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
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
If n = 2pq, where p and q are distinct prime numbers
This topic has expert replies
-
BTGmoderatorDC
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Let p=3 and q=5, with the result that n = 2*3*5 = 30.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
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Mitch's approach is definitely the best.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
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
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7249
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
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: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
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
-
BTGmoderatorDC
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Thanks a lot!Brent@GMATPrepNow wrote:Mitch's approach is definitely the best.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
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
-
BTGmoderatorDC
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Thanks a lot!Scott@TargetTestPrep wrote: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: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
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
