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How many different prime numbers are factors of the positive integer n
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21 Nov 2019, 08:48
21 Nov 2019, 08:48
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How many different prime numbers are factors of the positive integer n ?
(1) Four different prime numbers are factors of 2n
(2) Four different prime numbers are factors of n
A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.
(1) Four different prime numbers are factors of 2n
(2) Four different prime numbers are factors of n
A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: How many different prime numbers are factors of the positive integer n
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21 Nov 2019, 09:50
21 Nov 2019, 09:50
sargambhir wrote:
How many different prime numbers are factors of the positive integer n ?
(1) Four different prime numbers are factors of 2n
(2) Four different prime numbers are factors of n
A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.
(1) Four different prime numbers are factors of 2n
(2) Four different prime numbers are factors of n
A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.
vjalan Provide very good explanation stated below:
Well, from statement 1 you get that 2n has 4 different prime factors. This implies that n has at least 3 different prime factors (if n is not even) and 4 different prime factors (if n is even).
Two possibilities - A and D out.
From statement 2 we get that n^2 has 4 different prime factors. This would mean that n will also have the same 4 different prime factors as n^2 {why? because any additional factors that n^2 has over n will be composite and not prime. We can understand this better with an example. The smallest number with 4 different prime factors is 210 (2*3*5*7). 210^2 = (2^2)*(3^2)*(5^2)*(7^2). Thus, no new prime factors come into play.}
Answer is B
Please give kudos, if you find explanation good enough 
Re: How many different prime numbers are factors of the positive integer n
[#permalink]
21 Nov 2019, 10:32
21 Nov 2019, 10:32
Expert Reply
sargambhir wrote:
How many different prime numbers are factors of the positive integer n ?
(1) Four different prime numbers are factors of 2n
(2) Four different prime numbers are factors of n
A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.
(1) Four different prime numbers are factors of 2n
(2) Four different prime numbers are factors of n
A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.
This question is discussed here: how-many-different-prime-numbers-are-factors-of-the-positive-integer-n-126744.html?fl=similar Hope it helps.
THE TOPIC IS LOCKED AND ARCHIVED.
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!
