BTGmoderatorDC wrote:Is the value of 3^a/3^b a prime number?

(1) a + b = 8
(2) a - b = 2

We have to determine whether the value of 3^a/3^b a prime number.

3^a/3^b can be written as 3^(a - b).

Question rephrased: Is 3^(a - b) a prime number?

3^(a - b) can be a prime number only if (a - b) = 1; for any other value, 3^(a - b) is not prime. You may try for 0, 2, -2, 1/2, etc.

Let's take each statement one by one.

(1) a + b = 8

Case 1: Say a = 4.5 and b = 3.5, then (a - b) = 1; thus, 3^(a - b) is a prime number.
Case 2: Say a = 5 and b = 3, then (a - b) = 2; thus, 3^(a - b) = 3^2 = 9; 9 is NOT a prime number.

No unique answer. Insufficient.

(2) a - b = 2

=> 3^(a - b) = 3^2 = 9; 9 is NOT a prime number. A unique answer. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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