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# If n=4p where p is a prime number greater than 2, how many

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Manager
Joined: 05 Mar 2011
Posts: 122
If n=4p where p is a prime number greater than 2, how many [#permalink]

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15 Dec 2011, 19:01
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If n=4p where p is a prime number greater than 2, how many different positive even divisors does n have, including n?

A. two
B. three
C. four
D. six
E. eight
Magoosh Co-Founder
Joined: 17 Sep 2011
Posts: 41
Schools: UC Berkeley (Haas) - Class of 2010

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Updated on: 19 Dec 2011, 12:34
1
1
If we take the prime factorization of n we get:
2, 2, p (p is in the prime factorization since were told it is a prime number in the question)

Looking for positive even divisors, we have:
2
4 (because of 2*2)
2p (because of 2 * p)
4p (because of 2 * 2 * p)

So we have 4 different positive even divisors.
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Originally posted by bhavinp on 15 Dec 2011, 19:06.
Last edited by bhavinp on 19 Dec 2011, 12:34, edited 1 time in total.
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16 Dec 2011, 02:50
1
bhavinp wrote:
If we take the prime factorization of n we get:
2, 2, p (p is in the prime factorization since were told it is a prime number in the question)

Looking for positive even divisors, we have:
2
4 (because of 2*2)
2n (because of 2 * n)
4n (because of 2 * 2 * n)

The even divisors here are 2, 4, 2p and 4p (not '2n' and '4n').
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Joined: 17 Oct 2011
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03 Jan 2012, 22:33
C. Four divisors .
2, 4, 2p, 4p (which is n)
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Joined: 02 Mar 2015
Posts: 31
Re: If n=4p where p is a prime number greater than 2, how many [#permalink]

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21 Aug 2015, 08:52
1
ashiima wrote:
If n=4p where p is a prime number greater than 2, how many different positive even divisors does n have, including n?

A. two
B. three
C. four
D. six
E. eight

$$n = 4p = (2^2)p$$

total factors = $$(2+1)(1+1) = 6$$
even factors = 2 x (1+1) = 4
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Re: If n=4p where p is a prime number greater than 2, how many [#permalink]

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21 Aug 2015, 11:16
Hi All,

This question can be solved rather easily by TESTing VALUES:

We're told that N = 4P and that P is a prime number greater than 2. Let's TEST P = 3; so N = 12

The question now asks how many DIFFERENT positive EVEN divisors does 12 have, including 12?

12:
1,12
2,6
3,4

How many of these divisors are EVEN? 2, 4, 6, 12 …..4 even divisors.

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Re: If n=4p where p is a prime number greater than 2, how many [#permalink]

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05 Aug 2017, 00:25
I agree. Easier to build test case. Answer would be constant.
Re: If n=4p where p is a prime number greater than 2, how many   [#permalink] 05 Aug 2017, 00:25
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