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value | _fasttext_score float64 1 1 | reasoning stringlengths 1.44k 69.7k | deepseek_solution stringlengths 185 2.46k | __original_row_idx int64 34 31.6k | final_reasoning_trace stringlengths 1.84k 71.4k | conversations listlengths 2 2 |
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[
{
"content": "Let $A$ equal the number of four digit odd numbers. Let $B$ equal the number of four digit multiples of 5. Find $A+B$.",
"role": "user"
},
{
"content": "First, let's count the number of four-digit odd numbers $A$.\n\nA four-digit number is odd if and only if its last digit is odd, i.... | Let $A$ equal the number of four digit odd numbers. Let $B$ equal the number of four digit multiples of 5. Find $A+B$. | Let $A$ equal the number of four digit odd numbers. Let $B$ equal the number of four digit multiples of 5. Find $A+B$. | ai2-adapt-dev/openmath-2-math | 0.999995 | Alright, let's tackle this problem step by step. So, we need to find A, the number of four-digit odd numbers, and B, the number of four-digit multiples of 5. Then, we have to add them together to get A + B. Let me start by understanding each part separately.
First, let's figure out what a four-digit number is. A four-... | To find \(A\), the number of four-digit odd numbers, we note that the last digit must be one of the odd digits (1, 3, 5, 7, 9). Therefore, the number of choices for each digit is as follows:
- Thousands place: 9 choices (1-9)
- Hundreds place: 10 choices (0-9)
- Tens place: 10 choices (0-9)
- Ones place: 5 choices (1, ... | 21,380 | <think>
Alright, let's tackle this problem step by step. So, we need to find A, the number of four-digit odd numbers, and B, the number of four-digit multiples of 5. Then, we have to add them together to get A + B. Let me start by understanding each part separately.
First, let's figure out what a four-digit number is.... | [
{
"from": "human",
"value": "Let $A$ equal the number of four digit odd numbers. Let $B$ equal the number of four digit multiples of 5. Find $A+B$."
},
{
"from": "gpt",
"value": "<think>\nAlright, let's tackle this problem step by step. So, we need to find A, the number of four-digit odd numbe... |
[
{
"content": "In convex quadrilateral $ABCD$, $\\angle A = \\angle C$, $AB=CD=180$, and $AD \\ne BC$. The perimeter of $ABCD$ is 640. Find $\\cos A$.",
"role": "user"
},
{
"content": "In the given convex quadrilateral $ABCD$, $\\angle A = \\angle C$ and $AB = CD = 180$. We are also given that the p... | In convex quadrilateral $ABCD$, $\angle A = \angle C$, $AB=CD=180$, and $AD \ne BC$. The perimeter of $ABCD$ is 640. Find $\cos A$. | In convex quadrilateral $ABCD$, $\angle A = \angle C$, $AB=CD=180$, and $AD \ne BC$. The perimeter of $ABCD$ is 640. Find $\cos A$. | ai2-adapt-dev/openmath-2-math | 1.000004 | Okay, let's see. So we have this convex quadrilateral ABCD. The problem states that angle A is equal to angle C, sides AB and CD are each 180 units long, and the perimeter is 640. Also, AD is not equal to BC. We need to find cos A.
First, let's summarize the given information:
- Convex quadrilateral ABCD.
- ∠A = ∠C.
... | Given a convex quadrilateral \(ABCD\) with \(\angle A = \angle C\), \(AB = CD = 180\), and a perimeter of 640, we need to find \(\cos A\).
First, we note that the perimeter of \(ABCD\) is 640. Since \(AB + CD = 360\), the remaining sides \(BC\) and \(DA\) must sum to \(640 - 360 = 280\). Let \(BC = x\) and \(DA = y\)... | 31,119 | <think>
Okay, let's see. So we have this convex quadrilateral ABCD. The problem states that angle A is equal to angle C, sides AB and CD are each 180 units long, and the perimeter is 640. Also, AD is not equal to BC. We need to find cos A.
First, let's summarize the given information:
- Convex quadrilateral ABCD.
- ∠... | [
{
"from": "human",
"value": "In convex quadrilateral $ABCD$, $\\angle A = \\angle C$, $AB=CD=180$, and $AD \\ne BC$. The perimeter of $ABCD$ is 640. Find $\\cos A$."
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. So we have this convex quadrilateral ABCD. The problem states that angle ... |
[{"content":"In triangle $ABC$, the angle bisectors of angles $A$ and $B$ intersect at point $I$. Th(...TRUNCATED) | "In triangle $ABC$, the angle bisectors of angles $A$ and $B$ intersect at point $I$. The perpendicu(...TRUNCATED) | "In triangle $ABC$, the angle bisectors of angles $A$ and $B$ intersect at point $I$. The perpendicu(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | 0.999988 | "Alright, so I have this geometry problem here. Let me read it again and try to visualize what's goi(...TRUNCATED) | "Given triangle \\(ABC\\) with \\(\\angle ACB = 68^\\circ\\), the angle bisectors of angles \\(A\\) (...TRUNCATED) | 5,666 | "<think>\nAlright, so I have this geometry problem here. Let me read it again and try to visualize w(...TRUNCATED) | [{"from":"human","value":"In triangle $ABC$, the angle bisectors of angles $A$ and $B$ intersect at (...TRUNCATED) |
[{"content":"How many four-digit numbers have at least one pair of consecutive digits that are equal(...TRUNCATED) | How many four-digit numbers have at least one pair of consecutive digits that are equal? | How many four-digit numbers have at least one pair of consecutive digits that are equal? | ai2-adapt-dev/openmath-2-math | 1.000002 | "Okay, so I need to figure out how many four-digit numbers have at least one pair of consecutive dig(...TRUNCATED) | "To determine how many four-digit numbers have at least one pair of consecutive digits that are equa(...TRUNCATED) | 23,362 | "<think>\nOkay, so I need to figure out how many four-digit numbers have at least one pair of consec(...TRUNCATED) | [{"from":"human","value":"How many four-digit numbers have at least one pair of consecutive digits t(...TRUNCATED) |
[{"content":"What digit $B$ will make the number $27B3$ divisible by $3$?","role":"user"},{"content"(...TRUNCATED) | What digit $B$ will make the number $27B3$ divisible by $3$? | What digit $B$ will make the number $27B3$ divisible by $3$? | ai2-adapt-dev/openmath-2-math | 1.00001 | "Okay, so I need to figure out what digit B should be in the number 27B3 to make it divisible by 3. (...TRUNCATED) | "To determine the digit \\( B \\) that will make the number \\( 27B3 \\) divisible by 3, we use the (...TRUNCATED) | 22,583 | "<think>\nOkay, so I need to figure out what digit B should be in the number 27B3 to make it divisib(...TRUNCATED) | [{"from":"human","value":"What digit $B$ will make the number $27B3$ divisible by $3$?"},{"from":"gp(...TRUNCATED) |
[{"content":"How many three-digit positive integers have at least two digits the same?","role":"user(...TRUNCATED) | How many three-digit positive integers have at least two digits the same? | How many three-digit positive integers have at least two digits the same? | ai2-adapt-dev/openmath-2-math | 1.000003 | "Okay, so I need to figure out how many three-digit positive integers have at least two digits that (...TRUNCATED) | "To determine how many three-digit positive integers have at least two digits the same, we can use t(...TRUNCATED) | 22,498 | "<think>\nOkay, so I need to figure out how many three-digit positive integers have at least two dig(...TRUNCATED) | [{"from":"human","value":"How many three-digit positive integers have at least two digits the same?"(...TRUNCATED) |
[{"content":"For how many positive integers $x$ is $100 \\leq x^2 \\leq 200$?","role":"user"},{"cont(...TRUNCATED) | For how many positive integers $x$ is $100 \leq x^2 \leq 200$? | For how many positive integers $x$ is $100 \leq x^2 \leq 200$? | ai2-adapt-dev/openmath-2-math | 1.000001 | "Okay, so I need to find how many positive integers x satisfy the inequality 100 ≤ x² ≤ 200. Hm(...TRUNCATED) | "To determine how many positive integers \\( x \\) satisfy the inequality \\( 100 \\leq x^2 \\leq 20(...TRUNCATED) | 4,620 | "<think>\nOkay, so I need to find how many positive integers x satisfy the inequality 100 ≤ x² (...TRUNCATED) | [{"from":"human","value":"For how many positive integers $x$ is $100 \\leq x^2 \\leq 200$?"},{"from"(...TRUNCATED) |
[{"content":"Find the value of $\\sec 135^\\circ$.","role":"user"},{"content":"Recall that $\\sec \\(...TRUNCATED) | Find the value of $\sec 135^\circ$. | Find the value of $\sec 135^\circ$. | ai2-adapt-dev/openmath-2-math | 1.000009 | "Okay, so I need to find the value of sec 135 degrees. Hmm, let me remember what secant is. I think (...TRUNCATED) | "To find the value of \\(\\sec 135^\\circ\\), we start by recognizing that \\(\\sec \\theta = \\frac(...TRUNCATED) | 9,095 | "<think>\nOkay, so I need to find the value of sec 135 degrees. Hmm, let me remember what secant is.(...TRUNCATED) | [{"from":"human","value":"Find the value of $\\sec 135^\\circ$."},{"from":"gpt","value":"<think>\nOk(...TRUNCATED) |
[{"content":"Compute the value of $\\sin 105^\\circ$.","role":"user"},{"content":"To find $\\sin 105(...TRUNCATED) | Compute the value of $\sin 105^\circ$. | Compute the value of $\sin 105^\circ$. | ai2-adapt-dev/openmath-2-math | 1.000009 | "Okay, so I need to compute the value of sin 105 degrees. Hmm, 105 degrees isn't one of the standard(...TRUNCATED) | "To compute the value of \\(\\sin 105^\\circ\\), we can use the sine addition formula. We recognize (...TRUNCATED) | 14,648 | "<think>\nOkay, so I need to compute the value of sin 105 degrees. Hmm, 105 degrees isn't one of the(...TRUNCATED) | [{"from":"human","value":"Compute the value of $\\sin 105^\\circ$."},{"from":"gpt","value":"<think>\(...TRUNCATED) |
[{"content":"Determine the greatest integer value of $x$ such that $|x^2-3x+2|<10$.","role":"user"},(...TRUNCATED) | Determine the greatest integer value of $x$ such that $|x^2-3x+2|<10$. | Determine the greatest integer value of $x$ such that $|x^2-3x+2|<10$. | ai2-adapt-dev/openmath-2-math | 1.000005 | "Okay, so I need to figure out the greatest integer value of x such that the absolute value of x squ(...TRUNCATED) | "To determine the greatest integer value of \\( x \\) such that \\( |x^2 - 3x + 2| < 10 \\), we star(...TRUNCATED) | 901 | "<think>\nOkay, so I need to figure out the greatest integer value of x such that the absolute value(...TRUNCATED) | [{"from":"human","value":"Determine the greatest integer value of $x$ such that $|x^2-3x+2|<10$."},{(...TRUNCATED) |
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