[GMAT math practice question]
If n is the product of the squares of 4 different prime numbers, how many factors does n have?
A. 8
B. 16
C. 27
D. 64
E. 81
If n is the product of the squares of 4 different prime numb
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
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
-----------ASIDE------------------Max@Math Revolution wrote: If n is the product of the squares of 4 different prime numbers, how many factors does n have?
A. 8
B. 16
C. 27
D. 64
E. 81
If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.
Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40
-------------------------------------
n is the product of the squares of 4 different prime numbers
So, let's say n = (p²)(q²)(r²)(s²), where p, q, r and s are 4 different prime numbers
By the above rule, the number of positive divisors of n = (2+1)(2+1)(2+1)(2+1) =(3)(3)(3)(3) = 81
Answer: E
Cheers,
Brent
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
=>
n = p^2q^2r^2s^2 where p, q, r and s are 4 different prime numbers.
Then the number of factors of n is (2+1)(2+1)(2+1)(2+1) = 34 = 81.
Therefore, the answer is E.
Answer: E
n = p^2q^2r^2s^2 where p, q, r and s are 4 different prime numbers.
Then the number of factors of n is (2+1)(2+1)(2+1)(2+1) = 34 = 81.
Therefore, the answer is E.
Answer: E
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can use 2, 3, 5, and 7:Max@Math Revolution wrote: ↑Fri Jun 15, 2018 12:54 am[GMAT math practice question]
If n is the product of the squares of 4 different prime numbers, how many factors does n have?
A. 8
B. 16
C. 27
D. 64
E. 81
So, we have 2^2 x 3^2 x 5^2 x 7^2
To determine the total number of factors, we add 1 to each exponent attached to each base and multiply those values together.
(2 + 1) x (2 + 1) x (2 + 1) x (2 + 1) = 81
Answer: E
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