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Integer confusion

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by deagez » Sat Apr 11, 2009 3:50 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

The explanation made this problem more confusing than it originally was.
Help plz.

OA is A
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by mals24 » Sat Apr 11, 2009 4:06 am
A 2 digit integer can be written in the following way: 10a+b; where a is the 10ths digit and b the units digit.
For instance: 21 = 10*2 + 1

So let M = 10a+b
and N = 10b+a (reverse the 10ths and units digit of M).

M+N = 11a+11b
= 11(a+b)

Hence the sum of M and N should be divisible by 11.

Only A doesn't fit the bill.
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