BTGmoderatorDC wrote:X is a three-digit positive integer in which each digit is either 1 or 2. Y has the same digits as X, but in reverse order. What is the remainder when X is divided by 3?
(1) The hundreds digit of XY is 6.
(2) The tens digit of XY is 4.
OA A
Source: Manhattan Prep
This can be solved efficiently with some hit and trial approach.
Let's take each statement one by one.
(1) The hundreds digit of XY is 6.
Given that the hundreds digit of XY is 6, we can have two cases: 1. (X, Y):(121, 121) and 2. (X, Y):(112, 112). In each case, the remainder when X is divided by 3 is 1. Sufficient.
(2) The tens digit of XY is 4.
Given that the tens digit of XY is 4, we can have two cases: 1. (X, Y):(121, 121) and 2. (X, Y):(212, 212). In the first case, the remainder when X is divided by 3 is 1, while in the second case, the remainder when X is divided by 3 is 2.
No unique answer. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
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