messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 2, the resulting number is a multiple of 6. 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... | 24 | MATH |
[
{
"content": "let N be the largest 3-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 100.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 90 | MATH |
[
{
"content": "let N be the tenth greatest 3-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"
}
] | 895 | MATH |
[
{
"content": "let N be the maximum 4-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 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 1008 | 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 6. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10020 | MATH |
[
{
"content": "let N be the smallest 2-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 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 10 | MATH |
[
{
"content": "let N be the tenth greatest 3-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"
}
] | 932 | MATH |
[
{
"content": "let N be the smallest 3-digit positive integer with the property that whenever one 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 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{You... | 36 | MATH |
[
{
"content": "let N be the least 2-digit positive integer with the property that whenever two 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 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 1 | MATH |
[
{
"content": "let N be the smallest 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{Yo... | 4243 | MATH |
[
{
"content": "let N be the maximum 2-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 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 2 | 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 6. 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 biggest 4-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 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 1008 | 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 3. 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... | 3 | MATH |
[
{
"content": "let N be the maximum 6-digit positive integer with the property that whenever one of its digits changes to 1, 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... | 77784 | 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 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... | 3 | MATH |
[
{
"content": "let N be the minimum 2-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 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 1 | MATH |
[
{
"content": "let N be the least 5-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 19. 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... | 1135 | 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 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 ... | 108 | 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 3. Find N.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10008 | MATH |
[
{
"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 8, the resulting number is a multiple of 6. 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 tenth smallest 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"
}
] | 66 | 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 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... | 22224 | MATH |
[
{
"content": "let N be the maximum 2-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 10. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 9 | 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 5. 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... | 1004 | MATH |
[
{
"content": "let N be the maximum 2-digit positive integer with the property that whenever one 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 ... | 10 | MATH |
[
{
"content": "let N be the biggest 3-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 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 105 | 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 4. Find N mod 100000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 1 | MATH |
[
{
"content": "let N be the maximum 3-digit positive integer with the property that whenever one of its digits changes to 8, 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... | 18 | 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 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... | 22224 | 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 5. 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 greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 19. 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... | 78 | 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 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... | 22224 | MATH |
[
{
"content": "let N be the least 3-digit positive integer with the property that whenever two 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{Your a... | 30 | 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 5. 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... | 1 | MATH |
[
{
"content": "let N be the least 6-digit positive integer with the property that whenever two of its digits changes to 4, the resulting number is a multiple of 12. 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... | 11145 | MATH |
[
{
"content": "let N be the least 4-digit positive integer with the property that whenever two of its digits changes to 5, the resulting number is a multiple of 5. 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... | 1 | MATH |
[
{
"content": "let N be the minimum 2-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 7. Find N mod 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 1 | MATH |
[
{
"content": "let N be the smallest 4-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 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 1008 | 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 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... | 22224 | MATH |
[
{
"content": "let N be the biggest 3-digit positive integer with the property that whenever two 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 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 60 | MATH |
[
{
"content": "let N be the biggest 3-digit positive integer with the property that whenever two 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 100. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 94 | 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 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 4-digit positive integer with the property that whenever two 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 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 336 | MATH |
[
{
"content": "let N be the least 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 an... | 1 | MATH |
[
{
"content": "let N be the biggest 4-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 1000. Find Q + R.\n\nPresent the answer in LaTex format: \\boxed{Your... | 897 | 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 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... | 66672 | MATH |
[
{
"content": "let N be the maximum 2-digit positive integer with the property that whenever one of its digits changes to 1, 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... | 16 | 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 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 maximum 5-digit positive integer with the property that whenever one of its digits changes to 7, 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... | 8896 | 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 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{Yo... | 77781 | MATH |
[
{
"content": "let N be the least 3-digit positive integer with the property that whenever two of its digits changes to 1, 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... | 84 | 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 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 ans... | 7 | MATH |
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