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by ddm » Mon Aug 04, 2008 3:26 pm
If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?

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Re: HELP

by Ian Stewart » Mon Aug 04, 2008 4:20 pm
ddm wrote:If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?

8
9
16
23
24
We know:
-the remainder is 1 when 16 is divided by y;
-in other words, 16 is 1 larger than a multiple of y.

Well, 16 is one larger than 15, so 15 must be a multiple of y. Since y can't be 1 (the remainder would be zero), y could be 15, 5, or 3.

15+5+3 = 23.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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