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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 ## 2^p/2^q=? tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] 2^p/2^q=? 1) p = q + 2 2) pq=8 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only World’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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### GMAT/MBA Expert

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

What is the value of (2^p)/(2^q) ?

1) p = q + 2
2) pq = 8
Target question: What is the value of (2^p)/(2^q) ?
This is a good candidate for rephrasing the target question.
Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Take: (2^p)/(2^q)
Apply the Quotient law to get: 2^(p - q)
This means (2^p)/(2^q) = 2^(p - q)
So, in order to evaluate (2^p)/(2^q), all we need to do is determine the value of p - q
So,......
REPHRASED target question: What is the value of p-q ?

Statement 1: p = q + 2
Subtract q from both sides to get: p - q = 2
So, the answer to the target question is p - q = 2
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: pq = 8
There are several values of x and y that satisfy statement 2. Here are two:
Case a: p = 8 and q = 1. In this case, the answer to the REPHRASED target question is p - q = 7
Case b: p = 4 and q = 2. In this case, the answer to the REPHRASED target question is p - q = 2
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

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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.

Modifying the question:
What is the value of 2^p/2^q= 2^{p-q}?
So, we need to be able to find the value of p-q.

Thus, condition 1), which is equivalent to p - q = 2, is sufficient.

Condition 2):
If p =4 and q = 2, then 2^p/2^q= 2^{p-q} = 2^2 = 4.
If p =8 and q = 1, then 2^p/2^q= 2^{p-q} = 2^7 = 128.
Since we don’t have a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

_________________ Math Revolution
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