Data Repetition
Collection
47 items • Updated
idx int64 78 100k | query stringlengths 18 1.58k | response stringlengths 1.91k 42.3k | solution stringlengths 1 11 | correct bool 1
class |
|---|---|---|---|---|
2,729 | Each of \( w, x, y \), and \( z \) is an integer. If \( w+x=45 \), \( x+y=51 \), and \( y+z=28 \), what is the value of \( w+z \)?
(A) 28
(B) 22
(C) 17
(D) 23
(E) 15 | <think>
Okay, let me try to figure out this problem. So, we have four integers: w, x, y, and z. The equations given are:
1. w + x = 45
2. x + y = 51
3. y + z = 28
And we need to find the value of w + z. The answer choices are A through E, so I need to figure out which one is correct. Let me think step by step.
First... | 22 | false |
91,755 | What integer $n$ satisfies $0 \leq n < 103$ and $$100n \equiv 34 \pmod{103}~?$$ | <think>
Okay, so I need to find an integer n between 0 and 102 (inclusive) such that 100n is congruent to 34 modulo 103. Hmm, congruences can sometimes be tricky, but let me think about how to approach this.
First, I remember that solving an equation like ax ≡ b mod m involves finding the multiplicative inverse of a m... | 52 | false |
16,775 | Given a geometric sequence {a<sub>n</sub>} with a common ratio of $\frac{1}{2}$ and the sum of the first n terms as $S_n$, find the value of $\frac{S_4}{a_4}$.
A: 31
B: 15
C: 7
D: 1 | <think>
Okay, so I need to find the value of S₄ divided by a₄ in a geometric sequence where the common ratio is 1/2. The options are A: 31, B: 15, C: 7, D: 1. Let me think through this step by step.
First, let me recall what a geometric sequence is. A geometric sequence is a sequence where each term after the first is... | 15 | false |
83,706 | The picture shows a structure made from identical cubes. It is a cube with several holes that go through, all having the same cross-section. How many cubes is the structure made of?
(M. Krejčová)
Hint: Try counting layer by layer. | <think>
Okay, so I need to figure out how many cubes are in this structure. The problem says it's a cube with several holes that go through, all having the same cross-section. The hint suggests counting layer by layer. Hmm, since I don't have the actual picture, I need to visualize or maybe think of common structures l... | 112 | false |
64,228 | How many even integers between 5000 and 8000 have four different digits? | <think>
Okay, so I need to figure out how many even integers between 5000 and 8000 have four different digits. Let me break this down step by step. First, let me understand the problem.
We're looking for four-digit numbers that are even, between 5000 and 8000, and all digits are different. Let me note down the constra... | 672 | false |
8,334 | The constant term in the expansion of the binomial $\left( x^{6}-\frac{1}{x\sqrt{x}} \right)^{5}$ is
A: $-5$
B: $5$
C: $-10$
D: $10$ | <think>
Okay, so I need to find the constant term in the expansion of the binomial $\left( x^{6} - \frac{1}{x\sqrt{x}} \right)^{5}$. Let me think about how to approach this.
First, I remember that when expanding a binomial like $(a + b)^n$, each term can be found using the binomial theorem. The general term is given ... | 5 | false |
96,227 | If 3 < x < 6 < y < some number, then the greatest possible positive integer difference of x and y is 6. What is the upper bound for y? | <think>
Okay, so I need to figure out the upper bound for y given that 3 < x < 6 < y < some number, and the greatest possible positive integer difference of x and y is 6. Hmm, let me try to break this down step by step.
First, let me restate the problem in my own words. We have two variables, x and y. The value of x i... | 11 | false |
65,863 | If Francis spends $\frac{1}{3}$ of his day sleeping, $\frac{1}{4}$ of his day studying, and $\frac{1}{8}$ of his day eating, how many hours in the day does he have left?
(A) 4
(B) 6
(C) 5
(D) 7
(E) 9 | <think>
Okay, so Francis spends parts of his day on sleeping, studying, and eating, and we need to figure out how many hours he has left. Let me think through this step by step.
First, the problem says he spends 1/3 of his day sleeping, 1/4 studying, and 1/8 eating. So, we need to add up those fractions and subtract ... | 7 | false |
18,029 | Starting with the number 1, Nina repeatedly multiplies her number by 3 and then takes the greatest integer less than or equal to that number. If her number exceeds 100, she resumes by dividing by 2 each time and taking the greatest integer until her number becomes 1 or less. How many times must she multiply and divide ... | <think>
Okay, let's try to figure out this problem step by step. So Nina starts with the number 1. Then she repeatedly multiplies her number by 3 and takes the greatest integer less than or equal to that number. If her number exceeds 100, she then divides by 2 each time and takes the greatest integer until her number b... | 1 | false |
24,518 | From point $C$, Mark walked 30 yards north, 80 yards west, 20 yards south, and 30 yards east to point $D$. What is the length, in yards, of $\overline{CD}$? | <think>
Okay, so Mark starts at point C and walks 30 yards north, then 80 yards west, then 20 yards south, and finally 30 yards east to reach point D. I need to find the distance between points C and D. Hmm, let me visualize this. Maybe I can use coordinates to figure it out.
Let me set up a coordinate system. Let's ... | 51 | false |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 5