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If (x # y) represents the remainder that results when the po [#permalink]
20 Feb 2008, 08:22

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Difficulty:

35% (medium)

Question Stats:

66% (01:51) correct
34% (01:10) wrong based on 98 sessions

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?

Re: If (x # y) represents the remainder that results when the [#permalink]
13 May 2014, 06:28

Answer: D 16 = ky+1 since -- > 0 <=remainder < divisor therefore y>1 ky=15 => y =15/k :- possible values of k for y to be +int = 1,3,5 => y=15,5,3 hence, sum = 15+5+3 = 23

Re: If (x # y) represents the remainder that results when the po [#permalink]
13 May 2014, 06:35

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Expert's post

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?

A. 8 B. 9 C. 16 D. 23 E. 24

(x # y) represents the remainder that results when the positive integer x is divided by the positive integer y.

Thus (16 # y) = 1 implies that 16=yq+1 --> 15=yq --> y is a factor of 15. The factors of 15 are 1, 3, 5, and 15. Now, y cannot be 1, since 16 divided by 1 yields the remainder of 0 not 1.

Therefore the sum of all the possible values of y is 3+5+15=23.