idx int64 | problem string | answer string | solution string | response_1 string | response_2 string | response_3 string | response_4 string | response_5 string | response_6 string | response_7 string | response_8 string | n_correct int64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
22,000 | "Two sectors of a circle of radius $15$ overlap in the same manner as the original problem, with $P$(...TRUNCATED) | \frac{225\pi - 450\sqrt{2}}{4} | "<think>\nOkay, so I need to find the area of the shaded region where two sectors of a circle with r(...TRUNCATED) | "<think>\nOkay, so I need to find the area of the shaded region where two sectors of a circle with r(...TRUNCATED) | "<think>\nOkay, so I need to find the area of the shaded region where two sectors of a circle with r(...TRUNCATED) | "<think>\nOkay, so I need to find the area of the shaded region where two sectors of a circle with r(...TRUNCATED) | "<think>\nOkay, so I need to find the area of the shaded region where two sectors of a circle with r(...TRUNCATED) | "<think>\nOkay, so I need to find the area of the shaded region where two sectors of a circle with r(...TRUNCATED) | "<think>\nOkay, so I need to find the area of the shaded region where two sectors of a circle with r(...TRUNCATED) | "<think>\nOkay, so I need to find the area of the shaded region where two sectors of a circle with r(...TRUNCATED) | 0 | |
22,001 | "Let $\\triangle XYZ$ be a right triangle with $\\angle Y$ as the right angle. A circle with a diame(...TRUNCATED) | 4.5 | "<think>\nOkay, so I need to solve this geometry problem. Let me try to visualize it first. There's (...TRUNCATED) | "<think>\nOkay, let's try to solve this geometry problem. So, we have a right triangle XYZ with the (...TRUNCATED) | "<think>\nOkay, so I need to solve this geometry problem. Let me first try to visualize the triangle(...TRUNCATED) | "<think>\nOkay, so I need to solve this geometry problem. Let me try to visualize it first. There's (...TRUNCATED) | "<think>\nOkay, so I need to solve this geometry problem. Let me try to visualize it first. There's (...TRUNCATED) | "<think>\nOkay, so I need to solve this geometry problem. Let me try to visualize it first. There's (...TRUNCATED) | "<think>\nOkay, so I need to find the length of ZW in this right triangle XYZ where angle Y is the r(...TRUNCATED) | "<think>\nOkay, so I need to find the length of ZW in this right triangle XYZ where angle Y is the r(...TRUNCATED) | 8 | |
22,002 | "If the inequality system about $x$ is $\\left\\{\\begin{array}{l}{\\frac{x+3}{2}≥x-1}\\\\{3x+6＞(...TRUNCATED) | -3 | "<think>\nOkay, let's try to solve this problem step by step. The problem has two parts: an inequali(...TRUNCATED) | "<think>\nOkay, let's try to tackle this problem step by step. First, let me make sure I understand (...TRUNCATED) | "<think>\nOkay, let's try to tackle this problem step by step. First, let me make sure I understand (...TRUNCATED) | "<think>\nOkay, let's try to tackle this problem step by step. It's a bit complex with two inequalit(...TRUNCATED) | "<think>\nOkay, let's try to solve this problem step by step. First, let me make sure I understand t(...TRUNCATED) | "<think>\nOkay, let's try to tackle this problem step by step. First, let me make sure I understand (...TRUNCATED) | "<think>\nOkay, let's try to tackle this problem step by step. First, I need to understand what's be(...TRUNCATED) | "<think>\nOkay, let's try to solve this problem step by step. First, let me make sure I understand t(...TRUNCATED) | 7 | |
22,003 | "Sunshine High School is planning to order a batch of basketballs and jump ropes from an online stor(...TRUNCATED) | 5700 | "<think>\nOkay, let's tackle this problem step by step. So, Sunshine High School wants to buy 40 bas(...TRUNCATED) | "<think>\nOkay, let's tackle this problem step by step. So, Sunshine High School wants to buy 40 bas(...TRUNCATED) | "<think>\nOkay, let's tackle this problem step by step. It's about comparing two stores, A and B, fo(...TRUNCATED) | "<think>\nOkay, let's tackle this problem step by step. So, Sunshine High School wants to buy 40 bas(...TRUNCATED) | "<think>\nOkay, let's try to solve this problem step by step. First, let me make sure I understand t(...TRUNCATED) | "<think>\nOkay, let's try to solve this problem step by step. First, let me make sure I understand t(...TRUNCATED) | "<think>\nOkay, let's tackle this problem step by step. So, Sunshine High School wants to buy 40 bas(...TRUNCATED) | "<think>\nOkay, let's try to figure out this problem step by step. So, Sunshine High School wants to(...TRUNCATED) | 3 | |
22,004 | "In a bus station in the city, there are 10 waiting seats arranged in a row. Now, if 4 passengers ra(...TRUNCATED) | 480 | "<think>\nOkay, so I need to figure out how many ways 4 passengers can choose seats in a row of 10 s(...TRUNCATED) | "<think>\nOkay, let's try to figure out this problem. So, there are 10 seats in a row in a bus stati(...TRUNCATED) | "<think>\nOkay, so there's this problem about a bus station with 10 seats in a row. Four passengers (...TRUNCATED) | "<think>\nOkay, so there's this problem about a bus station with 10 seats in a row. Four passengers (...TRUNCATED) | "<think>\nOkay, so there's this problem about a bus station with 10 seats in a row. Four passengers (...TRUNCATED) | "<think>\nOkay, so I need to figure out how many ways 4 passengers can choose seats in a row of 10 s(...TRUNCATED) | "<think>\nOkay, let's try to figure out this problem. So, there are 10 seats in a row in a bus stati(...TRUNCATED) | "<think>\nOkay, so there's this problem about a bus station with 10 seats in a row. Four passengers (...TRUNCATED) | 8 | |
22,005 | "Quadrilateral $EFGH$ has right angles at $F$ and $H$, and $EG = 5$. If $EFGH$ has two sides with di(...TRUNCATED) | 12 | "<think>\nOkay, so I need to find the area of quadrilateral EFGH. Let me start by understanding the (...TRUNCATED) | "<think>\nOkay, let's try to figure out the area of quadrilateral EFGH. The problem says it has righ(...TRUNCATED) | "<think>\nOkay, so I need to find the area of quadrilateral EFGH. The problem says it has right angl(...TRUNCATED) | "<think>\nOkay, so I need to find the area of quadrilateral EFGH. Let me try to visualize this first(...TRUNCATED) | "<think>\nOkay, so I need to find the area of quadrilateral EFGH. Let me try to visualize it first. (...TRUNCATED) | "<think>\nOkay, so I need to find the area of quadrilateral EFGH. Let me start by understanding the (...TRUNCATED) | "<think>\nOkay, let's try to figure out the area of quadrilateral EFGH. The problem says it has righ(...TRUNCATED) | "<think>\nOkay, so I need to find the area of quadrilateral EFGH. The problem says it has right angl(...TRUNCATED) | 6 | |
22,006 | "Find $B^2$, where $B$ is the sum of the absolute values of all roots of the equation:\n\\[x = \\sqr(...TRUNCATED) | 502 | "<think>\nOkay, so I need to find B squared, where B is the sum of the absolute values of all roots (...TRUNCATED) | "<think>\nOkay, let's try to tackle this problem. So, we need to find B squared, where B is the sum (...TRUNCATED) | "<think>\nOkay, so I need to find B squared, where B is the sum of the absolute values of all roots (...TRUNCATED) | "<think>\nOkay, so I need to find B squared, where B is the sum of the absolute values of all roots (...TRUNCATED) | "<think>\nOkay, so I need to find B squared, where B is the sum of the absolute values of all roots (...TRUNCATED) | "<think>\nOkay, so I need to find B squared, where B is the sum of the absolute values of all roots (...TRUNCATED) | "<think>\nOkay, let's try to tackle this problem. So, we need to find B squared, where B is the sum (...TRUNCATED) | "<think>\nOkay, so I need to find B squared, where B is the sum of the absolute values of all roots (...TRUNCATED) | 2 | |
22,007 | "Subtract $256.26$ from $512.52$ and then multiply the result by $3$. Express the final result as a (...TRUNCATED) | 768.78 | "<think>\nOkay, let's see. I need to subtract 256.26 from 512.52 first, and then multiply the result(...TRUNCATED) | "<think>\nOkay, let's see. I need to subtract 256.26 from 512.52 and then multiply the result by 3. (...TRUNCATED) | "<think>\nOkay, let's see. I need to subtract 256.26 from 512.52 and then multiply the result by 3. (...TRUNCATED) | "<think>\nOkay, let's see. I need to subtract 256.26 from 512.52 and then multiply the result by 3. (...TRUNCATED) | "<think>\nOkay, let's see. I need to subtract 256.26 from 512.52 and then multiply the result by 3. (...TRUNCATED) | "<think>\nOkay, let's see. I need to subtract 256.26 from 512.52 and then multiply the result by 3. (...TRUNCATED) | "<think>\nOkay, let's see. I need to subtract 256.26 from 512.52 and then multiply the result by 3. (...TRUNCATED) | "<think>\nOkay, let's see. I need to subtract 256.26 from 512.52 and then multiply the result by 3. (...TRUNCATED) | 8 | |
22,008 | "Given two numbers, a and b, are randomly selected within the interval (-π, π), determine the prob(...TRUNCATED) | \dfrac{3}{4} | "<think>\nOkay, so I need to find the probability that the quadratic function f(x) = x² + 2a x - b(...TRUNCATED) | "<think>\nOkay, so I need to find the probability that the function f(x) = x² + 2a x - b² + π has(...TRUNCATED) | "<think>\nOkay, so I need to find the probability that the quadratic function f(x) = x² + 2a x - b(...TRUNCATED) | "<think>\nOkay, so I need to find the probability that the quadratic function f(x) = x² + 2a x - b(...TRUNCATED) | "<think>\nOkay, so I need to find the probability that the function f(x) = x² + 2a x - b² + π has(...TRUNCATED) | "<think>\nOkay, so I need to find the probability that the quadratic function f(x) = x² + 2a x - b(...TRUNCATED) | "<think>\nOkay, so I need to find the probability that the function f(x) = x² + 2a x - b² + π has(...TRUNCATED) | "<think>\nOkay, so I need to find the probability that the function f(x) = x² + 2a x - b² + π has(...TRUNCATED) | 0 | |
22,009 | "Two distinct positive integers $a$ and $b$ are factors of 48. If $a\\cdot b$ is not a factor of 48,(...TRUNCATED) | 18 | "<think>\nOkay, so I need to find two distinct positive integers a and b that are factors of 48, suc(...TRUNCATED) | "<think>\nOkay, let's try to figure out this problem. So, we have two distinct positive integers a a(...TRUNCATED) | "<think>\nOkay, so I need to find two distinct positive integers a and b that are factors of 48, suc(...TRUNCATED) | "<think>\nOkay, so I need to find two distinct positive integers a and b that are factors of 48, suc(...TRUNCATED) | "<think>\nOkay, so I need to find two distinct positive integers a and b that are factors of 48, suc(...TRUNCATED) | "<think>\nOkay, so I need to find two distinct positive integers a and b that are factors of 48, suc(...TRUNCATED) | "<think>\nOkay, so I need to find two distinct positive integers a and b that are factors of 48, suc(...TRUNCATED) | "<think>\nOkay, so I need to find two distinct positive integers a and b that are factors of 48, suc(...TRUNCATED) | 8 |
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