Data Sufficiency

[GMAT math practice question]

If x and y are positive integers, x/y=?

1) 2^{x+y}3^{xy}=72
2) 2^x3^y=12

Max@Math Revolution wrote:[GMAT math practice question]

If x and y are positive integers, x/y=?

1) 2^{x+y}3^{xy}=72
2) 2^x3^y=12

Statement 1:
Case 1: x=2 and y=1, with the result that 2^(x+y) * 3^(xy) = 2³3² = 72
In this case, x/y = 2/1 = 2.
Case 2: x=1 and y=2, with the result that 2^(x+y) * 3^(xy) = 2³3² = 72
In this case, x/y = 1/2 = 1/2.
Since x/y can be different values, INSUFFICIENT.

Statement 2:
Here, x=2 and y=1, with the result that (2^x)(3^y) = 2²3¹ = 12.
Thus, x/y = 2/1 = 2.
SUFFICIENT.

The correct answer is B.

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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. We then recheck the question.

Condition 2) tells us that 2^x3^y=12 = 2^23^1 and x = 2, y = 1.
Thus x/y = 2/1 = 2, and condition 2) is sufficient.

Condition 1)
2^{x+y}3^{xy}=72 = 2^33^2 yields the equations x+y=3 and xy=2.
So, x = 1 and y = 2, or x =2 and y = 1.
Thus, x/y = 1/2 or x/y = 2/1 = 2.
Condition 1) is not sufficient since it does not yield a unique solution.

Therefore, B is the answer.
Answer: B