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p, q, x, and y are positive integers. If p^mq^n=72, what is

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by Max@Math Revolution » Tue May 29, 2018 1:31 am

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[GMAT math practice question]

p, q, x, and y are positive integers. If p^mq^n=72, what is the value of p+q?

1) m>n
2) mn=6
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Source: — Data Sufficiency |
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by GMATGuruNY » Tue May 29, 2018 2:40 am
I believe that the prompt has a typo and should read as follows:
Max@Math Revolution wrote:[GMAT math practice question]

p, q, m, and n are positive integers. If p^mq^n=72, what is the value of p+q?

1) m>n
2) mn=6
Both statements are satisfied by the following cases:
Case 1: p=2, m=3, q=3 and n=2, with the result that m>n, mn=3*2=6, and (p^m)(q^n) = 2³3² = 72
In this case, p+q = 2+3 = 5.
Case 2: p=1, m=6, q=72 and n=1, with the result that m>n, mn=6*1=6, and (p^m)(q^n) = 1�72¹ = 72
In this case, p+q = 1+72 = 73.
Since p+q can be different values, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by Max@Math Revolution » Thu May 31, 2018 3:22 am
=>

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 4 variables (p, q, m and n) and 1 equation, 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):
We can write 72 = 2^33^2=1^672^1. (find the "hidden 1")
If p = 2, q = 3, m = 3 and n = 2, then p + q = 5.
If p = 1, q = 72, m = 6 and n = 1, then p + q = 73.
Since we don't have a unique solution, both conditions, taken together, are not sufficient.

Therefore, the answer is E.

Answer: E

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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