If n = 2pq, where p and q are distinct prime numbers

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sat Nov 18, 2017 3:42 am

If n = 2pq, where p and q are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight

How can i solve this problem? How will i start? Can some experts help me?

OA C

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Source: Beat The GMAT — Problem Solving | Sat Nov 18, 2017 3:42 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Nov 18, 2017 5:50 am

lheiannie07 wrote:If n = 2pq, where p and q are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight

Let p=3 and q=5, with the result that n = 2*3*5 = 30.
Factors pairs of 30:
1*30
2*15
3*10
5*6.

As illustrated by the blue values above, the number of even factors = 4.

The correct answer is C.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Nov 18, 2017 7:45 am

lheiannie07 wrote:If n = 2pq, where p and q are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight

Mitch's approach is definitely the best.
However, if you didn't come up with that approach, here's another.

If p and q are distinct prime numbers greater than 2, then p and q are each odd
So, if n = 2pq, then the positive EVEN divisors of n are: 2, 2p, 2q and 2pq (4 in total)
Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Dec 13, 2017 12:22 pm

lheiannie07 wrote:If n = 2pq, where p and q are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight

We can let p = 3 and q = 5. Thus, the product of 2pq is 2 x 3 x 5 = 30. The factors of 30 are:

1, 30, 2, 15, 3, 10, 5, 6

Since 30 has 4 even factors, n has 4 even factors.

Alternatively, we can solve the problem algebraically. Keep in mind that p and q will be odd primes since they are greater than 2.

The factors of n are:

1, 2pq, 2, pq, p, 2q, q, 2p

We see that the even factors of n are 2pq, 2, 2q, and 2p, so there are 4 even factors.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Jan 10, 2018 9:44 pm

Brent@GMATPrepNow wrote:
lheiannie07 wrote:If n = 2pq, where p and q are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Mitch's approach is definitely the best.
However, if you didn't come up with that approach, here's another.

If p and q are distinct prime numbers greater than 2, then p and q are each odd
So, if n = 2pq, then the positive EVEN divisors of n are: 2, 2p, 2q and 2pq (4 in total)
Answer: C

Cheers,
Brent

Thanks a lot!

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Jan 10, 2018 9:45 pm

Scott@TargetTestPrep wrote:
lheiannie07 wrote:If n = 2pq, where p and q are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
We can let p = 3 and q = 5. Thus, the product of 2pq is 2 x 3 x 5 = 30. The factors of 30 are:

1, 30, 2, 15, 3, 10, 5, 6

Since 30 has 4 even factors, n has 4 even factors.

Alternatively, we can solve the problem algebraically. Keep in mind that p and q will be odd primes since they are greater than 2.

The factors of n are:

1, 2pq, 2, pq, p, 2q, q, 2p

We see that the even factors of n are 2pq, 2, 2q, and 2p, so there are 4 even factors.

Answer: C

Thanks a lot!

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