instruction_seed stringlengths 16 5.35k | response_seed stringlengths 0 5.35k ⌀ | reasoning stringlengths 491 92.1k | deepseek_solution stringlengths 188 5.23k | __original_row_idx int64 29 40k ⌀ | source stringclasses 4
values | final_reasoning_trace stringlengths 963 93.9k | conversations listlengths 2 2 |
|---|---|---|---|---|---|---|---|
If I distribute $8$ bronze coins into each treasure chest, I end up with $4$ empty chests. However, when I put $4$ bronze coins into each chest, I have $8$ bronze coins remaining. How many bronze coins do I possess in total? | Let's define the variables:
- Let \( c \) be the total number of treasure chests.
- Let \( b \) be the total number of bronze coins.
From the problem, we have two scenarios:
1. If \( 8 \) bronze coins are distributed into each chest, 4 chests remain empty:
- This means that the number of chests that were filled is ... | Okay, let's see. I have this problem here about distributing bronze coins into treasure chests. Let me try to parse it step by step.
First scenario: If I distribute 8 bronze coins into each treasure chest, I end up with 4 empty chests. Hmm. So, that means if I put 8 coins in each chest, some number of chests get 8 coi... | Let \( C \) be the total number of treasure chests.
In the first scenario, distributing 8 bronze coins into each chest results in 4 empty chests. This means \( C - 4 \) chests are filled with 8 coins each. The total number of coins is given by:
\[
8(C - 4)
\]
In the second scenario, distributing 4 bronze coins into ... | 9,076 | MetaMath-AIME | <think>
Okay, let's see. I have this problem here about distributing bronze coins into treasure chests. Let me try to parse it step by step.
First scenario: If I distribute 8 bronze coins into each treasure chest, I end up with 4 empty chests. Hmm. So, that means if I put 8 coins in each chest, some number of chests g... | [
{
"from": "human",
"value": "If I distribute $8$ bronze coins into each treasure chest, I end up with $4$ empty chests. However, when I put $4$ bronze coins into each chest, I have $8$ bronze coins remaining. How many bronze coins do I possess in total?"
},
{
"from": "gpt",
"value": "<think>\nOk... |
36.52 A person looked at their watch just after 6:00 PM while having dinner, and the hands formed a $110^{\circ}$ angle. They returned before 7:00 PM and noticed the hands also formed a $110^{\circ}$ angle. The total minutes spent dining by this person is
(A) $36 \frac{2}{3}$.
(B) 40 .
(C) 42 .
(D) 42.4 .
(E) 45 .
(13t... | null | Okay, so I need to figure out how much time passed between two moments just after 6:00 PM and before 7:00 PM when the angle between the clock hands was 110 degrees each time. The answer choices are given, so that might help check my work later.
First, let me recall that the angle between the hour and minute hands of a... | To determine the total minutes spent dining, we need to find the times just after 6:00 PM and before 7:00 PM when the angle between the clock hands is 110 degrees.
The formula for the angle between the hour and minute hands is:
\[
\left| 30H - 5.5M \right|
\]
where \( H \) is the hour and \( M \) is the minutes past ... | null | AI-MO/NuminaMath-1.5 | <think>
Okay, so I need to figure out how much time passed between two moments just after 6:00 PM and before 7:00 PM when the angle between the clock hands was 110 degrees each time. The answer choices are given, so that might help check my work later.
First, let me recall that the angle between the hour and minute ha... | [
{
"from": "human",
"value": "36.52 A person looked at their watch just after 6:00 PM while having dinner, and the hands formed a $110^{\\circ}$ angle. They returned before 7:00 PM and noticed the hands also formed a $110^{\\circ}$ angle. The total minutes spent dining by this person is\n(A) $36 \\frac{2}{3}... |
An aquarium holds fish and turtles, which can be either tropical or non-tropical. Five percent of the animals are turtles. X percent of the fish are tropical. 38 percent of the animals in the aquarium are non-tropical fish. What is the value of the unknown variable X? | To solve for the unknown variable X, we need to analyze the information given step by step:
1. We know that 5% of the animals in the aquarium are turtles.
2. Therefore, the remaining animals, which are fish, account for 100% - 5% = 95% of the total animals.
3. Among the fish, we have tropical fish and non-tropical fi... | Okay, let's see. I need to figure out the value of X, which is the percentage of fish that are tropical. The problem gives me some information about the aquarium's inhabitants: 5% are turtles, X% of the fish are tropical, and 38% of all animals are non-tropical fish. Hmm. Let me break this down step by step.
First, le... | Given that 5% of the animals in the aquarium are turtles and the remaining 95% are fish, we need to determine the percentage of fish that are tropical (denoted as \( X \)). We know that 38% of all animals are non-tropical fish.
1. **Total Animals Assumption**:
- Assume there are 100 animals in total for simplicity.... | 8,768 | MetaMath-AIME | <think>
Okay, let's see. I need to figure out the value of X, which is the percentage of fish that are tropical. The problem gives me some information about the aquarium's inhabitants: 5% are turtles, X% of the fish are tropical, and 38% of all animals are non-tropical fish. Hmm. Let me break this down step by step.
F... | [
{
"from": "human",
"value": "An aquarium holds fish and turtles, which can be either tropical or non-tropical. Five percent of the animals are turtles. X percent of the fish are tropical. 38 percent of the animals in the aquarium are non-tropical fish. What is the value of the unknown variable X?"
},
{
... |
At Summit Academy, the grading scale indicates: [A: 90 - 100, B: 80 - 89, C: 70 - 79, D: 60 - 69, F: below 60]. Ms. Green's class produced the following scores: [68, 89, 79, 85, 92, 88, 72, 63, 75, 55, 80, 90]. What percent of X received a grade of C? (A) 25% (B) 30% (C) 33.33% (D) 40% (E) 50% If we know the answer to ... | To find the percentage of students who received a grade of C, we first need to identify how many students scored in the range of 70 to 79, according to the grading scale provided.
1. **Identify C scores from the given list**: The provided scores are [68, 89, 79, 85, 92, 88, 72, 63, 75, 55, 80, 90]. From this list, the... | Okay, let's try to figure out this problem step by step. So, the question is asking: What percent of X received a grade of C? And the options are given. But then it says if the answer is 25, what is the value of X? Hmm, that seems a bit confusing at first, but let me parse it out.
First, let's recap the grading scale ... | To determine the percentage of students who received a grade of C, we first count the number of scores falling within the C range (70-79) from the given list: [68, 89, 79, 85, 92, 88, 72, 63, 75, 55, 80, 90]. The scores that qualify for a C are 79, 72, and 75, which totals 3 students.
Next, we know the answer to the q... | 14,508 | MetaMath-AIME | <think>
Okay, let's try to figure out this problem step by step. So, the question is asking: What percent of X received a grade of C? And the options are given. But then it says if the answer is 25, what is the value of X? Hmm, that seems a bit confusing at first, but let me parse it out.
First, let's recap the gradin... | [
{
"from": "human",
"value": "At Summit Academy, the grading scale indicates: [A: 90 - 100, B: 80 - 89, C: 70 - 79, D: 60 - 69, F: below 60]. Ms. Green's class produced the following scores: [68, 89, 79, 85, 92, 88, 72, 63, 75, 55, 80, 90]. What percent of X received a grade of C? (A) 25% (B) 30% (C) 33.33% ... |
The base of a triangle is 15 cm longer than its altitude. The area of the triangle is equal to 120 cm^2. Find the length of the base of the triangle.
Note: This problem requires a different approach than the original problem, as it involves using the formula for the area of a triangle (A = 0.5bh) and solving for the b... | The base of a triangle is 15 cm longer than its altitude. The area of the triangle is equal to 120 cm^2. Find the length of the base of the triangle.
Note: This problem requires a different approach than the original problem, as it involves using the formula for the area of a triangle (A = 0.5bh) and solving for the b... | Okay, so I need to find the length of the base of a triangle. The problem says that the base is 15 cm longer than its altitude, and the area is 120 cm². Hmm, let me recall the formula for the area of a triangle. It's A equals 0.5 times base times height, right? So, A = 0.5 * b * h.
Alright, let's assign variables. Le... | Given that the base of a triangle is 15 cm longer than its altitude and the area of the triangle is 120 cm², we need to find the length of the base.
1. Let \( h \) be the altitude of the triangle. Then, the base is \( h + 15 \).
2. The area of the triangle is given by the formula \( A = 0.5 \times \text{base} \times \... | 5,330 | ai2-adapt-dev/openmath-2-math | <think>
Okay, so I need to find the length of the base of a triangle. The problem says that the base is 15 cm longer than its altitude, and the area is 120 cm². Hmm, let me recall the formula for the area of a triangle. It's A equals 0.5 times base times height, right? So, A = 0.5 * b * h.
Alright, let's assign varia... | [
{
"from": "human",
"value": "The base of a triangle is 15 cm longer than its altitude. The area of the triangle is equal to 120 cm^2. Find the length of the base of the triangle.\n\nNote: This problem requires a different approach than the original problem, as it involves using the formula for the area of a... |
Consider a sequence denoted by $F_n$ of non-square numbers . $F_1=2$,$F_2=3$,$F_3=5$ and so on . Now , if $m^2\leq F_n<(m+1)^2$ . Then prove that $m$ is the integer closest to $\sqrt{n}$. | null | Okay, so I need to prove that if we have this sequence F_n of non-square numbers, starting with F_1=2, F_2=3, F_3=5, and so on, then whenever m² ≤ F_n < (m+1)², the integer m is the closest to √n. Hmm. Let me try to wrap my head around this.
First, let me make sure I understand the sequence F_n correctly. The sequence... | Given a sequence \( F_n \) of non-square numbers, where \( F_1 = 2 \), \( F_2 = 3 \), \( F_3 = 5 \), and so on, we need to prove that if \( m^2 \leq F_n < (m+1)^2 \), then \( m \) is the integer closest to \( \sqrt{n} \).
1. **Understanding the Sequence**:
- The sequence \( F_n \) consists of all non-square numbers... | null | AI-MO/NuminaMath-1.5 | <think>
Okay, so I need to prove that if we have this sequence F_n of non-square numbers, starting with F_1=2, F_2=3, F_3=5, and so on, then whenever m² ≤ F_n < (m+1)², the integer m is the closest to √n. Hmm. Let me try to wrap my head around this.
First, let me make sure I understand the sequence F_n correctly. The ... | [
{
"from": "human",
"value": "Consider a sequence denoted by $F_n$ of non-square numbers . $F_1=2$,$F_2=3$,$F_3=5$ and so on . Now , if $m^2\\leq F_n<(m+1)^2$ . Then prove that $m$ is the integer closest to $\\sqrt{n}$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to prove that if we h... |
Which of the following calculations is correct?
A: $(a-b)^{2}=a^{2}-b^{2}$
B: $-x(3x^{2}-1)=-3x^{3}-x$
C: $(a+b)\left(a-b\right)=a^{2}+b^{2}$
D: $(m+n)\left(m-2n\right)=m^{2}-mn-2n^{2}$ | null | Alright, let's see. I need to figure out which of these calculations is correct. There are four options: A, B, C, D. Let me go through each one step by step. Hmm, okay, starting with option A.
Option A says that (a - b) squared equals a squared minus b squared. Wait, isn't that the formula for the difference of square... | To determine which calculation is correct, we analyze each option step by step:
**Option A**: \((a - b)^2 = a^2 - b^2\)
The correct expansion of \((a - b)^2\) is \(a^2 - 2ab + b^2\). The given answer is missing the \(-2ab\) term, so A is incorrect.
**Option B**: \(-x(3x^2 - 1) = -3x^3 - x\)
Distributing \(-x\) gi... | null | AI-MO/NuminaMath-1.5 | <think>
Alright, let's see. I need to figure out which of these calculations is correct. There are four options: A, B, C, D. Let me go through each one step by step. Hmm, okay, starting with option A.
Option A says that (a - b) squared equals a squared minus b squared. Wait, isn't that the formula for the difference o... | [
{
"from": "human",
"value": "Which of the following calculations is correct?\n\nA: $(a-b)^{2}=a^{2}-b^{2}$\n\nB: $-x(3x^{2}-1)=-3x^{3}-x$\n\nC: $(a+b)\\left(a-b\\right)=a^{2}+b^{2}$\n\nD: $(m+n)\\left(m-2n\\right)=m^{2}-mn-2n^{2}$"
},
{
"from": "gpt",
"value": "<think>\nAlright, let's see. I nee... |
the average of 6 observations is 12 . a new observation is included and the new average is decreased by 1 . the seventh observation is ? | null | Okay, let's see. The problem says that the average of 6 observations is 12. Then a new observation is added, and the new average decreases by 1. We need to find the seventh observation. Hmm, averages can sometimes be tricky, but let me break it down step by step.
First, the average of the initial 6 observations is 12.... | The average of 6 observations is 12. Therefore, the total sum of these 6 observations is calculated as follows:
\[
6 \times 12 = 72
\]
When a new observation is added, the new average becomes 11 (since the average decreases by 1). The total sum of the 7 observations is then:
\[
7 \times 11 = 77
\]
The seventh observa... | null | AI-MO/NuminaMath-1.5 | <think>
Okay, let's see. The problem says that the average of 6 observations is 12. Then a new observation is added, and the new average decreases by 1. We need to find the seventh observation. Hmm, averages can sometimes be tricky, but let me break it down step by step.
First, the average of the initial 6 observation... | [
{
"from": "human",
"value": "the average of 6 observations is 12 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The problem says that the average of 6 observations is 12. Then a new obs... |
Solve \[\frac{x-3}{x+2}=2\] for $x$. | Solve \[\frac{x-3}{x+2}=2\] for $x$. | "Okay, so I need to solve the equation (x - 3)/(x + 2) = 2 for x. Hmm, let me think about how to app(...TRUNCATED) | "To solve the equation \\(\\frac{x-3}{x+2} = 2\\) for \\(x\\):\n\n1. Cross-multiply to eliminate the(...TRUNCATED) | 20,417 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to solve the equation (x - 3)/(x + 2) = 2 for x. Hmm, let me think about h(...TRUNCATED) | [{"from":"human","value":"Solve \\[\\frac{x-3}{x+2}=2\\] for $x$."},{"from":"gpt","value":"<think>\n(...TRUNCATED) |
"For how many values of the digit $B$ is it true that $84$ is divisible by $B$ and $654{,}2B8$ is di(...TRUNCATED) | "For how many values of the digit $B$ is it true that $84$ is divisible by $B$ and $654{,}2B8$ is di(...TRUNCATED) | "Okay, so I need to figure out how many digits B make it such that 84 is divisible by B and 654,2B8 (...TRUNCATED) | "To determine how many values of the digit \\( B \\) satisfy the conditions that \\( 84 \\) is divis(...TRUNCATED) | 7,098 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to figure out how many digits B make it such that 84 is divisible by B and(...TRUNCATED) | [{"from":"human","value":"For how many values of the digit $B$ is it true that $84$ is divisible by (...TRUNCATED) |
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