BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

If n is a multiple of 5 and n = p^2q, where p and q are....

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 28
Joined: Sat May 26, 2007 10:12 am
Thanked: 1 times
by galinaphillips » Sun Jun 03, 2007 6:25 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

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!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Community Manager
Posts: 789
Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member
Location: Silicon valley, California
Thanked: 30 times

Re: If n is a multiple of 5 and n = p^2q, where p and q are.

by jayhawk2001 » Sun Jun 03, 2007 6:53 pm
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

The answer is p^2q^2 on this problem from mba.com but I'm not sure how to solve?
Thanks!
If n is a multiple of 5, then either p is a multiple of 5 or q is a multiple of 5
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.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 28
Joined: Sat May 26, 2007 10:12 am
Thanked: 1 times

Thanks

by galinaphillips » Mon Jun 04, 2007 5:30 am
Thanks a lot!!! :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 108
Joined: Sun Mar 15, 2009 2:04 pm

Re: Thanks

by alexdallas » Sun Jun 28, 2009 3:05 pm
"p^2*q^2 will be a multiple of 25 if either p or q is a multiple of 5. "

why is this?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Sat Jun 27, 2009 1:31 am

by AymanMath » Sun Jun 28, 2009 11:35 pm
I think these type of question you cannot solve it without assuming real figures

So I assume that P=2 and q=5 which is coincide with forth answer

Am I correct guys ?? :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 108
Joined: Sun Mar 15, 2009 2:04 pm

by alexdallas » Mon Jun 29, 2009 5:14 pm
anyone?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 122
Joined: Mon Sep 22, 2008 5:11 pm
Thanked: 1 times

by abcdefg » Mon Jun 29, 2009 6:43 pm
does p^2q^2 = p^(4q)?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Wed Sep 24, 2008 8:47 am
Location: Pune , India
Thanked: 1 times

by pallavisingh12 » Tue Jun 30, 2009 3:15 am
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.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 108
Joined: Sun Mar 15, 2009 2:04 pm

by alexdallas » Wed Jul 01, 2009 4:12 am
i think he meant to say "mult. of 25", not mult. of 5. then it makes sense.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 447
Joined: Sun Apr 19, 2009 9:08 pm
Location: Kolkata,India
Thanked: 7 times
GMAT Score:670

by uptowngirl92 » Wed Aug 26, 2009 3:27 am
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.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Tue Nov 24, 2009 4:55 am

by sranga » Thu Nov 26, 2009 5:27 am
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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 30
Joined: Sat Apr 10, 2010 7:04 pmFollowed by: 1 member
Thanked: 3 times

by greentealeaf » Sat Apr 24, 2010 5:42 pm
jayhawk2001 wrote:
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

The answer is p^2q^2 on this problem from mba.com but I'm not sure how to solve?
Thanks!
If n is a multiple of 5, then either p is a multiple of 5 or q is a multiple of 5
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.
very nice explaination!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Senior | Next Rank: 100 Posts
Posts: 56
Joined: Mon Feb 07, 2011 7:57 am
Thanked: 1 times
GMAT Score:600

by crisro » Wed May 25, 2011 6:58 pm
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)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8136
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

by Scott@TargetTestPrep » Wed Jul 04, 2018 6:07 pm
jayhawk2001 wrote:
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
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.

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]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1