Integer confusion

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deagez: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Sun Dec 28, 2008 2:52 am; Location: Denver; Thanked: 2 times

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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Source: Beat The GMAT — Problem Solving | Sat Apr 11, 2009 3:50 am

mals24: Legendary Member; Posts: 683; Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members; Location: Dubai; Thanked: 73 times

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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