If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?
p^2
q^2
pq
p^2q^2
p^3q
The answer is p^2q^2 on this problem from mba.com but I'm not sure how to solve?
Thanks!
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
If n is a multiple of 5 and n = p^2q, where p and q are....
This topic has expert replies
-
galinaphillips
- Junior | Next Rank: 30 Posts
- Posts: 28
- Joined: Sat May 26, 2007 10:12 am
- Thanked: 1 times
-
jayhawk2001
- Community Manager
- Posts: 789
- Joined: Sun Jan 28, 2007 3:51 pm
- Location: Silicon valley, California
- Thanked: 30 times
- Followed by:1 members
If n is a multiple of 5, then either p is a multiple of 5 or q is a multiple of 5galinaphillips wrote:If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?
p^2
q^2
pq
p^2q^2
p^3q
The answer is p^2q^2 on this problem from mba.com but I'm not sure how to solve?
Thanks!
or both.
Since the question asks for "must be a multiple of 25", we have to find
the answer that we know WILL match
p^2 alone cannot be the answer since it could be q that is the multiple of
5. Same story for q^2.
pq we know will yield a multiple of 25, only when p and q are multiples
of 5 or when either of p or q is a multiple of 25. We don't know this
for sure as well. Discard. Same story for p^3*q.
p^2*q^2 will be a multiple of 25 if either p or q is a multiple of 5.
We know that n is a multiple of 5, so either p or q SHOULD be a multiple
of 5 and hence p^2*q^2 will be a multiple of 25.
-
galinaphillips
- Junior | Next Rank: 30 Posts
- Posts: 28
- Joined: Sat May 26, 2007 10:12 am
- Thanked: 1 times
-
alexdallas
- Master | Next Rank: 500 Posts
- Posts: 108
- Joined: Sun Mar 15, 2009 2:04 pm
"p^2*q^2 will be a multiple of 25 if either p or q is a multiple of 5. "
why is this?
why is this?
-
alexdallas
- Master | Next Rank: 500 Posts
- Posts: 108
- Joined: Sun Mar 15, 2009 2:04 pm
-
pallavisingh12
- Newbie | Next Rank: 10 Posts
- Posts: 1
- Joined: Wed Sep 24, 2008 8:47 am
- Location: Pune , India
- Thanked: 1 times
If n is a multiple of 5, then either p is a multiple of 5 or q is a multiple of 5
or both.
Im sorry but this dsn make sense.. For the above..Should'nt "p" HAVE to be 5.
or both.
Im sorry but this dsn make sense.. For the above..Should'nt "p" HAVE to be 5.
-
alexdallas
- Master | Next Rank: 500 Posts
- Posts: 108
- Joined: Sun Mar 15, 2009 2:04 pm
-
uptowngirl92
- Master | Next Rank: 500 Posts
- Posts: 447
- Joined: Sun Apr 19, 2009 9:08 pm
- Location: Kolkata,India
- Thanked: 7 times
- GMAT Score:670
If n is a multiple of 5, then either p is a multiple of 5 or q is a multiple of 5
or both.
Please explain the above..i dnt understand the logic.
or both.
Please explain the above..i dnt understand the logic.
For N to be a multiple of 5 [which is as per the question] then either P or Q must be 5 because both P and Q are prime numbers.
eg,
N being a multiple of 5 can take values 10 , 15, 20 and so on
which is 5*2 or 2*5 = 10 [here either p or q is 5]
similarly 5*3 or 3*5 = 15 [here either p or q is 5]
and so on...
so in order to be a multiple of 25 we need one of the number to be 25, which can be obtained by squaring either P or Q, since we do not know which of the both is 5 ,we are better off squaring both
hence the answer is (p^2)(q^2)
HTH
eg,
N being a multiple of 5 can take values 10 , 15, 20 and so on
which is 5*2 or 2*5 = 10 [here either p or q is 5]
similarly 5*3 or 3*5 = 15 [here either p or q is 5]
and so on...
so in order to be a multiple of 25 we need one of the number to be 25, which can be obtained by squaring either P or Q, since we do not know which of the both is 5 ,we are better off squaring both
hence the answer is (p^2)(q^2)
HTH
-
greentealeaf
- Senior | Next Rank: 100 Posts
- Posts: 30
- Joined: Sat Apr 10, 2010 7:04 pm
- Thanked: 3 times
- Followed by:1 members
very nice explaination!jayhawk2001 wrote:If n is a multiple of 5, then either p is a multiple of 5 or q is a multiple of 5galinaphillips wrote:If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?
p^2
q^2
pq
p^2q^2
p^3q
The answer is p^2q^2 on this problem from mba.com but I'm not sure how to solve?
Thanks!
or both.
Since the question asks for "must be a multiple of 25", we have to find
the answer that we know WILL match
p^2 alone cannot be the answer since it could be q that is the multiple of
5. Same story for q^2.
pq we know will yield a multiple of 25, only when p and q are multiples
of 5 or when either of p or q is a multiple of 25. We don't know this
for sure as well. Discard. Same story for p^3*q.
p^2*q^2 will be a multiple of 25 if either p or q is a multiple of 5.
We know that n is a multiple of 5, so either p or q SHOULD be a multiple
of 5 and hence p^2*q^2 will be a multiple of 25.
-
crisro
- Senior | Next Rank: 100 Posts
- Posts: 56
- Joined: Mon Feb 07, 2011 7:57 am
- Thanked: 1 times
- GMAT Score:600
if p^2q^2 is a multiple of 5, with p and q prime numbers then we can have only three possible options
1) p=5, when p^2=25
2) q=5, when q^2=25
3) p=q=5, when pq=25
the only answer choise that has all three options is answer d)
1) p=5, when p^2=25
2) q=5, when q^2=25
3) p=q=5, when pq=25
the only answer choise that has all three options is answer d)
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7242
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
jayhawk2001 wrote:A common phrase that is used on the GMAT is the word must. In this question, we are asked which of the following must be a multiple of 25. This means that one of our answer choices will always be a multiple of 25, no matter what. It is our job to determine which one, based on the given information.galinaphillips wrote:If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?
p^2
q^2
pq
p^2q^2
p^3q
We are given that n is a multiple of 5, n = (p^2)q, and that p and q are prime numbers.
Because n is a multiple of 5, a prime number, we know that either p or q is 5. Let's now analyze each answer choice to determine which one MUST (in all cases) be a multiple of 25.
A) p^2
If p = 3, then p^2 = 9 is not a multiple of 25. Answer choice A is not correct.
B) q^2
If q = 3, then q^2 = 9 is not a multiple of 25. Answer choice B is not correct.
C) pq
If p = 5 and q = 3 (or vice versa), pq = 15 is not a multiple of 25. Answer choice C is not correct.
D) (p^2)(q^2)
Regardless of which values we select for p and q, since we know that either p or q is 5, (p^2)(q^2) will always be a multiple of 25. If this is difficult to see, let's use numbers.
If p = 5 and q = 3, (p^2)(q^2) = (25)(9) is a multiple of 25.
If p = 3 and q = 5, (p^2)(q^2) = (9)(25) is also a multiple of 25.
Answer choice D is correct.
For practice, let's analyze answer choice E.
E) (p^3)q
If p = 3 and q = 5, then (p^3)q = 135 is not a multiple of 25. Answer choice E is not correct.
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
