide(#2,n1)|multiply(#3,const_100)| | "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,14 = 14 / 100 x = 80 * 14 / 100 x = 11.2 11.2 / 10 = 1,12 = 112 % , answer b" | gain |
math_qa__ds3JR6WLXz7Emc9v | What is the 100th digit of (3!*5! + 4!*3!)/2? Choose the correct choice from the following
A) 4 B) 3 C) 2 D) 7 E) 6 | <gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">factorial(5)</gadget>
<output>120</output>
<gadget id="calculator">6 * 120</gadget>
<output>720</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">24 * 6</gadget>
<output>144</output>
<gadget id="calculator">720 + 144</gadget>
<output>864</output>
<gadget id="calculator">864 / 2</gadget>
<output>432</output>
<gadget id="calculator">432 / 100</gadget>
<output>108/25 = around 4.32</output>
<gadget id="calculator">floor(108/25)</gadget>
<output>4</output>
<result>A</result> | A | 4 | What is the 100th digit of (3!*5! + 4!*3!)/2? | {
"A": "4",
"B": "3",
"C": "2",
"D": "7",
"E": "6"
} | floor(divide(divide(add(multiply(factorial(3), factorial(5)), multiply(factorial(4), factorial(3))), 2), 100)) | factorial(n1)|factorial(n2)|factorial(n3)|multiply(#0,#1)|multiply(#2,#0)|add(#3,#4)|divide(#5,n5)|divide(#6,n0)|floor(#7) | ( 3 ! * 5 ! + 4 ! * 3 ! ) / 2 = 3 ! ( 5 ! + 4 ! ) / 2 = 6 ( 120 + 24 ) / 2 = 432 100 th digit of the above product will be equal to 4 answer a | general |
math_qa__5f0PCQdugd7XBFa7 | The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 9408 sq. m, the cost of fencing the field @ 25 paise per metre is Choose one:
A) rs . 55.50
B) rs . 67.50
C) rs . 86.50
D) rs . 98.00
E) none of these | <gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">9_408 / 12</gadget>
<output>784</output>
<gadget id="calculator">784 ** (1/2)</gadget>
<output>28</output>
<gadget id="calculator">3 * 28</gadget>
<output>84</output>
<gadget id="calculator">4 * 28</gadget>
<output>112</output>
<gadget id="calculator">2 * (84 + 112)</gadget>
<output>392</output>
<gadget id="calculator">392 * 25</gadget>
<output>9_800</output>
<gadget id="calculator">9_800 / 100</gadget>
<output>98</output>
<result>D</result> | D | 98 | The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 9408 sq. m, the cost of fencing the field @ 25 paise per metre is | {
"A": "rs . 55.50",
"B": "rs . 67.50",
"C": "rs . 86.50",
"D": "rs . 98.00",
"E": "none of these"
} | divide(multiply(rectangle_perimeter(multiply(3, sqrt(divide(9408, multiply(3, 4)))), multiply(4, sqrt(divide(9408, multiply(3, 4))))), 25), const_100) | multiply(n0,n1)|divide(n2,#0)|sqrt(#1)|multiply(n0,#2)|multiply(n1,#2)|rectangle_perimeter(#3,#4)|multiply(n3,#5)|divide(#6,const_100) | solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 9408 ⇔ 12 x 2 = 9408 ⇔ x 2 = 784 ⇔ x = 28 . so , length = 84 m and breadth = 112 m . perimeter = [ 2 ( 84 + 112 ) ] m = 392 m . ∴ cost of fencing = rs . ( 0.25 × 392 ) = rs . 98.00 . answer d | physics |
math_qa__Oh6JqbhUUj6Eiq54 | An error 2%in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square? Choose the correct choice from the following answers
A) 4.04
B) 4.02
C) 4.01
D) 4.05
E) 4.06 | <gadget id="calculator">100 + 2</gadget>
<output>102</output>
<gadget id="calculator">102 ** 2</gadget>
<output>10_404</output>
<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>
<gadget id="calculator">10_404 - 10_000</gadget>
<output>404</output>
<gadget id="calculator">404 * 100</gadget>
<output>40_400</output>
<gadget id="calculator">40_400 / 10_000</gadget>
<output>101/25 = around 4.04</output>
<result>A</result> | A | 4.04 | An error 2%in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square? | {
"A": "4.04",
"B": "4.02",
"C": "4.01",
"D": "4.05",
"E": "4.06"
} | divide(multiply(subtract(square_area(add(const_100, 2)), square_area(const_100)), const_100), square_area(const_100)) | add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)| | "formula for calculation of percentage error is : = ( x − y − ( xy ) / 100 ) % = ( 2 + 2 + ( 2 × 2 ) / 100 ) % = 4.04 % answer is a ." | gain |
math_qa__gCXBvOuHz38ebRGY | At a certain university, 70% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured? Choose the correct answer:
A) 25
B) 37.5
C) 50
D) 62.5
E) 75 | <gadget id="calculator">100 - 70</gadget>
<output>30</output>
<gadget id="calculator">90 - 70</gadget>
<output>20</output>
<gadget id="calculator">30 + 20</gadget>
<output>50</output>
<result>C</result> | C | 50 | At a certain university, 70% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured? | {
"A": "25",
"B": "37.5",
"C": "50",
"D": "62.5",
"E": "75"
} | add(subtract(const_100, 70), subtract(90, 70)) | subtract(const_100,n0)|subtract(n2,n0)|add(#0,#1)| | "answer is 75 % total women = 70 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 20 % but question wants to know the percent of men that are tenured 20 % / 40 % = 50 % c" | gain |
math_qa__2LF9QhYbDe969NXR | If p and t are positive integers such that p > t > 1, what is the remainder when 92p × 5p+t + 11t × 6pt is divided by 10? Choose the most appropriate option
A) a . 0 B) b . 1 C) c . 3 D) d . 4 E) e . 5 | <gadget id="calculator">6 - 5</gadget>
<output>1</output>
<result>B</result> | B | 1 | If p and t are positive integers such that p > t > 1, what is the remainder when 92p × 5p+t + 11t × 6pt is divided by 10? | {
"A": "a . 0",
"B": "b . 1",
"C": "c . 3",
"D": "d . 4",
"E": "e . 5"
} | subtract(6, 5) | subtract(n4,n2) | 92 p × 5 p + t + 11 t × 6 pt - - 1 = b | general |
math_qa__mmhWW9rGU2dPkQmy | A person buys an article at Rs.350. At what price should he sell the article so as to make a profit of 30%? Pick one.
A) 455 B) 277 C) 269 D) 261 E) 281 | <gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">350 * (3/10)</gadget>
<output>105</output>
<gadget id="calculator">350 + 105</gadget>
<output>455</output>
<result>A</result> | A | 455 | A person buys an article at Rs.350. At what price should he sell the article so as to make a profit of 30%? | {
"A": "455",
"B": "277",
"C": "269",
"D": "261",
"E": "281"
} | add(350, multiply(350, divide(30, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | "cost price = rs . 350 profit = 30 % of 350 = rs . 105 selling price = cost price + profit = 350 + 105 = 455 answer : a" | gain |
math_qa__Az5Ic5ghGMtEmoAV | Two trains 140 m and 200 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? Choose the correct choice from the following answers:
A) 10.9 sec B) 10.1 sec C) 10.6 sec D) 10.8 sec E) 12.24 sec | <gadget id="calculator">140 + 200</gadget>
<output>340</output>
<gadget id="calculator">60 + 40</gadget>
<output>100</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">100 * (5/18)</gadget>
<output>250/9 = around 27.777778</output>
<gadget id="calculator">340 / (250/9)</gadget>
<output>306/25 = around 12.24</output>
<result>E</result> | E | 12.24 | Two trains 140 m and 200 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? | {
"A": "10.9 sec",
"B": "10.1 sec",
"C": "10.6 sec",
"D": "10.8 sec",
"E": "12.24 sec"
} | divide(add(140, 200), multiply(add(60, 40), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 200 = 340 m . required time = 340 * 9 / 250 = 12.24 sec . answer : e" | physics |
math_qa__DNal2UZbELMeFm3Q | How many cubes of 5 cm edge can be put in a cubical box of 1 m edge.
Choose the correct choice from the following options
A) 1770 cm B) 8000 cm C) 7860 cm D) 6170 cm E) 1870 cm | <gadget id="calculator">1 ** 3</gadget>
<output>1</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) ** 3</gadget>
<output>1/8_000 = around 0.000125</output>
<gadget id="calculator">1 / (1/8_000)</gadget>
<output>8_000</output>
<result>B</result> | B | 8,000 | How many cubes of 5 cm edge can be put in a cubical box of 1 m edge. | {
"A": "1770 cm",
"B": "8000 cm",
"C": "7860 cm",
"D": "6170 cm",
"E": "1870 cm"
} | divide(volume_cube(1), volume_cube(divide(5, const_100))) | divide(n0,const_100)|volume_cube(n1)|volume_cube(#0)|divide(#1,#2)| | "number of cubes = 100 â ˆ — 100 â ˆ — 100 / 5 * 5 * 5 = 8000 note : 1 m = 100 cm answer : b" | physics |
math_qa__el2v4ecVnwVKi9Es | There are 5 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total number of chess games possible to be played in the tournament?
Choose one:
A) 10
B) 20
C) 40
D) 60
E) 120 | <gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<result>A</result> | A | 10 | There are 5 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total number of chess games possible to be played in the tournament? | {
"A": "10",
"B": "20",
"C": "40",
"D": "60",
"E": "120"
} | divide(multiply(5, 4), const_2) | multiply(n0,n1)|divide(#0,const_2)| | "method 1 : take the first amateur . he plays a game with each of the other four i . e . 4 games . now take the second one . he has already played a game with the first one . he plays 3 games with the rest of the 3 amateurs i . e . 3 more games are played . now take the third amateur . he has already played a game each with the first and the second amateur . now he plays 2 games with the remaining 2 amateurs so 2 more games are played . now go on to the fourth amateur . he has already played 3 games with the first 3 amateurs . he just needs to play a game with the last one i . e . 1 more game is played . the last amateur has already played 4 games . total no of games = 4 + 3 + 2 + 1 = 10 method 2 : each person is one participant of 4 games . so there are in all 4 * 5 = 20 instances of one participant games . but each game has 2 participants so total number of games = 20 / 2 = 10 answer : a ." | general |
math_qa__9MO6sRi3NdzeRu5H | In a urban village of india named "owlna" , 75% people have refrigerator , 90% people have television , 85% people got computers and 75% got Air-conditionor. how many people(minimum) got all these luxury. Choices:
A) 23 %
B) 17 %
C) 11 %
D) 10 %
E) 25 % | <gadget id="calculator">100 - 75</gadget>
<output>25</output>
<gadget id="calculator">100 - 90</gadget>
<output>10</output>
<gadget id="calculator">25 + 10</gadget>
<output>35</output>
<gadget id="calculator">100 - 85</gadget>
<output>15</output>
<gadget id="calculator">35 + 15</gadget>
<output>50</output>
<gadget id="calculator">50 + 25</gadget>
<output>75</output>
<result>E</result> | E | 25 | In a urban village of india named "owlna" , 75% people have refrigerator , 90% people have television , 85% people got computers and 75% got Air-conditionor. how many people(minimum) got all these luxury. | {
"A": "23 %",
"B": "17 %",
"C": "11 %",
"D": "10 %",
"E": "25 %"
} | subtract(const_100, add(add(add(subtract(const_100, 75), subtract(const_100, 90)), subtract(const_100, 85)), subtract(const_100, 75))) | subtract(const_100,n0)|subtract(const_100,n1)|subtract(const_100,n2)|subtract(const_100,n3)|add(#0,#1)|add(#4,#2)|add(#5,#3)|subtract(const_100,#6)| | "e 10 % 100 - [ ( 100 - 75 ) + ( 100 - 90 ) + ( 100 - 85 ) + ( 100 - 75 ) ] = 100 - ( 25 + 10 + 15 + 25 ) = 100 - 75" | general |
math_qa__4wAuKIY7AKTG7iBx | A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 67 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used? Choose the correct option
A) 16 B) 20 C) 32 D) 44 E) 48 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 67</gadget>
<output>67/5 = around 13.4</output>
<gadget id="calculator">15 - (67/5)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) - (1/5)</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(8/5) / (1/20)</gadget>
<output>32</output>
<result>C</result> | C | 32 | A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 67 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used? | {
"A": "16",
"B": "20",
"C": "32",
"D": "44",
"E": "48"
} | divide(subtract(15, multiply(divide(20, const_100), 67)), subtract(divide(25, const_100), divide(20, const_100))) | divide(n0,const_100)|divide(n1,const_100)|multiply(n2,#0)|subtract(#1,#0)|subtract(n3,#2)|divide(#4,#3)| | "lets say x ounces of p is mixed with q . = > 67 - x ounces of q is present in the mixture ( as the total = 67 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 67 - x ) = 15 = > x = 35 = > 67 - 35 = 32 ounces of q is present in the mixture . answer is c ." | general |
math_qa__AQmxKshlhWv7QNTE | If $ 5,000 is invested in an account that earns 8% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?
Choose the correct choice from the following choices: A) $ 4 B) $ 8 C) $ 12 D) $ 16 E) $ 432 | <gadget id="calculator">8 * 1</gadget>
<output>8</output>
<result>B</result> | B | 8 | If $ 5,000 is invested in an account that earns 8% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest? | {
"A": "$ 4",
"B": "$ 8",
"C": "$ 12",
"D": "$ 16",
"E": "$ 432"
} | multiply(8, const_1) | multiply(n1,const_1)| | "solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.08 / 2 ) ^ 2 = 5408 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 8 / 100 ) = 5400 difference = 5408 - 5400 = 8 $ answer : b" | gain |
math_qa__KnL6gip1tnpmKYXL | The length of a rectangular garden is three times its width. If the area of the rectangular garden is 675 square meters, then what is the width of the rectangular garden?
Choose the most appropriate option:
A) 14 B) 15 C) 16 D) 17 E) 18 | <gadget id="calculator">675 / 3</gadget>
<output>225</output>
<gadget id="calculator">225 ** (1/2)</gadget>
<output>15</output>
<result>B</result> | B | 15 | The length of a rectangular garden is three times its width. If the area of the rectangular garden is 675 square meters, then what is the width of the rectangular garden? | {
"A": "14",
"B": "15",
"C": "16",
"D": "17",
"E": "18"
} | sqrt(divide(675, const_3)) | divide(n0,const_3)|sqrt(#0)| | "let x be the width of the garden . 3 x ^ 2 = 675 x ^ 2 = 225 x = 15 the answer is b ." | geometry |
math_qa__lzkXwQar34arTvyI | how many odd 3 - digit integers smaller than 500 are there such that all their digits are different ?
Choose the correct choice from the following answers.
A) 72 B) 88 C) 112 D) 122 E) 144 | <gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">factorial(9)</gadget>
<output>362_880</output>
<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">9 - 2</gadget>
<output>7</output>
<gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>
<gadget id="calculator">362_880 / 5_040</gadget>
<output>72</output>
<gadget id="calculator">500 - 100</gadget>
<output>400</output>
<gadget id="calculator">400 / 100</gadget>
<output>4</output>
<gadget id="calculator">72 * 4</gadget>
<output>288</output>
<gadget id="calculator">288 / 2</gadget>
<output>144</output>
<result>E</result> | E | 144 | how many odd 3 - digit integers smaller than 500 are there such that all their digits are different ? | {
"A": "72",
"B": "88",
"C": "112",
"D": "122",
"E": "144"
} | divide(multiply(divide(factorial(subtract(const_10, const_1)), factorial(subtract(subtract(const_10, const_1), subtract(3, const_1)))), divide(subtract(500, const_100), const_100)), const_2) | subtract(const_10,const_1)|subtract(n0,const_1)|subtract(n1,const_100)|divide(#2,const_100)|factorial(#0)|subtract(#0,#1)|factorial(#5)|divide(#4,#6)|multiply(#7,#3)|divide(#8,const_2) | case 1 : numbers starting with 1 1 _ _ the unit digit can take 4 numbers ( 3,5 , 7,9 ) to be odd so 4 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 4 = 32 case 2 : numbers starting with 2 2 _ _ the unit digit can take 5 numbers ( 1 , 3,5 , 7,9 ) to be odd so 5 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 5 = 40 case 3 : numbers starting with 3 3 _ _ the unit digit can take 4 numbers ( 1,5 , 7,9 ) to be odd so 4 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 4 = 32 case 4 : numbers starting with 4 4 _ _ the unit digit can take 5 numbers ( 1 , 3,5 , 7,9 ) to be odd so 5 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 5 = 40 hence 32 + 40 + 32 + 40 = 144 , correct answer is e | general |
math_qa__jJzt7KolXnPN52VH | A van takes 5 hours to cover a distance of 435 km. What speed in kph should the van maintain to cover the same distance in 3/2 of the previous time? Answers:
A) 50 B) 52 C) 54 D) 56 E) 58 | <gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 5</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">435 / (15/2)</gadget>
<output>58</output>
<result>E</result> | E | 58 | A van takes 5 hours to cover a distance of 435 km. What speed in kph should the van maintain to cover the same distance in 3/2 of the previous time? | {
"A": "50",
"B": "52",
"C": "54",
"D": "56",
"E": "58"
} | divide(435, multiply(divide(3, 2), 5)) | divide(n2,n3)|multiply(n0,#0)|divide(n1,#1)| | "( 3 / 2 ) * 5 = 7.5 hours 435 / 7.5 = 58 kph the answer is e ." | physics |
math_qa__wJDHesPXchNpx7LK | If the price of a TV is first decreased by 20% and then increased by 50%, then the net change in the price will be :
Pick.
A) 20 % increase
B) 10 % increase
C) 10 % decrease
D) 6 % increase
E) none of these | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">80 * 150</gadget>
<output>12_000</output>
<gadget id="calculator">12_000 / 100</gadget>
<output>120</output>
<gadget id="calculator">120 - 100</gadget>
<output>20</output>
<result>A</result> | A | 20 | If the price of a TV is first decreased by 20% and then increased by 50%, then the net change in the price will be : | {
"A": "20 % increase",
"B": "10 % increase",
"C": "10 % decrease",
"D": "6 % increase",
"E": "none of these"
} | subtract(divide(multiply(subtract(const_100, 20), add(const_100, 50)), const_100), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(#3,const_100)| | "explanation : solution : let the original price be rs . 100 . new final price = 150 % of ( 80 % of 100 ) = rs . 150 / 100 * 80 / 100 * 100 = rs . 120 . . ' . increase = 20 % answer : a" | general |
math_qa__JC3FxJkp5TW4ARRy | A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done? Choose one: A) 11 B) 5 C) 70 D) 11 E) 13 | <gadget id="calculator">40 - 30</gadget>
<output>10</output>
<gadget id="calculator">24 - 10</gadget>
<output>14</output>
<gadget id="calculator">14 - 4</gadget>
<output>10</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<result>D</result> | D | 11 | A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done? | {
"A": "11",
"B": "5",
"C": "70",
"D": "11",
"E": "13"
} | add(subtract(subtract(24, subtract(40, 30)), 4), const_1) | subtract(n2,n1)|subtract(n0,#0)|subtract(#1,n3)|add(#2,const_1) | x / 24 + x / 30 + x / 40 = 1 x = 11 days answer : d | physics |
math_qa__0syPBhZ7brVpRmNF | Of the 120 passengers on Flight 750, 45% are female. 10% of the passengers sit in first class, and the rest of the passengers sit in coach class. If 1/3 of the passengers in first class are male, how many females are there in coach class? Choose the most appropriate option
A) 44 B) 48 C) 46 D) 52 E) 56 | <gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">120 * (9/20)</gadget>
<output>54</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">120 * (1/10)</gadget>
<output>12</output>
<gadget id="calculator">12 / 3</gadget>
<output>4</output>
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">54 - 8</gadget>
<output>46</output>
<result>C</result> | C | 46 | Of the 120 passengers on Flight 750, 45% are female. 10% of the passengers sit in first class, and the rest of the passengers sit in coach class. If 1/3 of the passengers in first class are male, how many females are there in coach class? | {
"A": "44",
"B": "48",
"C": "46",
"D": "52",
"E": "56"
} | subtract(multiply(120, divide(45, const_100)), subtract(multiply(120, divide(10, const_100)), divide(multiply(120, divide(10, const_100)), 3))) | divide(n2,const_100)|divide(n3,const_100)|multiply(n0,#0)|multiply(n0,#1)|divide(#3,n5)|subtract(#3,#4)|subtract(#2,#5)| | "number of passengers on flight = 120 number of female passengers = . 45 * 120 = 54 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 54 - 8 = 46 answer c" | gain |
math_qa__cHh0GhRs09drar24 | If x is equal to the sum of the integers from 10 to 20, inclusive, and y is the number of EVEN integers from 10 to 20, inclusive, what is the value of x+y ?
Choose the correct choice from the following options: A) 171 B) 175 C) 180 D) 190 E) 200 | <gadget id="calculator">10 + 20</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<gadget id="calculator">20 - 10</gadget>
<output>10</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">15 * 11</gadget>
<output>165</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">165 + 6</gadget>
<output>171</output>
<result>A</result> | A | 171 | If x is equal to the sum of the integers from 10 to 20, inclusive, and y is the number of EVEN integers from 10 to 20, inclusive, what is the value of x+y ? | {
"A": "171",
"B": "175",
"C": "180",
"D": "190",
"E": "200"
} | add(multiply(divide(add(10, 20), const_2), add(subtract(20, 10), const_1)), add(divide(subtract(20, 10), const_2), const_1)) | add(n0,n1)|subtract(n1,n0)|add(#1,const_1)|divide(#1,const_2)|divide(#0,const_2)|add(#3,const_1)|multiply(#2,#4)|add(#5,#6) | sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 10 + ( 11 - 1 ) * 1 } = 11 * 15 = 165 = x number of even number = ( 20 - 10 ) / 2 + 1 = 6 = y x + y = 165 + 6 = 171 a | general |
math_qa__TJR8goBsQ5SBktIw | Find the least number which when divided by 33 and 8 leaves a remainder of 2 in each case. Choose the correct answer
A) 266 B) 268 C) 270 D) 272 E) 274 | <gadget id="calculator">lcm(33, 8)</gadget>
<output>264</output>
<gadget id="calculator">2 + 264</gadget>
<output>266</output>
<result>A</result> | A | 266 | Find the least number which when divided by 33 and 8 leaves a remainder of 2 in each case. | {
"A": "266",
"B": "268",
"C": "270",
"D": "272",
"E": "274"
} | add(2, lcm(33, 8)) | lcm(n0,n1)|add(n2,#0)| | "the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 33 , 8 ) + 2 = 266 . answer : a" | general |
math_qa__giWCjru2BpMapGQG | There are 4 runners on a track team who run an average of 4.5 seconds per 40 yards. If another runner joins their team who runs 4.3 seconds per 40 yards, what will the new average 40 yard time be? Choose the correct answer: A) 4.46 B) 4.39 C) 4.42 D) 4.49 E) 4.33 | <gadget id="calculator">4.5 + 4.3</gadget>
<output>8.8</output>
<gadget id="calculator">8.8 / 2</gadget>
<output>4.4</output>
<result>A</result> | A | 4.46 | There are 4 runners on a track team who run an average of 4.5 seconds per 40 yards. If another runner joins their team who runs 4.3 seconds per 40 yards, what will the new average 40 yard time be? | {
"A": "4.46",
"B": "4.39",
"C": "4.42",
"D": "4.49",
"E": "4.33"
} | divide(add(4.5, 4.3), const_2) | add(n1,n3)|divide(#0,const_2) | ( sum of the 4 times ) / 4 = 4.5 sum of the 4 times = 18 new sum = 18 + 4.3 = 22.3 new average = 22.3 / 5 = 4.46 ans : a | general |
math_qa__BYuV28TNKHMily1m | A train is moving at 4/5 of its usual speed. The train is 30 minutes too late. What is the usual time (in hours) for the train to complete the journey?
Choose the correct choice from the following answers
A) 1
B) 1.5
C) 2
D) 2.5
E) 3 | <gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">30 * (4/5)</gadget>
<output>24</output>
<gadget id="calculator">1 - (4/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / (1/5)</gadget>
<output>5</output>
<gadget id="calculator">24 * 5</gadget>
<output>120</output>
<gadget id="calculator">120 / 60</gadget>
<output>2</output>
<result>C</result> | C | 2 | A train is moving at 4/5 of its usual speed. The train is 30 minutes too late. What is the usual time (in hours) for the train to complete the journey? | {
"A": "1",
"B": "1.5",
"C": "2",
"D": "2.5",
"E": "3"
} | divide(multiply(multiply(30, divide(4, 5)), inverse(subtract(const_1, divide(4, 5)))), const_60) | divide(n0,n1)|multiply(n2,#0)|subtract(const_1,#0)|inverse(#2)|multiply(#3,#1)|divide(#4,const_60)| | "new time = d / ( 4 v / 5 ) = 5 / 4 * usual time 30 minutes represents 1 / 4 of the usual time . the usual time is 2 hours . the answer is c ." | physics |
math_qa__k05521xXo0thfbfP | The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 50 kms. what was the total distance traveled in 12 hours? Choose the correct choice from the following:
A) 252 kms
B) 152 kms
C) 732 kms
D) 752 kms
E) 152 kms | <gadget id="calculator">2 * 50</gadget>
<output>100</output>
<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">100 + 22</gadget>
<output>122</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">122 * 6</gadget>
<output>732</output>
<result>C</result> | C | 732 | The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 50 kms. what was the total distance traveled in 12 hours? | {
"A": "252 kms",
"B": "152 kms",
"C": "732 kms",
"D": "752 kms",
"E": "152 kms"
} | multiply(add(multiply(2, 50), multiply(subtract(12, const_1), 2)), divide(12, 2)) | divide(n2,n0)|multiply(n0,n1)|subtract(n2,const_1)|multiply(n0,#2)|add(#1,#3)|multiply(#4,#0)| | "explanation : total distance travelled in 12 hours = ( 50 + 52 + 54 + . . . . . upto 12 terms ) this is an a . p with first term , a = 50 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 50 + { 12 - 1 ) x 2 ] = 6 ( 122 ) = 732 kms . answer : c" | physics |
math_qa__GHMmv4qPsEeIl7qx | If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $90. If Greg buys 7 shirts, 2 trousers and 2 ties, the total cost is $50. How much will it cost him to buy 3 trousers, 5 shirts and 2 ties? Choose the correct choice from the following options: A) $ 60 B) $ 70 C) $ 75 D) $ 96 E) can not be determined | <gadget id="calculator">50 + 90</gadget>
<output>140</output>
<gadget id="calculator">140 / 2</gadget>
<output>70</output>
<result>B</result> | B | 70 | If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $90. If Greg buys 7 shirts, 2 trousers and 2 ties, the total cost is $50. How much will it cost him to buy 3 trousers, 5 shirts and 2 ties? | {
"A": "$ 60",
"B": "$ 70",
"C": "$ 75",
"D": "$ 96",
"E": "can not be determined"
} | divide(add(50, 90), 2) | add(n3,n7)|divide(#0,n2)| | "solution : 3 x + 4 y + 2 z = 90 7 x + 2 y + 2 z = 50 adding both the equations = 10 x + 6 y + 4 z = 140 5 x + 3 y + 2 z = 70 ans b" | general |
math_qa__HoEw9SO2o0EHajdu | In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 8% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy? Choose the correct choice from the following
A) 22 % B) 23.9 % C) 24 % D) 25 % E) 34 % | <gadget id="calculator">100 - 8</gadget>
<output>92</output>
<gadget id="calculator">92 / 100</gadget>
<output>23/25 = around 0.92</output>
<gadget id="calculator">22 / (23/25)</gadget>
<output>550/23 = around 23.913043</output>
<result>B</result> | B | 23.9 | In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 8% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy? | {
"A": "22 %",
"B": "23.9 %",
"C": "24 %",
"D": "25 %",
"E": "34 %"
} | divide(22, divide(subtract(const_100, 8), const_100)) | subtract(const_100,n1)|divide(#0,const_100)|divide(n0,#1)| | "since 8 % of the customers who sample the candyare notcaught , then 88 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.92 = 0.22 ; { % of customers who sample candy } = 0.239 . answer : b ." | gain |
math_qa__HnZBWl89mRnjC8Bw | A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for? Choose one.
A) 12 days B) 12 1 / 4 days C) 14 days D) 24 1 / 2 days E) none of these | <gadget id="calculator">1 / 21</gadget>
<output>1/21 = around 0.047619</output>
<gadget id="calculator">1 / 28</gadget>
<output>1/28 = around 0.035714</output>
<gadget id="calculator">(1/21) + (1/28)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>A</result> | A | 12 | A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for? | {
"A": "12 days",
"B": "12 1 / 4 days",
"C": "14 days",
"D": "24 1 / 2 days",
"E": "none of these"
} | divide(const_1, add(divide(const_1, 21), divide(const_1, 28))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2) | let total money be rs . x a ' s 1 day ' s wages = rs . x / 21 , b ' s 1 day ' s wages = rs . x / 28 ( a + b ) ' s 1 day ' s wages = rs . ( x / 21 + x / 28 ) = rs . x / 12 ; money is sufficient to pay the wages of both for 12 days . correct option : a | general |
math_qa__IvoDPGqW4RAq2bZm | In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 24. What is the total number of students in the school? Select the correct option
A) 50
B) 80
C) 120
D) 150
E) 100 | <gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">24 * (2/3)</gadget>
<output>16</output>
<gadget id="calculator">24 + 16</gadget>
<output>40</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">40 / (4/5)</gadget>
<output>50</output>
<result>A</result> | A | 50 | In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 24. What is the total number of students in the school? | {
"A": "50",
"B": "80",
"C": "120",
"D": "150",
"E": "100"
} | divide(add(24, multiply(24, divide(2, 3))), subtract(const_1, divide(20, const_100))) | divide(n3,n4)|divide(n0,const_100)|multiply(n6,#0)|subtract(const_1,#1)|add(n6,#2)|divide(#4,#3)| | "explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 24 + 2 / 3 of 24 80 / 100 x = 40 x = 50 . answer : option a" | general |
math_qa__dYNXJmxBrMvQyGx9 | The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is: Choices: A) 28 B) 32 C) 40 D) 53 E) 54 | <gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">48 / 6</gadget>
<output>8</output>
<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">24 + 16</gadget>
<output>40</output>
<result>C</result> | C | 40 | The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is: | {
"A": "28",
"B": "32",
"C": "40",
"D": "53",
"E": "54"
} | add(multiply(divide(48, multiply(2, 3)), 3), multiply(divide(48, multiply(2, 3)), 2)) | multiply(n1,n2)|divide(n0,#0)|multiply(n2,#1)|multiply(n1,#1)|add(#2,#3)| | "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 48 or x = 8 . the numbers are 16 and 24 . hence , required sum = ( 16 + 24 ) = 40 . answer : option c" | other |
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