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# x, y, a, and b are positive integers. When x is divided by

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Intern
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x, y, a, and b are positive integers. When x is divided by [#permalink]  23 Mar 2008, 20:22
x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?

a. 24
b. 21
c. 20
d. 17
e. 15

found this problem on Manhattan GMAT. besides answering this question. does anyone any equations for formulas to tackle remainder questions? Are these type of questions always conceptual?
 Manhattan GMAT Discount Codes Kaplan GMAT Prep Discount Codes Knewton GMAT Discount Codes
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Re: challenging remainder problem! [#permalink]  23 Mar 2008, 20:51
E

To get those remainders, y and b should be greaterthan 9 and 6, so adding them up - 15.
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Re: challenging remainder problem! [#permalink]  24 Mar 2008, 15:23
I found the solution but thanks for the explanation. I have a more detail explanation for those who are interested.

The problem states that when x is divided by y the remainder is 6. In general, the divisor (y in this case) will always be greater than the remainder. To illustrate this concept, let's look at a few examples:

15/4 gives 3 remainder 3 (the divisor 4 is greater than the remainder 3)
25/3 gives 8 remainder 1 (the divisor 3 is greater than the remainder 1)
46/7 gives 6 remainder 4 (the divisor 7 is greater than the remainder 4)

In the case at hand, we can therefore conclude that y must be greater than 6.

The problem also states that when a is divided by b the remainder is 9. Therefore, we can conclude that b must be greater than 9.

If y > 6 and b > 9, then y + b > 6 + 9 > 15. Thus, 15 cannot be the sum of y and b.

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Re: challenging remainder problem! [#permalink]  24 Mar 2008, 17:17
This problem is about the common sense rather than the concepts.

divisor can't be equal to the remainder.
that's why y is not equal to 6
Same way, b is not equal to 9
hence y+b can't be equal to 15
Re: challenging remainder problem!   [#permalink] 24 Mar 2008, 17:17
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