messages listlengths 2 2 |
|---|
[
{
"content": "Question: \\nFind the sum of all possible integer values of $x$ for which $xy - 2x + 3y = 10$, where $y$ is also an integer.\\n\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find all integer values... |
[
{
"content": "Question: \\nA three-digit number $\\\\overline{ABC}$ has the property that the sum of its digits is 15. If the digits are reversed to form $\\\\overline{CBA}$, and this new number is subtracted from the original number, the result is 198. Additionally, the tens digit $B$ is the average of the hun... |
[
{
"content": "Question: \\nTwo circles are externally tangent to each other and are both tangent to the same line. The distance between the points of tangency on the line is 12. If the radius of one circle is 4, what is the radius of the other circle?\\n\nPlease reason step by step, and put your final answer wi... |
[
{
"content": "Question: Let $P(x) = x^3 - 3x^2 + 5x - 7$. If $a, b, c$ are the roots of the polynomial $P(x)$, find the value of $(a+1)(b+1)(c+1)$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the value of... |
[
{
"content": "Question: Find the sum of all positive integers $n$ such that $\\frac{n^2 + 2n + 12}{n+2}$ is an integer.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find all positive integers n such that the ex... |
[
{
"content": "Question: Find the sum of all positive integers $n$ such that $\\frac{n^2 + 2n + 12}{n + 2}$ is an integer.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find all positive integers n such that the ... |
[
{
"content": "Question: \\nTwo circles with radii 9 and 4 are tangent to the x-axis. They are also externally tangent to each other. What is the distance between their points of tangency on the x-axis?\\n\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
... |
[
{
"content": "Question: How many positive integers less than or equal to 1000 are divisible by 2 and by 3, but not by 5?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figure out how many positive integers up to ... |
[
{
"content": "Question: \\nFind the sum of all positive integers $n$ such that $\\\\frac{n^2 + 2n + 12}{n+2}$ is an integer.\\n\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find all positive integers n such tha... |
[
{
"content": "Question: Find the sum of all integers $n$ for which $\\frac{n^2 + 20}{n - 2}$ is an integer.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find all integers n for which the expression (n² + 20)/(n... |
[
{
"content": "Question: Find the sum of all positive integers n such that n < 200, n leaves a remainder of 2 when divided by 5, and n leaves a remainder of 3 when divided by 7.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, l... |
[
{
"content": "Question: Find the number of positive integers n strictly less than 1000 such that n^2 + 1 is divisible by 5.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the number of positive integers n le... |
[
{
"content": "Question: \\nFind the number of positive integers $n$ such that $n^2 + 2024$ is a perfect square.\\n\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the number of positive integers n such that n... |
[
{
"content": "Question: \\nFind the number of positive integers $n$ such that $n^2 + 2024$ is divisible by $n+2$.\\n\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the number of positive integers n such that... |
[
{
"content": "Question: How many 5-digit positive integers can be formed using the digits {1, 2, 3, 4, 5} exactly once, such that the number is divisible by 4?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figur... |
[
{
"content": "Question: Find the number of positive integers $n$ such that $n^2 + 2024$ is a perfect square.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the number of positive integers n such that n² + 20... |
[
{
"content": "Question: Point P is an interior point of square ABCD. The area of triangle PAB is 15, the area of triangle PBC is 20, and the area of triangle PCD is 30. What is the area of triangle PDA?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"c... |
[
{
"content": "Question: \\nFind the number of positive integers $n$ such that $n^2 + 2023$ is a perfect square.\\n\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the number of positive integers n such that n... |
[
{
"content": "Question: How many positive integers less than 1000 have the property that the sum of their digits is equal to 7?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figure out how many positive integers... |
End of preview. Expand
in Data Studio
README.md exists but content is empty.
- Downloads last month
- 5