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20 Oct 2021, 11:59
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
59% (01:46) correct
41%
(01:57)
wrong
based on 110
sessions
History
Date
Time
Result
Not Attempted Yet
Is positive integer \(k\), the square of an integer?
(1) \(9k\) is the cube of an integer
(2) \(\frac{k}{9} \)is the square of an integer
(1) \(9k\) is the cube of an integer
(2) \(\frac{k}{9} \)is the square of an integer
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
20 Oct 2021, 13:47
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GMATWhizTeam
Statement 1 Alone:
Since the result 9k is a cube, the prime factorization of 9k must have cubes for each prime factor. We are missing a factor of 3 to complete the cube of 3's if we only look at 9. That factor of 3 must come from k, then we know k is a cube multiplied by three.
We may have \(k = 3^3 *3\), then k is a square. We could also have \(k = 2^3 * 3\), then k is not a square. So this statement is insufficient.
Statement 2 Alone:
\(\frac{k}{9} = i^2\), where \(i\) is any positive integer.
\(k = 9i^2 = (3*i)^2\) must be a square then.
Answer: B
16 Dec 2023, 16:17
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