If n is a multiple of 5 and n=(p^2)q , where p and q are prime numbers, which of the following must be a multiple of 25?
a) p^2
b) q^2
c) pq
d) (p^2)(q^2)
e) (p^3)q
The answer is D, and I have not been able to satisfy myself completely on how this is exactly done. If anyone could shed some light I would greatly appreciate it. Thanks.
Target Test Prep is 20% off right now!
Use code FLASH20
Available with Beat the GMAT members only code
MORE DETAILS
prime number, multiple question from GMAT prep 1
This topic has expert replies
-
kaulnikhil
- Master | Next Rank: 500 Posts
- Posts: 338
- Joined: Fri Apr 17, 2009 1:49 am
- Thanked: 9 times
- Followed by:3 members
since n is s multiple pf 5 so product of p and q should end in 5 or 0
let p =3 and q = 5
we can eliminate p^2,pq and p^3q
now put p =5 and q =3
we can eliminate q^2
Only D is remaining.
let p =3 and q = 5
we can eliminate p^2,pq and p^3q
now put p =5 and q =3
we can eliminate q^2
Only D is remaining.
Question says that (p^2)q is a multiple of 5. Check which of the following answer choices has (p^2)q. Only D has.
{(p^2)q}{q}.
Why? Because we know that {(p^2)q} is a multiple of 5 and anything you multiply to this number will still be a multiple of 5.
{(p^2)q}{q}.
Why? Because we know that {(p^2)q} is a multiple of 5 and anything you multiply to this number will still be a multiple of 5.
GMAT/MBA Expert
-
Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
If n is divisible by 5, then a 5 must appear in the prime factorization of n. We know the prime factorization of n is (p^2)(q), so either p = 5 or q = 5. Thus, either p^2 = 25 or q^2 = 25. We can't be sure which, but we can be sure that (p^2)(q^2) is a multiple of 25.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
