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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.
The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.
Modifying the question:
\(\frac{9^{a+2b}}{3^{a+3b}}=?\)
\(⇔ \frac{(3^2)^{a+2b}}{3^{a+3b}}=?\)
\(⇔ \frac{3^{2a+4b}}{3^{a+3b}}=?\)
\(⇔ 3^{a+b}=?\)
Condition 1)
Since the exponent is \(a + b\), this condition is sufficient.
Condition 2)
The value of \(a – b\) does not tell us anything about the value of \(a + b\).
For example, if \(a = 6\) and \(b = 3\), \(a + b = 9\); and if \(a = 7\) and \(b = 4, a + b = 11\).
Since there is no unique answer, condition 2) is NOT sufficient.
Therefore, the answer is A.
Answer: A
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