sodha.rakesh wrote:GMATGuruNY wrote:sodha.rakesh wrote:If 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
Source : OG 12th Edition, Q-182
Official Ans. A
Is there any shortcut/efficient method ?
Look at the units digits of the answer choices.
For the sum of M and N to have a units digit of 1, the sum of the units digits of M and the units digit of N must be 11.
Thus, to obtain answer choice A (181) or answer choice C (121), the units digits of M and N must be either 2 and 9, 3 and 8, 4 and 7, or 5 and 6.
29 + 92 = 38 + 83 = 47 + 74 = 56 + 65 = 121.
No way to get a sum of 181.
The correct answer is
A.
Thank you for your reply and good strategy (that is the reason why I posted this que. here), Would you please provide some details why we are considering the answer choices 121 & 181 only and how to eliminate other options e.g. 99,44,165?
Two reasons I focused on answer choices A and C:
-- they each have the same units digit (1), increasing the likelihood that one of them won't be possible.
-- there is only way to get a units digit of 1: the sum of the digits M and N must be 11.
Once I determined that MN + NM = 181 is impossible, there was no reason to check the other answer choices.
The other answers choices can be eliminated because they are all easily achieved:
E) 44 = 13+31 (any two digits whose sum is 4 will work)
D) 99 = 45+54 (any two digits whose sum is 9 will work)
B) 165 = 78+87 (any two digits whose sum is 15 will work)
Hope this helps!
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