Hi All,
These types of 'remainder' questions are almost always easily solved by TESTing VALUES.
We're told that X is a positive integer. We're asked for the remainder when X is divided by 3.
Fact 1: When X is divided by 6, the remainder is 2
I'm going to list out the first few integers that fit this description:
X = 2, 8, 14, 20, 26, 32, etc....
The pattern here is that each number is "6 more" than the one before it. Now, let's see what happens when we use these values in the question:
IF...
X = 2
2/3 = 0 remainder 2
X = 8
8/3 = 2 remainder 2
X = 14
14/3 = 4 remainder 2
X = 20
20/3 = 6 remainder 2
Etc.
The pattern here is clear (and you could probably name the next few "results" without doing any calculations at all). The remainder is ALWAYS 2.
Fact 1 is SUFFCIENT
Fact 2: When X is divided by 15, the remainder is 2
Here are the first few terms that fit this Fact:
X = 2, 17, 32, 47, etc.
IF....
X = 2
2/3 = 0 remainder 2
X = 17
17/3 = 5 remainder 2
X = 32
32/3 = 10 remainder 2
X = 47
47/3 = 15 remainder 2
Etc.
Just as in Fact 1, we have a clear pattern here. The answer is ALWAYS 2.
Fact 2 is SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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