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Prime factors DS

by raceformula » Sun Apr 15, 2012 10:13 am
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 n2.

Could anyone please answer with explanation.
Thank you.
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by killer1387 » Sun Apr 15, 2012 10:29 am
raceformula 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 n2.

Could anyone please answer with explanation.
Thank you.
statement 1) four prime factors may include 2 so we cant anything concrete.
INSUFFICIENT

statement 2) four prime factors mean its for n.
sufficient

hence B
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by Anurag@Gurome » Sun Apr 15, 2012 7:21 pm
raceformula 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 n2.

Could anyone please answer with explanation.
Thank you.
(1) Four different prime numbers are factors of 2n implies that one of the four prime numbers is 2 but 2 may be a factor of n, and if that is so then the total number of prime factors will not change.
If n = 2 * 3 * 5 * 7 (here n has 4 prime factors), then 2n = 2 * 2 * 3 * 5 * 7. Here 2n has 4 prime factors.
If n = 3 * 5 * 7 (here n has 3 prime factors), then 2n = 2 * 3 * 5 * 7. Here 2n has 4 prime factors.
From the above examples, it can be seen that number of different prime numbers may vary; NOT sufficient.

(2) Four different prime numbers are factors of n² implies four different prime numbers are factors of n as well; SUFFICIENT.

The correct answer is B.
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by raceformula » Mon Apr 16, 2012 9:30 am
Thanks a lot Anurag for the answer and expln.
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by Anaira Mitch » Wed Dec 28, 2016 3:20 am
1). When n is 105, or 210, 2*n has four different prime factors: 2, 3, 5, 7, but 105 has 3 prime factors, and 210 has 4 prime factors.

2). Sufficient.

Answer is B
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