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When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y?
- a)15
- b)20
- c)28
- d)35
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Normal 0 false false false EN-US JA X-NONE ...
When the positive integer x is divided by 5 and 7, the remainder is 3 and 4, respectively: x=5q+3x=5q+3 (x could be 3, 8, 13, 18, 23, ...) and x=7p+4x=7p+4 (x could be 4, 11, 18, 25, ...).
There is a way to derive general formula based on above two statements:
Divisor will be the least common multiple of above two divisors 5 and 7, hence 3535.
Remainder will be the first common integer in above two patterns, hence 1818 --> so, to satisfy both this conditions x must be of a type x=35m+18x=35m+18 (18, 53, 88, ...);
The same for y (as the same info is given about y): y=35n+18y=35n+18;
x−y=(35m+18)−(35n+18)=35(m−n)x−y=(35m+18)−(35n+18)=35(m−n) --> thus x-y must be a multiple of 35.
Most Upvoted Answer
Normal 0 false false false EN-US JA X-NONE ...
Explanation:
Given information:
- When x is divided by 5, the remainder is 3
- When x is divided by 7, the remainder is 4
- When y is divided by 5, the remainder is 3
- When y is divided by 7, the remainder is 4
Find the values of x and y:
- Let's find the possible values of x and y based on the given remainders:
- x = 5a + 3 (where a is a positive integer)
- x = 7b + 4 (where b is a positive integer)
- y = 5c + 3 (where c is a positive integer)
- y = 7d + 4 (where d is a positive integer)
Comparing x and y:
- Since x > y, we can say that x - y > 0
- Substituting the values of x and y, we get: (5a + 3) - (5c + 3) = 5(a - c) and (7b + 4) - (7d + 4) = 7(b - d)
Factors of x - y:
- From the above expressions, we can see that x - y is divisible by 5 and 7
- Therefore, x - y must be divisible by the least common multiple of 5 and 7, which is 35
- Hence, the correct answer is option 'D' (35) as it must be a factor of x - y.
Given information:
- When x is divided by 5, the remainder is 3
- When x is divided by 7, the remainder is 4
- When y is divided by 5, the remainder is 3
- When y is divided by 7, the remainder is 4
Find the values of x and y:
- Let's find the possible values of x and y based on the given remainders:
- x = 5a + 3 (where a is a positive integer)
- x = 7b + 4 (where b is a positive integer)
- y = 5c + 3 (where c is a positive integer)
- y = 7d + 4 (where d is a positive integer)
Comparing x and y:
- Since x > y, we can say that x - y > 0
- Substituting the values of x and y, we get: (5a + 3) - (5c + 3) = 5(a - c) and (7b + 4) - (7d + 4) = 7(b - d)
Factors of x - y:
- From the above expressions, we can see that x - y is divisible by 5 and 7
- Therefore, x - y must be divisible by the least common multiple of 5 and 7, which is 35
- Hence, the correct answer is option 'D' (35) as it must be a factor of x - y.
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Community Answer
Normal 0 false false false EN-US JA X-NONE ...
- When the positive integer x is divided by 5 and 7, the remainder is 3 and 4, respectively: x=5q+3 (x could be 3, 8, 13, 18, 23, ...) and x=7p+4 (x could be 4, 11, 18, 25, ...).
- There is a way to derive a general formula based on the above two statements:
- Divisor will be the least common multiple of the above two divisors 5 and 7, hence 35.
- The remainder will be the first common integer in the above two patterns, hence 18 --> so, to satisfy both these conditions x must be of a type x=35m+18 (18, 53, 88, ...);
- The same for y (as the same info is given about y): y=35n+18
- x−y=(35m+18)−(35n+18)=35(m−n)) --> thus x-y must be a multiple of 35.
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Normal 0 false false false EN-US JA X-NONE When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y? a)15b)20c)28d)35Correct answer is option 'D'. Can you explain this answer?
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Normal 0 false false false EN-US JA X-NONE When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y? a)15b)20c)28d)35Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Normal 0 false false false EN-US JA X-NONE When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y? a)15b)20c)28d)35Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Normal 0 false false false EN-US JA X-NONE When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y? a)15b)20c)28d)35Correct answer is option 'D'. Can you explain this answer?.
Normal 0 false false false EN-US JA X-NONE When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y? a)15b)20c)28d)35Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Normal 0 false false false EN-US JA X-NONE When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y? a)15b)20c)28d)35Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Normal 0 false false false EN-US JA X-NONE When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y? a)15b)20c)28d)35Correct answer is option 'D'. Can you explain this answer?.
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ample number of questions to practice Normal 0 false false false EN-US JA X-NONE When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y? a)15b)20c)28d)35Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
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