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If x and y are positive integers, is x^m+y a multiple of 9?

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If x and y are positive integers, is x^m+y a multiple of 9?  [#permalink]

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New post Updated on: 13 Feb 2017, 01:26
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

76% (02:00) correct 24% (01:52) wrong based on 43 sessions

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If x and y are positive integers, is\(x^m+y\) a multiple of 9?

1) m is a multiple of 3
2) x+y is a multiple of 9

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Originally posted by MathRevolution on 10 Feb 2017, 02:04.
Last edited by Bunuel on 13 Feb 2017, 01:26, edited 1 time in total.
Edited the OA.
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Re: If x and y are positive integers, is x^m+y a multiple of 9?  [#permalink]

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New post 10 Feb 2017, 08:29
Top Contributor
MathRevolution wrote:
If x and y are positive integers, is \(x^m + y\) a multiple of 9?

1) m is a multiple of 3
2) x+y is a multiple of 9


Are you sure the correct answer is B?
Or perhaps you transcribed the question incorrectly?

I ask because....

Target question: Is x^m + y a multiple of 9?

Statement 2: x+y is a multiple of 9
There are several values of x and y that satisfy statement 1, YET yield conflicting answers to the target question:
Case a: x = 2, y = 7 and m = 1. Here, x+y = 2+7 = 9, and 9 is a multiple of 9. In this case x^m + y = 2^1 + 7 = 9, and 9 IS a multiple of 9
Case b: x = 2, y = 7 and m = 2. Here, x+y = 2+7 = 9, and 9 is a multiple of 9. In this case x^m + y = 2^2 + 7 = 11, and 119 is NOT a multiple of 9
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Or perhaps I'm missing something.

Cheers,
Brent
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Re: If x and y are positive integers, is x^m+y a multiple of 9?  [#permalink]

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New post 12 Feb 2017, 17:23
==> In the original condition, there are 3 variables (x, y, m) and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), (x,y,m)=(1,8,3) yes, but (x,y,m)=(2,7,3) no, hence it is not sufficient.

Therefore, the answer is E.
Answer: E
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Re: If x and y are positive integers, is x^m+y a multiple of 9?  [#permalink]

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New post 12 Feb 2017, 18:58
MathRevolution wrote:
==> In the original condition, there are 3 variables (x, y, m) and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), (x,y,m)=(1,8,3) yes, but (x,y,m)=(2,7,3) no, hence it is not sufficient.

Therefore, the answer is E.
Answer: E


Then,please correct the OA
Thanks :-D
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Re: If x and y are positive integers, is x^m+y a multiple of 9? &nbs [#permalink] 12 Feb 2017, 18:58
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If x and y are positive integers, is x^m+y a multiple of 9?

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