If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?
a. 8
b. 9
c. 12
d. 15
e. 27
The OA is the option D.
How can I know the number of factor without knowing the value of m, p and t?
Experts, may you give me some help here? Please. <i class="em em-disappointed"></i>
If m, p, and t are distinct positive prime numbers
This topic has expert replies
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---------------------M7MBA wrote:If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?
a. 8
b. 9
c. 12
d. 15
e. 27
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
-----ONTO THE QUESTION!!----------------------------
(m^3)(p)(t) = (m^3)(p^1)(t^1)
So, the number of positive divisors of (m^3)(p)(t) = (3+1)(1+1)(1+1) = (4)(2)(2) = 16
IMPORTANT: We have included 1 as one of the 16 factors in our solution above, but the question asks us to find the number of positive factors greater than 1.
So, the answer to the question = 16 - 1 = 15
Answer: D
Cheers,
Brent
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7294
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
To determine the total number of factors of a number, we can add 1 to the exponent of each distinct prime factor and multiply together the resulting numbers.M7MBA wrote:If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?
a. 8
b. 9
c. 12
d. 15
e. 27
Thus, (m^3)(p)(t) = (m^3)(p^1)(t^1) has (3 + 1)(1 + 1)(1 + 1) = 4 x 2 x 2 = 16 total factors. Since 1 is one of those 16 factors, there are actually 15 different positive factors greater than 1.
Answer:D
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
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7294
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
To determine the total number of factors of a number, we can add 1 to the exponent of each distinct prime factor and multiply together the resulting numbers.M7MBA wrote:If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?
a. 8
b. 9
c. 12
d. 15
e. 27
Thus, (m^3)(p)(t) = (m^3)(p^1)(t^1) has (3 + 1)(1 + 1)(1 + 1) = 4 x 2 x 2 = 16 total factors. Since 1 is one of those 16 factors, there are actually 15 different positive factors greater than 1.
Answer:D
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