2 Digit numbers in reversed order

justharsha 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

[spoiler]OA: A[/spoiler]

This question relies on our ability to determine the VALUE of any 2-digit number.
For example, what is the VALUE of 83?
For most of us, it has been a very long time since we examined this (we learned this when we were 5 or 6). Most of us just say that 83 has a value of 83, but 83 is really just a "recipe" for determining value.
83 is equal to 8 tens plus 3 ones.
Similarly, 76 is equal to 7 tens plus 6 ones.

In general, if tu represents a 2-digit number (where the t stands for the digit in the tens position, and the u stands for the digit in the units position), then the value of tu is 10t + u

So, if M = tu, then N = ut
The value of M is 10t + u, and the value of N us 10u + t
So, the value of M+N = (10t + u) + (10u + t) = 11t + 11u = 11(t + u)

So, we can see that M+N must be a MULTIPLE OF 11

Answer choices B, C, D and E are all multiples of 11.
Since 181 is not a multiple of 11, M+N cannot equal 181

Answer: A

Cheers,
Brent

Hi justharsha,

This type of question can be solved with algebra or "brute force"; here's how you use "brute force" to figure out what's possible and what's not.

We're told that M and N are each two-digit numbers with the two digits in reverse order (e.g. 23 and 32). We're asked which of the 5 answers CANNOT BE the sum of the M and N.

Let's see if we can sum to the given answers (starting with the easiest; keep in mind that there might be more than one way to "hit" each answer):

44? 13 + 31
99? 45 + 54
121? 56 + 65
165? 78 + 87

Since we can sum to each of those 4 answers, the answer that we CANNOT sum to must be A

GMAT assassins aren't born, they're made,
Rich