qid stringlengths 1 6 | question stringlengths 12 5.02k | latent_states listlengths 1 21 | answer_digits listlengths 5 5 | num_latents int32 0 20 | k_max int32 20 20 | K_star int32 0 20 |
|---|---|---|---|---|---|---|
0 | Given that the graph of the function $y=f(x)$ is symmetric to curve $C$ about the $y$-axis, and after shifting curve $C$ 1 unit to the left, we obtain the graph of the function $y=\log_{2}(-x-a)$. If $f(3)=1$, then the real number $a=$ ． | [
[
-0.328125,
-0.10791015625,
0.1875,
-1.65625,
-0.4375,
-0.2734375,
-2.1875,
-0.349609375,
2.0625,
0.96484375,
-0.421875,
-1.734375,
1.5546875,
0.1728515625,
-0.58203125,
2.109375,
-0.1611328125,
-1.171875,
-1.171875,
-0.34765625,
0... | [
0,
0,
0,
0,
2
] | 5 | 20 | 5 |
1 | If a person walks at 15 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance traveled by him? | [
[
-1.53125,
-0.78125,
0.169921875,
-0.470703125,
-0.875,
0.87109375,
-1,
-0.6015625,
0.6171875,
-0.7109375,
-0.125,
-2.078125,
1.734375,
1.8359375,
0.7421875,
0.89453125,
-0.75,
0.2177734375,
-0.578125,
0.51171875,
1.3671875,
-1... | [
0,
0,
0,
4,
0
] | 1 | 20 | 1 |
6 | The moon has a surface area that is 1/5 that of Earth. The surface area of the Earth is 200 square acres. The land on the moon is worth 6 times that of the land on the Earth. If the total value of all the land on the earth is 80 billion dollars, what is the total value in billions of all the land on the moon? | [
[
-1.375,
-0.76171875,
0.9296875,
-1.015625,
-1.5625,
1.765625,
-1.6328125,
-1.0625,
2.0625,
-1.5,
0.3828125,
-1.34375,
2.453125,
0.1708984375,
0.296875,
1.515625,
0.6015625,
0.484375,
-2.15625,
-0.9296875,
1.28125,
-0.63671875,... | [
0,
0,
0,
9,
6
] | 2 | 20 | 2 |
13 | "(1) Calculate: $\\int_{-2}^{2}{\\sqrt{4-{x}^{2}}}dx=$\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_.\n\n(2) I(...TRUNCATED) | [[2.453125,3.890625,-1.0078125,-3.4375,1.1875,-4.875,-0.1845703125,3.765625,-0.466796875,2.1875,-1.0(...TRUNCATED) | [
0,
0,
0,
0,
6
] | 2 | 20 | 2 |
14 | "It was Trevor's job to collect fresh eggs from the family's 4 chickens every morning. He got some e(...TRUNCATED) | [[-0.53125,-0.515625,0.68359375,-2.09375,-2.484375,1.7421875,-2.359375,0.07080078125,1.4140625,-1.18(...TRUNCATED) | [
0,
0,
0,
0,
4
] | 13 | 20 | 13 |
15 | "A man is 18 years older than his son. In two years, his age will be twice the age of his son. What (...TRUNCATED) | [[-1.40625,-0.58203125,0.71484375,-0.447265625,-0.025390625,-0.1455078125,-1.9765625,0.318359375,0.2(...TRUNCATED) | [
0,
0,
0,
1,
6
] | 1 | 20 | 1 |
18 | "For an odd function $f(x)$ with the domain of all real numbers $\\mathbb{R}$, find the value of $f((...TRUNCATED) | [[-0.06201171875,1.9921875,0.1123046875,0.609375,0.5234375,0.42578125,-1.296875,2.203125,2.828125,-1(...TRUNCATED) | [
0,
0,
0,
0,
0
] | 1 | 20 | 1 |
19 | "Tom decides to take some dance lessons that cost $10 each, but he gets two of them for free. He pay(...TRUNCATED) | [[-1.28125,-0.8828125,0.6015625,-1.4375,-2.625,1.390625,-0.83984375,0.271484375,1.3046875,0.12402343(...TRUNCATED) | [
0,
0,
0,
1,
0
] | 1 | 20 | 1 |
25 | "For an ellipse centered at point (2, -1) with a semi-major axis of 5 units and a semi-minor axis of(...TRUNCATED) | [[-0.76953125,-0.578125,0.9140625,-0.419921875,-1.734375,0.5859375,-1.9140625,-0.171875,2.03125,-1.6(...TRUNCATED) | [
0,
0,
0,
0,
8
] | 1 | 20 | 1 |
27 | "In a bag, there are 3 red balls and 2 white balls. If two balls are drawn successively without repl(...TRUNCATED) | [[-0.8515625,0.10888671875,0.466796875,-1.90625,-1.1171875,-1.5703125,-0.6796875,-0.007049560546875,(...TRUNCATED) | [
0,
0,
0,
0,
1
] | 6 | 20 | 6 |
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