X and Y are both two-digit numbers, with X Y. If X and Y contain the

Question

X and Y are both two-digit numbers, with X > Y. If X and Y contain the same digits, but in reverse order, which of the following must be a factor of (X − Y)?

(A) 4

(B) 5

(C) 6

(D) 9

(E) 11

BrentGMATPrepNow · Accepted Answer

The quickest approach here is to find values of X and Y that satisfy the given information, and then test those values.

For example, it could be the case that X = 32 and Y = 23, in which case X - Y = 32 - 23 =   9  
Among the given answer choices, 9 is the only one that is a factor of   9  .
Answer: D

Alternatively, we could have chosen X = 53 and Y = 35, in which case X - Y = 53 - 35 =   18  
Among the given answer choices, 6 and 9 are both factors of   18  , which means we'd have to test another pair of values in order to eliminate one of those two remaining answer choices.

Showmeyaa · Answer

Let X = 10a + b
Y = 10b + a
Where X > Y
(X-Y) = 10a + b - 10b - a
=9a - 9b
9(a - b)
IMO, (D)!

Abhishek009 · Answer

This is a property of any number...

Difference between a 2 digit number and the number formed by reversing the digits (of the 2 digit number) will always be divisible by 9, Hence Answer must be (D)

Proof has been wonderfully shown by  Showmeyaa

X and Y are both two-digit numbers, with X > Y. If X and Y contain the

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