Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
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https://www.mathrevolution.com/gmat/lesson for details.
Second of the seven properties of exponents: \(\frac{a^m}{a^n}=a^{\left(m-n\right)}\)
Multiplication of the same base numbers with the same or different exponents = Addition of the exponents
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https://www.mathrevolution.com/gmat/lesson for details.
Now we will solve this DS question using the Variable Approach.
Let’s apply the 3 steps suggested previously.
Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.
We have to find the value of \(\frac{3^{\left(a+b\right)}}{3^{\left(a-2b\right)}}\)
Second property of exponents: \(\frac{3^{\left(a+b\right)}}{3^{\left(a-2b\right)}}=3^{\left(a+b-\left(a-2b\right)\right)}=3^b\)
We have to find the value of 3b
Condition (2) tells us that 3b = 8
=> \(3^{3b}\) = \(3^{8}\) = 6,561
The answer is unique, so condition (2) alone is sufficient, according to CMT 2 - there must be one answer.
Condition (1) tells us that a = 4
=> Cannot determine the unique value of 3b
The answer is not unique, so condition (1) alone is not sufficient, according to CMT 2 - there must be one answer.
Condition (2) alone is sufficient.
Therefore, B is the correct answer.
Answer: B
