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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If x and y are positive integers, x/y=? tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## If x and y are positive integers, x/y=? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [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 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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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) = 2Â³3Â² = 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) = 2Â³3Â² = 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) = 2Â²3Â¹ = 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.

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