instruction_seed string | response_seed string | reasoning string | deepseek_solution string | __original_row_idx int64 | source string | final_reasoning_trace string | conversations list | text string | difficulty float64 | topic string | r1_solution_1 string | r1_solution_2 string | r1_solution_3 string | generated_solution string | problem_source string | solution string | is_correct bool | solution_steps sequence | rtg sequence | undiscounted_rtg sequence | target_answer string | completion int64 | trajectory int64 | reference_answer string | responses list | input string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Determine the total number of triangles formed when connecting the midpoints of opposite sides of an X and its diagonals. If we know the answer to the above question is 24, what is the value of unknown variable X? | To find the number of triangles formed when connecting the midpoints of opposite sides of an X and its diagonals, let's first visualize the structure that we are analyzing. An 'X' is typically formed by connecting two intersecting lines (diagonals), which creates four angles and thus splits the area into several region... | Alright, let me try to figure out this problem. So, the question is about determining the total number of triangles formed when connecting the midpoints of opposite sides of an X and its diagonals. We know the answer is 24, and we need to find the value of X. Hmm, okay, let's break this down step by step.
First, I nee... | To determine the value of \( X \) such that the total number of triangles formed when connecting the midpoints of opposite sides of an \( X \)-sided polygon and its diagonals is 24, we start by considering the structure of the polygon and the effect of connecting midpoints and diagonals.
1. **Visualizing the Polygon**... | 31,946 | MetaMath-AIME | <think>
Alright, let me try to figure out this problem. So, the question is about determining the total number of triangles formed when connecting the midpoints of opposite sides of an X and its diagonals. We know the answer is 24, and we need to find the value of X. Hmm, okay, let's break this down step by step.
Firs... | [
{
"from": "human",
"value": "Determine the total number of triangles formed when connecting the midpoints of opposite sides of an X and its diagonals. If we know the answer to the above question is 24, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nAlright, let ... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
"statement 1": Sita can knit the same in 6 days, "statement 2" :Sita can knit the same in more than 5 days, "options: " Entailment or contradiction or neutral? Let's program in Python in the response. | null | Okay, let's tackle this problem. So, we have two statements about Sita's knitting time. Statement 1 says she can knit the same in 6 days. Statement 2 claims she can do it in more than 5 days. We need to determine if these two statements entail each other, contradict each other, or are neutral.
First, let's parse the s... | To determine the relationship between the two statements, we analyze their numerical values and logical implications.
**Step-by-Step Explanation:**
1. **Statement 1:** Sita can knit in exactly 6 days.
2. **Statement 2:** Sita can knit in more than 5 days.
3. **Analysis:** Since 6 days (Statement 1) is strictly greater... | null | TIGER-Lab/MathInstruct | <think>
Okay, let's tackle this problem. So, we have two statements about Sita's knitting time. Statement 1 says she can knit the same in 6 days. Statement 2 claims she can do it in more than 5 days. We need to determine if these two statements entail each other, contradict each other, or are neutral.
First, let's par... | [
{
"from": "human",
"value": " \"statement 1\": Sita can knit the same in 6 days, \"statement 2\" :Sita can knit the same in more than 5 days, \"options: \" Entailment or contradiction or neutral? Let's program in Python in the response."
},
{
"from": "gpt",
"value": "<think>\nOkay, let's tackle ... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
A lecture began at 10:30 a.m. and continued for X minutes. The lecture finished at 4:00. What is the value of the unknown variable X? | To solve this problem, we need to determine how many minutes the lecture lasted from its start time until its end time.
Let's break down the information given:
- The lecture began at 10:30 a.m.
- The lecture finished at 4:00 p.m.
1. First, we need to find the total duration of the lecture from 10:30 a.m. to 4... | Okay, let me see. The problem says that a lecture started at 10:30 a.m. and continued for X minutes, ending at 4:00 p.m. I need to find X. Hmm, time problems can sometimes be tricky because of the different hours and minutes, but let me break it down step by step.
First, let me figure out how much time passed between ... | The lecture started at 10:30 a.m. and finished at 4:00 p.m. To find the duration \( X \) in minutes, we calculate the time difference between 10:30 a.m. and 4:00 p.m.
1. Convert the times to a 24-hour format:
- 10:30 a.m. is 10:30.
- 4:00 p.m. is 16:00.
2. Subtract the start time from the end time:
- Hours: ... | 21,792 | MetaMath-AIME | <think>
Okay, let me see. The problem says that a lecture started at 10:30 a.m. and continued for X minutes, ending at 4:00 p.m. I need to find X. Hmm, time problems can sometimes be tricky because of the different hours and minutes, but let me break it down step by step.
First, let me figure out how much time passed ... | [
{
"from": "human",
"value": "A lecture began at 10:30 a.m. and continued for X minutes. The lecture finished at 4:00. What is the value of the unknown variable X?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let me see. The problem says that a lecture started at 10:30 a.m. and continued for X m... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
The equation of motion for a body is given by $$s = \frac{1}{4}t^4 - 3$$. Calculate the instantaneous velocity at t = 5. | null | Okay, so I need to find the instantaneous velocity at t = 5 for the equation of motion given by s = (1/4)t⁴ - 3. Hmm, let me think. I remember that in calculus, the instantaneous velocity is the derivative of the position function with respect to time. So, basically, I need to find the derivative of s with respect to t... | To find the instantaneous velocity at \( t = 5 \) for the equation of motion \( s = \frac{1}{4}t^4 - 3 \), we need to compute the derivative of the position function \( s \) with respect to time \( t \).
1. **Differentiate the position function**:
- The first term is \( \frac{1}{4}t^4 \). Using the power rule, the ... | null | AI-MO/NuminaMath-1.5 | <think>
Okay, so I need to find the instantaneous velocity at t = 5 for the equation of motion given by s = (1/4)t⁴ - 3. Hmm, let me think. I remember that in calculus, the instantaneous velocity is the derivative of the position function with respect to time. So, basically, I need to find the derivative of s with resp... | [
{
"from": "human",
"value": "The equation of motion for a body is given by $$s = \\frac{1}{4}t^4 - 3$$. Calculate the instantaneous velocity at t = 5."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the instantaneous velocity at t = 5 for the equation of motion given by s = (1/4)... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
If each of the five advertisements shown during a televised race lasted 3 minutes and the cost of advertising is $4000 per minute, what was the total cost of transmitting these advertisements during the race? | Each advertisement lasted 3 minutes, so the total duration of all 5 advertisements is 3 minutes x 5 advertisements = 15 minutes.
The cost of advertising is $4000 per minute, so the total cost of transmitting the advertisements is $4000 x 15 minutes = $60000.
#### 60000
The answer is 60000 | Okay, let's see here. The problem is about calculating the total cost of transmitting five advertisements during a televised race. Each ad lasts 3 minutes, and the cost per minute is $4000. Hmm, let me break this down step by step.
First, I need to find out how long all five advertisements are in total. Since each one... | To find the total cost of transmitting five advertisements during the race, we start by calculating the total duration of all advertisements. Each advertisement lasts 3 minutes, and there are five advertisements:
\[
5 \text{ ads} \times 3 \text{ minutes/ad} = 15 \text{ minutes}
\]
Next, we calculate the total cost by... | 26,960 | TIGER-Lab/MATH-plus | <think>
Okay, let's see here. The problem is about calculating the total cost of transmitting five advertisements during a televised race. Each ad lasts 3 minutes, and the cost per minute is $4000. Hmm, let me break this down step by step.
First, I need to find out how long all five advertisements are in total. Since ... | [
{
"from": "human",
"value": "If each of the five advertisements shown during a televised race lasted 3 minutes and the cost of advertising is $4000 per minute, what was the total cost of transmitting these advertisements during the race?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see he... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
"A problem involving mutually externally tangent circles is given. The new problem inspired by this (...TRUNCATED) | "A problem involving mutually externally tangent circles is given. The new problem inspired by this (...TRUNCATED) | "Alright, so I came across this geometry problem, and it seems a bit tricky but interesting. Let me (...TRUNCATED) | "To solve the problem of finding the radius of the third circle tangent to both the existing circles(...TRUNCATED) | 1,705 | ai2-adapt-dev/openmath-2-math | "<think>\nAlright, so I came across this geometry problem, and it seems a bit tricky but interesting(...TRUNCATED) | [{"from":"human","value":"A problem involving mutually externally tangent circles is given. The new (...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
"In a college, 45 percent of the students are freshmen, 30 percent are sophomores, 15 percent are ju(...TRUNCATED) | "To solve this problem, let\\'s break down the information step by step:\n\n1. **Percentages of each(...TRUNCATED) | "Okay, so I need to find the value of X, which is the percentage of seniors in the college. The prob(...TRUNCATED) | "Given the percentages of students in each class and the percentages of each class taking German, we(...TRUNCATED) | 10,018 | MetaMath-AIME | "<think>\nOkay, so I need to find the value of X, which is the percentage of seniors in the college.(...TRUNCATED) | [{"from":"human","value":"In a college, 45 percent of the students are freshmen, 30 percent are soph(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
"An animal with X cells is a connected figure consisting of 1500 equal-sized square cells. A butterf(...TRUNCATED) | "To solve for the unknown variable X, we need to understand the problem involving the definition of (...TRUNCATED) | "Okay, so I need to figure out the value of X given that a primitive butterfly has a maximum of 5998(...TRUNCATED) | "The problem involves determining the value of \\( X \\) given that the maximum number of cells in a(...TRUNCATED) | 22,159 | MetaMath-AIME | "<think>\nOkay, so I need to figure out the value of X given that a primitive butterfly has a maximu(...TRUNCATED) | [{"from":"human","value":"An animal with X cells is a connected figure consisting of 1500 equal-size(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
"A bakery is making a special batch of cookies that requires a specific ratio of butter to flour to (...TRUNCATED) | "A bakery is making a special batch of cookies that requires a specific ratio of butter to flour to (...TRUNCATED) | "Okay, let's see. The problem is about a bakery making cookies with a specific ratio of butter to fl(...TRUNCATED) | "The bakery needs to determine the number of batches they can make with 15 pounds of flour, given th(...TRUNCATED) | 24,071 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, let's see. The problem is about a bakery making cookies with a specific ratio of but(...TRUNCATED) | [{"from":"human","value":"A bakery is making a special batch of cookies that requires a specific rat(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
"If Lee is saving up for a new pair of sneakers that cost $90 and he already has $15 saved, he plans(...TRUNCATED) | null | "Okay, let's see. Lee wants to buy sneakers that cost $90. He already has $15 saved up. So, he needs(...TRUNCATED) | "Lee needs $90 for the sneakers and already has $15 saved, so he initially requires an additional **(...TRUNCATED) | null | AI-MO/NuminaMath-1.5 | "<think>\nOkay, let's see. Lee wants to buy sneakers that cost $90. He already has $15 saved up. So,(...TRUNCATED) | [{"from":"human","value":"If Lee is saving up for a new pair of sneakers that cost $90 and he alread(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
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