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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# Rich Cohen

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