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28 Feb 2017, 04:16
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
37% (02:25) correct
63%
(02:30)
wrong
based on 164
sessions
History
Date
Time
Result
Not Attempted Yet
Can the total number of integers that divide x be expressed in the form of \(2k + 1\), where k is a positive integer?
(1) \(√12x\) is an integer
(2) The product of \(√x\) and \(√y\) is an integer, where the total number of factors of \(\frac{y}{3}\) is odd.
Answer Choices:
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Thanks,
Saquib
Quant Expert
e-GMAT
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(1) \(√12x\) is an integer
(2) The product of \(√x\) and \(√y\) is an integer, where the total number of factors of \(\frac{y}{3}\) is odd.
Answer Choices:
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Thanks,
Saquib
Quant Expert
e-GMAT
Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts
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
28 Feb 2017, 17:55
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D.
Question asked if the x has odd number total of factors.
S1: Plug in x = 3 & x = 27 --> both get √12x integer and both 3, 27 have even number total of factors. Sufficient
S2: y/3 has odd number total of factors --> y = 3A (with A is prime factorize of Y/3) --> y has even number total of factors.
In order for √xy integer, x must have odd exponent --> x has even number total of factors. Sufficient
Question asked if the x has odd number total of factors.
S1: Plug in x = 3 & x = 27 --> both get √12x integer and both 3, 27 have even number total of factors. Sufficient
S2: y/3 has odd number total of factors --> y = 3A (with A is prime factorize of Y/3) --> y has even number total of factors.
In order for √xy integer, x must have odd exponent --> x has even number total of factors. Sufficient
11 Mar 2017, 07:19
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dunghoang110
Good solution.
Just exploring possible s1 without testing numbers:
Another way to think of S1 is sqrt(12x)=sqrt(2².3.x), which means x has to have an odd number of 3 factors. (3^1, 3^3, 3^5, ...), which means no x will have an odd total number of factors.
