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?
Related Test: Test: Remainders- 1

GMAT Question

Aakash Pandey
Jul 31, 2018
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.

This discussion on 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? is done on EduRev Study Group by GMAT Students. The Questions and Answers of 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? are solved by group of students and teacher of GMAT, which is also the largest student community of GMAT. If the answer is not available please wait for a while and a community member will probably answer this soon. You can study other questions, MCQs, videos and tests for GMAT on EduRev and even discuss your questions like 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? over here on EduRev! Apart from being the largest GMAT community, EduRev has the largest solved Question bank for GMAT.
This discussion on 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? is done on EduRev Study Group by GMAT Students. The Questions and Answers of 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? are solved by group of students and teacher of GMAT, which is also the largest student community of GMAT. If the answer is not available please wait for a while and a community member will probably answer this soon. You can study other questions, MCQs, videos and tests for GMAT on EduRev and even discuss your questions like 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? over here on EduRev! Apart from being the largest GMAT community, EduRev has the largest solved Question bank for GMAT.