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# If (x # y) represents the remainder that results when the po

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Intern
Joined: 18 Oct 2013
Posts: 1
If (x # y) represents the remainder that results when the po  [#permalink]

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Updated on: 29 Mar 2014, 14:55
17
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:11) correct 26% (01:37) wrong based on 273 sessions

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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

Is there a quick and easy way to find divisors to an integer/expression when we are looking for a distinct remainders?

23
, I found the answer by calculating and doing several divisions, is there an easier way?

Originally posted by jokkemauritzen on 29 Mar 2014, 14:23.
Last edited by Bunuel on 29 Mar 2014, 14:55, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 48074
Re: If (x # y) represents the remainder that results when the po  [#permalink]

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29 Mar 2014, 15:02
2
4
jokkemauritzen 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?

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

Is there a quick and easy way to find divisors to an integer/expression when we are looking for a distinct remainders?

23
, I found the answer by calculating and doing several divisions, is there an easier way?

(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.

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Re: If (x # y) represents the remainder that results when the po  [#permalink]

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16 Dec 2017, 06:05
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Re: If (x # y) represents the remainder that results when the po &nbs [#permalink] 16 Dec 2017, 06:05
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