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If \(n = 4p,\) where \(p\) is a prime number greater than \(2,\) how many different positive even divisors does \(n\)

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If \(n = 4p,\) where \(p\) is a prime number greater than \(2,\) how many different positive even divisors does \(n\)

by VJesus12 » Sat Sep 25, 2021 12:46 am

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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

Answer: C

Source: Official Guide
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Re: If \(n = 4p,\) where \(p\) is a prime number greater than \(2,\) how many different positive even divisors does \(n\

by Brent@GMATPrepNow » Sun Sep 26, 2021 7:19 am
VJesus12 wrote: ↑
Sat Sep 25, 2021 12:46 am
 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

Answer: C

Source: Official Guide
We can solve a lot of Integer Properties questions by testing a value

If p is prime, let's let p = 3
So, n = 4p = (4)(3) = 12

The positive EVEN divisors of 12 are: 2, 4, 6 and 12
So, there are FOUR even divisors of n.

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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