Data Sufficiency

faraz_jeddah wrote:If a,b,c are integers all greater than 1, and 15^8 = a * (b)^c. What is the value of c?

(1) a is not divisible by 5
(2) b is not divisible by 3

Target question: What is the value of c?

Given: a,b,c are integers all greater than 1, and 15^8 = a * (b)^c

Here are a few possibilities:
15^8 = (3^8)(5^8)
15^8 = (5^8)(3^8)
15^8 = (3^8)(25^4) since 25 = 5^2, we get (3^8)(25^4) = (3^8)(5^2)^4 = (3^8)(5^8) = 15^8
15^8 = (3^8)(625^2) since 625 = 5^4, we get (3^8)(625^2) = (3^8)(5^4)^2 = (3^8)(5^8) = 15^8

Okay, now onto the question

Statement 1: a is not divisible by 5
There are several sets of values that meet this condition. Here are two:
Case a: 15^8 = (3^8)(5^8), in which case a = 3^8, b = 5 and c = 8
Case b: 15^8 = (3^8)(25^4), in which case a = 3^8, b = 25 and c = 4
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: b is not divisible by 3
There are several sets of values that meet this condition. Here are two:
Case a: 15^8 = (3^8)(5^8), in which case a = 3^8, b = 5 and c = 8
Case b: 15^8 = (3^8)(25^4), in which case a = 3^8, b = 25 and c = 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
There are still different sets of values that meet this condition. Here are two:
Case a: 15^8 = (3^8)(5^8), in which case a = 3^8, b = 5 and c = 8
Case b: 15^8 = (3^8)(25^4), in which case a = 3^8, b = 25 and c = 4
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent