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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 ## p, q, and r are different prime numbers. What is the value o tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## p, q, and r are different prime numbers. What is the value o ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] p, q, and r are different prime numbers. What is the value of q? 1) (pq)^2=36 2) (qr)^2= 225 _________________ 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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Max@Math Revolution wrote:
[GMAT math practice question]

p, q, and r are different prime numbers. What is the value of q?

1) (pq)^2=36
2) (qr)^2= 225
Statement 1:
(pq)² = 36
pq = 6
Case 1: p=2 and q=3
Case 2: p=3 and q=2
Since q can be different values, INSUFFICIENT.

Statement 2:
(qr)² = 225
qr = 15
Case 1: q=3 and r=5
Case 2: q=5 and r=3
Since q can be different values, INSUFFICIENT.

Statements combined:
Only one case satisfies pq = 6 and qr = 15:
p=2, q=3 and r=5
Thus, q=3.
SUFFICIENT.

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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.

Since we have 3 variables (p, q and r) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

Since p^2q^2=2^23^2 and q^2r^2 = 3^25^2, we have p = 2, q = 3 and r = 5.
Conditions 1) & 2) are sufficient, when applied together.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Since p^2q^2=2^23^2, we must have p = 2, q = 3 or p = 3, q = 2.
Condition 1) is not sufficient since it does not yield a unique solution.

Condition 2)
Since q^2r^2=3^25^2, we have q = 3, r = 5 or q = 5, r = 3.
Condition 2) is not sufficient since it does not yield a unique solution.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

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