Given: a and b are integers
Target question: What is the value of ab?
Statement 1: 5^(a+b) = 125
Express the right side as follows: 5^(a+b) = 5^3
Since the bases are equal, the exponents must be equal to get: a + b = 3
There are several values of a and b that satisfy statement the condition that a + b = 3. Here are two:
Case a: a = -1 and b = 4. In this case, the answer to the target question is ab = (-1)(4) = -4
Case b: a = 1 and b = 2. In this case, the answer to the target question is ab = (1)(2) = 2
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3^(a/b) = 1
The only way to express the right side with base 3 is as follows: 3^(a/b) = 3^0
Since the bases are equal, the exponents must be equal to get: a/b = 0
If a/b = 0, then we can't be certain that a = 0
If a = 0, then we can be certain that ab = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
