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If the two-digit integers M and N are positive and have the

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If the two-digit integers M and N are positive and have the [#permalink] New post 07 Aug 2007, 21:48
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14. If the two-digit integers M and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N ?
(A) 181
(B) 163
(C) 121
(D) 99
(E) 44
y is OA A here
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Re: PS Section 29 Q 14 [#permalink] New post 08 Aug 2007, 00:15
crazy123 wrote:
14. If the two-digit integers M and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N ?
(A) 181
(B) 163
(C) 121
(D) 99
(E) 44
y is OA A here


The 2 mumbers can be represented as (10x+y) and (10y+x).
Their sum would then be 11(x+y) and, hence, must be divisible by 11.
181 is the only choice not divisible by 11. Hence, A is the answer.
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 [#permalink] New post 08 Aug 2007, 00:26
M is represented by XY and N is represented by YX.

So M+N = 10X + Y + 10Y + X = 10(x+y) + (x+y) = 11(x+y)

So the solution must not be a multiple of 11.

C,D,E are all multiples of 11 --> Out.

Are you sure B is 163 and not 165 because both 181 and 163 are not divisible by 11. Since your OA is A, I think your choice B should be 165.
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 [#permalink] New post 09 Aug 2007, 08:04
I am confused..A and B are both answers to the question???
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 [#permalink] New post 09 Aug 2007, 10:02
There must be an error in copying down the question. I have seen this before and the answer was 181 (A). The second choice was 165.
  [#permalink] 09 Aug 2007, 10:02
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