What is the remainder when the positive integer x is divided by 3 ?

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