messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 17. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 471 | MATH |
[
{
"content": "let N be the third greatest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 6 | MATH |
[
{
"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 3 | MATH |
[
{
"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 224 | MATH |
[
{
"content": "let N be the least 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 18 | MATH |
[
{
"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 1472 | MATH |
[
{
"content": "let N be the greatest 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 18 | MATH |
[
{
"content": "let N be the largest 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 3. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 999 | MATH |
[
{
"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 96 | MATH |
[
{
"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 336 | MATH |
[
{
"content": "let N be the largest 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 11. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 999 | MATH |
[
{
"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 8 | MATH |
[
{
"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 4384 | MATH |
[
{
"content": "let N be the third smallest 2-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "let N be the least 4-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 18. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 18 | MATH |
[
{
"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 18 | MATH |
[
{
"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 6 | MATH |
[
{
"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 68 | MATH |
[
{
"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 18 | MATH |
[
{
"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 3 | MATH |
[
{
"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 466 | MATH |
[
{
"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 14. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 118 | MATH |
[
{
"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 88896 | MATH |
[
{
"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 4943 | MATH |
[
{
"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 7, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 48 | MATH |
[
{
"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 6672 | MATH |
[
{
"content": "let N be the tenth greatest 5-digit positive integer with the property that the sum of the digits of n is divisible by 9. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 99918 | MATH |
[
{
"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 1 | MATH |
[
{
"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 6107 | MATH |
[
{
"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 1, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Y... | 4958 | MATH |
[
{
"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 18 | MATH |
[
{
"content": "let N be the tenth greatest 4-digit positive integer with the property that the sum of the digits of n is divisible by 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9972 | MATH |
[
{
"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 940 | MATH |
[
{
"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 12. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 30 | MATH |
[
{
"content": "let N be the maximum 4-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 699 | MATH |
[
{
"content": "let N be the largest 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 10. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 999 | MATH |
[
{
"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 7784 | MATH |
[
{
"content": "let N be the greatest 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 16. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{... | 89000 | MATH |
[
{
"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 10008 | MATH |
[
{
"content": "let N be the least 6-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 17 | MATH |
[
{
"content": "let N be the tenth greatest 2-digit positive integer with the property that the sum of the digits of n is divisible by 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 99997 | MATH |
[
{
"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 81 | MATH |
[
{
"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Y... | 44448 | MATH |
[
{
"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 5, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Y... | 55560 | MATH |
[
{
"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 5356 | MATH |
[
{
"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 96 | MATH |
[
{
"content": "let N be the minimum 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 6. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 1 | MATH |
[
{
"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 361 | MATH |
[
{
"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 74 | MATH |
[
{
"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 16. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Y... | 8904 | MATH |
[
{
"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 14 | MATH |
[
{
"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 96 | MATH |
[
{
"content": "let N be the largest 6-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 5. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 99999 | MATH |
[
{
"content": "let N be the tenth smallest 5-digit positive integer with the property that the sum of the digits of n is divisible by 8. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10078 | MATH |
[
{
"content": "let N be the tenth smallest 5-digit positive integer with the property that the sum of the digits of n is divisible by 10. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10090 | MATH |
[
{
"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 6 | MATH |
[
{
"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 24 | MATH |
[
{
"content": "let N be the smallest 5-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 3 | MATH |
[
{
"content": "let N be the biggest 3-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 57 | MATH |
[
{
"content": "let N be the third greatest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 12. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9804 | MATH |
[
{
"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 18 | MATH |
[
{
"content": "let N be the greatest 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 18. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Y... | 9990 | MATH |
[
{
"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 3336 | MATH |
[
{
"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 1 | MATH |
[
{
"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 16 | MATH |
[
{
"content": "let N be the biggest 2-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 18 | MATH |
[
{
"content": "let N be the least 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 4 | MATH |
[
{
"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 3 | MATH |
[
{
"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 55560 | MATH |
[
{
"content": "let N be the tenth greatest 4-digit positive integer with the property that the sum of the digits of n is divisible by 11. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9897 | MATH |
[
{
"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 6, the resulting number is a multiple of 6. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 3 | MATH |
[
{
"content": "let N be the biggest 5-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 10008 | MATH |
[
{
"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 4. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 99997 | MATH |
[
{
"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Y... | 66672 | MATH |
[
{
"content": "let N be the maximum 5-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 6672 | MATH |
[
{
"content": "let N be the smallest 4-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 672 | MATH |
[
{
"content": "let N be the tenth smallest 5-digit positive integer with the property that the sum of the digits of n is divisible by 7. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10067 | MATH |
[
{
"content": "let N be the third smallest 5-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 4. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10008 | MATH |
[
{
"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 12 | MATH |
[
{
"content": "let N be the third smallest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 10. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1200 | MATH |
[
{
"content": "let N be the biggest 6-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 33336 | MATH |
[
{
"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 72 | MATH |
[
{
"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 6, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 96 | MATH |
[
{
"content": "let N be the largest 4-digit positive integer with the property that the absolute value of the alternating sum (starting with adding the most significant digit) of the digits of n is divisible by 8. Find N mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 999 | MATH |
[
{
"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 8, the resulting number is a multiple of 8. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 1 | MATH |
[
{
"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 3, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 3 | MATH |
[
{
"content": "let N be the third smallest 4-digit positive integer with the property that whenever you swap the positions of two of its adjacent digits, the resulting number is a multiple of 11. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1212 | MATH |
[
{
"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 79 | MATH |
[
{
"content": "let N be the least 2-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 1 | MATH |
[
{
"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 9 | MATH |
[
{
"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 22224 | MATH |
[
{
"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Y... | 22224 | MATH |
[
{
"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 84 | MATH |
[
{
"content": "let N be the smallest 2-digit positive integer with the property that whenever one of its digits changes to 2, the resulting number is a multiple of 3. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 2 | MATH |
[
{
"content": "let N be the least 5-digit positive integer with the property that whenever two of its digits changes to 9, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 3336 | MATH |
[
{
"content": "let N be the least 2-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 9 | MATH |
[
{
"content": "let N be the smallest 3-digit positive integer with the property that whenever one of its digits changes to 4, the resulting number is a multiple of 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 64 | MATH |
[
{
"content": "let N be the smallest 6-digit positive integer with the property that whenever one of its digits changes to 3, the resulting number is a multiple of 9. Let Q and R be the quotient and remainder, respectively, when N is divided by 100000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Y... | 33336 | MATH |
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