If \(a\) and \(b\) are integers, what is the value of \(ab?\)

[M7MBA]

If \(a\) and \(b\) are integers, what is the value of \(ab?\)

(1) \(5^{a+b} = 125\)

(2) \(3^{a/b} = 1\)

Answer: B

Source: e-GMAT

[Brent@GMATPrepNow]

If \(a\) and \(b\) are integers, what is the value of \(ab?\)

(1) \(5^{a+b} = 125\)

(2) \(3^{a/b} = 1\)

Answer: B

Source: e-GMAT

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