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## If two digit integer M and N are positive and have same digits, but in reverse order, which of the following cannot be the sum of M and N. (GMAT-MATHS)

##### If two digit integer M and N are positive and have same digits, but in reverse order, which of thefollowing cannot be the sum of M and N. (GMAT-MATHS)a) 181b) 165c) 121d) 99e) 44

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Option A is correct.
solution:
M=10x+y
N=10y+x
M+N=11x+11y=11(x+y)
In other words the answer is a multiple of 11.
Now the question becomes " which of the following is NOT a multiple of 11?"

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|PrashantIIST

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Lets try this question by trial and error. Lets try to get all answers starting with smallest
value 44. It can be sum of 22 and 22. So (E) is ruled out. Now move to 99. It could be
sum of 54 and 45. So (D) goes. Next 121 could be written as 56 + 65. So even (C) goes.
Now try out 165. It could be the sum of 87 and 78. So after POE rest four (A) becomes
the answer, as it cannot be written as sum of desired combination.

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|Jaynil-Gaglani

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