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

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

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20 Feb 2008, 08:22
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-y-represents-the-remainder-that-results-when-the-po-169530.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 13 May 2014, 06:35, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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20 Feb 2008, 08:28
16 = yk + 1, where y is a positive integer and k is an integer
15 = yk

possible values of y are 1+3+5+15 = 24

can soemone tell me why 1 is excluded? the OA is 23
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20 Feb 2008, 08:30
bmwhype2 wrote:
16 = yk + 1, where y is a positive integer and k is an integer
15 = yk

possible values of y are 1+3+5+15 = 24

can soemone tell me why 1 is excluded? the OA is 23

because the remainder would be 0.
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20 Feb 2008, 08:31
bmwhype2 wrote:
16 = yk + 1, where y is a positive integer and k is an integer
15 = yk

possible values of y are 1+3+5+15 = 24

can soemone tell me why 1 is excluded? the OA is 23

1 goes into 16, sixteen times with no remainder.

in other words 16/1 = 16
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20 Feb 2008, 08:33
maratikus wrote:
bmwhype2 wrote:
16 = yk + 1, where y is a positive integer and k is an integer
15 = yk

possible values of y are 1+3+5+15 = 24

can soemone tell me why 1 is excluded? the OA is 23

because the remainder would be 0.

thanks. cant believe i overlooked that.
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20 Feb 2008, 18:27
so question basically boils down to: what are the numbers that, when 16 is divided by that number, gives a remainder of 1 ?

quickly, you can get 3, 5 and 15. sum of those 3 numbers are 23
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Re: If (x # y) represents the remainder that results when the [#permalink]

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

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13 May 2014, 06:35
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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

(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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-y-represents-the-remainder-that-results-when-the-po-169530.html
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Re: If (x # y) represents the remainder that results when the po   [#permalink] 13 May 2014, 06:35
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