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CANNOT be the sum

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CANNOT be the sum

by gmatblood » Mon Oct 31, 2011 10:30 am
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

Would like to know if there is any shortcut to check it!
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by ripulgupta » Mon Oct 31, 2011 11:08 am
As we are adding two two-digit numbers and both the number contain the same digits but in reverse order. The last two digits of there addition have to be either same or tens digit can be one more than the units digits. This condition is true for all the options except A. Thus the solution.
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by shankar.ashwin » Mon Oct 31, 2011 11:09 am
Well it should be a multiple of 11.
10X+Y +10Y+X = 11(X+Y) A is not.
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by gmatblood » Mon Oct 31, 2011 11:14 am
shankar.ashwin wrote:Well it should be a multiple of 11.
10X+Y +10Y+X = 11(X+Y) A is not.
Is this condition valid all the time?
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by gmatblood » Mon Oct 31, 2011 11:14 am
ripulgupta wrote:As we are adding two two-digit numbers and both the number contain the same digits but in reverse order. The last two digits of there addition have to be either same or tens digit can be one more than the units digits. This condition is true for all the options except A. Thus the solution.
Is this a valid condition! Thanks anyways :)
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by shankar.ashwin » Mon Oct 31, 2011 11:24 am
Yup, it is. Similarly if the digits of 2 numbers are reversed and subtracted,

10X+Y -10Y-X = 9(X-Y), the number would be a multiple of 9.

gmatblood wrote:
shankar.ashwin wrote:Well it should be a multiple of 11.
10X+Y +10Y+X = 11(X+Y) A is not.
Is this condition valid all the time?
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