shopaholic wrote:
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?
thanks in advance
Welcome to GMAT Club. Below is a solution to your question.
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. 12
B. 15
C. 20
D. 28
E. 35
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 general formula based on above two statements:Divisor will be the least common multiple of above two divisors 5 and 7, hence
35.
Remainder will be the first common integer in above two patterns, hence
18 --> so, to satisfy both this 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.
Answer: E.
More about this concept:
manhattan-remainder-problem-93752.html?hilit=derive#p721341good-problem-90442.html?hilit=derive#p722552Hope it helps.
P.S. Please post answer choices for PS questions.
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