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

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VP
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If the two-digit integers M and N are positive and have the [#permalink]

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02 Oct 2007, 11:43
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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) 165
(C) 121
(D) 99
(E) 44
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02 Oct 2007, 11:46
product cannot be a multiple of 11, so 181...
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02 Oct 2007, 11:49
M = x*10 + y
N = 10*y + x

so:

x*10 + y + 10*y + x = 11*y + 11*x = 11*(y+x)

so the answer cannot be a multiply of 11

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02 Oct 2007, 12:09
Ravshonbek wrote:
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) 165
(C) 121
(D) 99
(E) 44

A.

1st integer = MN = 10M + N
2nd integer = NM = 10N + M

Sum = 10M + N + 10N + M = 11M + 11N = 11 (M+N)
Therefore, sum of M+N is a multiple of 11. Anything that isn't a multiple of 11 in the answer choices is out answer. 181 is it.
Re: back to basics   [#permalink] 02 Oct 2007, 12:09
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