Hi All,

This question can be solved by TESTing VALUES and pattern-matching.

We're told that A and B are POSITIVE INTEGERS. We're asked if \sqrt{(A+B} is an INTEGER. This is a YES/NO question.

Fact 1: A < B+3

IF.....

A = 1

B = 3

Then \sqrt{(1+3)} = 2 and the answer to the question is YES.

IF....

A = 1

B = 1

Then \sqrt{(1+1)} = NOT an integer and the answer to the question is NO.

Fact 1 is INSUFFICIENT

Fact: 2: A = B(B-1)

IF....

B = 2

A = 2(1) = 2

Then \sqrt{(2+2)} = 2 and the answer to the question is YES.

IF....

B = 3

A = (3)(2) = 6

Then \sqrt{(6+3)} = 3 and the answer to the question is YES.

IF....

B = 4

A = (4)(3) = 12

Then \sqrt{(12+4)} = 4 and the answer to the question is YES.

As you can see, as B increases, we ALWAYS end up with a perfect square "under" the square root, so we ALWAYS end up with an integer in the end.

Fact 2 is SUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,

Rich

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