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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