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When positive integer x is divided by 5, the remainder is 3 [#permalink]
02 Mar 2012, 09:39

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22% (02:03) wrong based on 223 sessions

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?

Re: How to solve this problem [#permalink]
02 Mar 2012, 10:16

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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.

Re: When positive integer x is divided by 5, the remainder is 3 [#permalink]
06 Jun 2013, 08:50

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I do the "for dummies" way on this, because it is the first thing that popped in my mind, and the first thing I would have tried. It actually doesn't take that long on paper. Easily under 2 minutes.

The thing about PS problems is that there can only be one answer. So as long as you can find it one time, it will be the same for all other times. The question is asking for the larger number minus the smaller number so, 53-18 = 35

Re: How to solve this problem [#permalink]
23 Oct 2013, 18:45

Bunuel wrote:

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.

there must be some other way to solve this; I have no idea how anyone that reads that question could sit there and think of what you wrote out, in under two minutes. It's a great solution, but I think there must be some other way to crack this nut.

Re: How to solve this problem [#permalink]
23 Oct 2013, 23:29

Expert's post

AccipiterQ wrote:

Bunuel wrote:

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.

there must be some other way to solve this; I have no idea how anyone that reads that question could sit there and think of what you wrote out, in under two minutes. It's a great solution, but I think there must be some other way to crack this nut.

If you know the trick to derive general formula you can solve the question just under 2 minutes.

Else, you can find common numbers (18 and 53) and see that 53-18 is a multiple of only 35 from answer choices. _________________

Actually, on this problem, if 5 is a factor of it, as is 7, couldn't you just look at the stem, and multiply 5 by 7 without doing any extra work, to get the answer?

Actually, on this problem, if 5 is a factor of it, as is 7, couldn't you just look at the stem, and multiply 5 by 7 without doing any extra work, to get the answer?

No. Neither 5 nor 7 is a factor of either x or y. _________________