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
