SOLUTION: 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) 163 (C)

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Question 3864: 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) 163
(C) 121
(D) 99
(E) 44
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Let M = 10a + b, then N = 10 b+ a,
So M + N = 11 a + 11 b = 11 (a+b) , this means
M + N should be a multiple of 11.

Note amont these 5 integers
(A) 181 (B) 163
are not multiple of 11.
Hope you can see by direct view without any calculations.
In fact an ineger is a multiple of 11 if and only if the
difference of the sum of odd digits and the sum even digits is a multiple
of 11 . e.g. 286, 8294,73524.
Kenny