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29 May 2018, 02:38
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
23% (01:54) correct
77%
(01:30)
wrong
based on 13
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Not Attempted Yet
[GMAT math practice question]
\(p, q, x\), and \(y\) are positive integers. If \(p^mq^n=72\), what is the value of \(p+q\)?
\(1) m>n\)
\(2) mn=6\)
\(p, q, x\), and \(y\) are positive integers. If \(p^mq^n=72\), what is the value of \(p+q\)?
\(1) m>n\)
\(2) mn=6\)
Archived Topic
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
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29 May 2018, 03:52
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MathRevolution
This question seems to be incorrectly worded. It mentions x & y are positive integers but reference in made to m & n. Kindly clarify.
31 May 2018, 04:34
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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 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.
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.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
