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shelrod007
Joined: 23 Jan 2013
Last visit: 16 Sep 2016
Posts: 99
Given Kudos: 41
Concentration: Technology, Other
Schools: Berkeley Haas
GMAT Date: 01-14-2015
WE:Information Technology (Computer Software)
Updated on: 22 Jul 2023, 03:48
Originally posted by shelrod007 on 31 May 2014, 10:33.
Last edited by Bunuel on 22 Jul 2023, 03:48, edited 2 times in total.
Last edited by Bunuel on 22 Jul 2023, 03:48, edited 2 times in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
43% (01:26) correct
57%
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wrong
based on 261
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How many different prime numbers are factors of the positive integer \(n\) ?
(1) \(2n\) has one prime factor.
(2) \(3n\) has one prime factor.
M18-37
(1) \(2n\) has one prime factor.
(2) \(3n\) has one prime factor.
M18-37
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31 May 2014, 15:54
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shelrod007
How many different prime numbers are factors of the positive integer \(n\) ?
(1) \(2n\) has one prime factor.
Clearly, the sole prime factor of \(2n\) is 2. Thus, possible values for \(2n\) include 2, 4, 8, etc., implying \(n\) could be 1, 2, 4, and so forth. If \(n=1\), it doesn't have any prime factor, but if \(n\) takes any other value (2, 4, ...), it has one prime factor: 2. Not sufficient.
(2) \(3n\) has one prime factor.
The situation here mirrors the first: the only prime factor of \(3n\) is 3. Hence, \(3n\) could be 3, 9, 27, etc., which implies \(n\) could be 1, 3, 9, and so on. If \(n=1\), then it doesn't have a prime factor, but if \(n\) takes any other value (3, 9, ...), it has one prime factor: 3. Not sufficient.
(1)+(2) From above, the only possible value of \(n\) is 1, and 1 does not have any prime factors. Sufficient.
Answer: C
General Discussion
21 Jan 2024, 10:49
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Bunuel
Hello,
I understand that n=1 is common case for both statements.
However, if we combine the 2 statements, we get 2n and 3n have 1 distinct prime divisor.
Isn't this ambiguous ?
