If n = 4p, where p is a prime number greater than 2, how man : GMAT Problem Solving (PS)
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# If n = 4p, where p is a prime number greater than 2, how man

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

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24 Aug 2007, 08:41
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-4p-where-p-is-a-prime-number-greater-than-2-how-man-144781.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Sep 2013, 12:13, edited 1 time in total.
Edited the question and added the OA
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24 Aug 2007, 09:10
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n=4p

since n = 4p then even divisors are:

4p/4p = 1

4p/2p = 2

4p/4 = p

4p/2 = 2p

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24 Aug 2007, 10:19
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umm..lets see..

n=4p where p is a prime >2

lets pick a number 3..

n=12

even divisors are 0, 2, 4, 6

4 divisors
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24 Aug 2007, 10:35
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fresinha12 wrote:
umm..lets see..

n=4p where p is a prime >2

lets pick a number 3..

n=12

even divisors are 0, 2, 4, 6

4 divisors

zero is not a divisor of 12 since 12/0 is undefined ! but 12 is a divisor of 12.

so 2,4,6,12.

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24 Aug 2007, 11:03
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tinman1412 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)2
B)3
C)4
D)6
E)8

C. +ve even divisors = 2, 4, 2p and 4p. altogather 4.
+ve divisors = 1, 2, 4, p, 2p and 4p. altogather 6.
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24 Aug 2007, 11:22
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yup...what was i thinking...12 is a divisor..

KillerSquirrel wrote:
fresinha12 wrote:
umm..lets see..

n=4p where p is a prime >2

lets pick a number 3..

n=12

even divisors are 0, 2, 4, 6

4 divisors

zero is not a divisor of 12 since 12/0 is undefined ! but 12 is a divisor of 12.

so 2,4,6,12.

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24 Aug 2007, 11:46
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fresinha12 wrote:
yup...what was i thinking...12 is a divisor..

I know - Your reasoning is always so perfect. I was surprised to see you write something like that.

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24 Aug 2007, 13:21
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fresinha12 wrote:
yup...what was i thinking...12 is a divisor..

KillerSquirrel wrote:
fresinha12 wrote:
umm..lets see..

n=4p where p is a prime >2

lets pick a number 3..

n=12

even divisors are 0, 2, 4, 6

4 divisors

zero is not a divisor of 12 since 12/0 is undefined ! but 12 is a divisor of 12.

so 2,4,6,12.

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

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14 Sep 2013, 11:34
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Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink]

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14 Sep 2013, 12:14
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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

Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positive even divisors will 4p have.

p = 3 --> 4p = 12--> 12 has 4 even divisors: 2, 4, 6, and 12.

Or this way: since p is prime greater than 2, then p=odd, thus 4p=even, which means that it has 4 even divisors: 2, 4, 2p, and 4p.

Similar question to practice: if-n-is-a-prime-number-greater-than-3-what-is-the-remainder-137869.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-4p-where-p-is-a-prime-number-greater-than-2-how-man-144781.html
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Re: If n = 4p, where p is a prime number greater than 2, how man   [#permalink] 14 Sep 2013, 12:14
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# If n = 4p, where p is a prime number greater than 2, how man

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