BTGModeratorVI wrote: ↑Fri Mar 06, 2020 5:51 pm
X, Y, and Z are three different prime numbers, the product XYZ is divisible by how many different positive numbers?
A. 4
B. 6
C. 8
D. 9
E. 12
Answer:
C
Source: GMATPrep
----ASIDE-------------------------
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
-----------------------------------
Since X, Y and Z are different PRIME numbers, we can say: XYZ = (X^
1)(Y^
1)(Z^
1)
So, the number of positive divisors of XYZ = (
1+1)(
1+1)(
1+1) =(2)(2)(2) = 8
Answer: C
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
