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 →

Question on Perfect Square 7

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 698
Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members
Location: Noida, India
Thanked: 32 times
GMAT Score:740
by richachampion » Mon Oct 17, 2016 3:11 am
If positive integer y is a perfect square and is the product of r, s, 8, 9, and 11, then rs must be divisible by which of the following? (Assume both r and s are positive integers.)

A. 18
B. 22
C. 36
D. 44
E. 64
R I C H A,
My GMAT Journey: 470 → 720 → 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 698
Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members
Location: Noida, India
Thanked: 32 times
GMAT Score:740

by richachampion » Mon Oct 17, 2016 3:11 am
OA: B
R I C H A,
My GMAT Journey: 470 → 720 → 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 216
Joined: Sun Jul 31, 2016 9:55 pmFollowed by: 7 members
Location: Punjab
Thanked: 31 times

by fiza gupta » Mon Oct 17, 2016 4:57 am
y(perfect square) = r*s*9*11*8
y = rs*9*4*2*11
9 and 4 are perfect square but not 2 and 11
to make y a perfect square rs should be 22 or multiple of 22
rs=22 or rs=22*z(z should a perfect square)(22*4,22*9......)
B is the answer
Fiza Gupta
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Mon Oct 17, 2016 10:00 am
Hi richachampion,

This question is based on the same concept as the other prime-factor question that you posted: when you prime-factor a perfect square, each of the prime factors MUST show up an EVEN number of times...

eg. 9 = (3)(3) here, there are TWO 3s.
eg. 100 = (2)(2)(5)(5) here, there are TWO 2s and TWO 5s
eg. 16 = (2)(2)(2)(2) = here, there are FOUR 2s
Etc.

We're told that Y is a perfect square that is the product of R, S, 8, 9 and 11. Thus, prime-factoring Y will get us...

Y = (8)(9)(11)(R)(S)
Y = (2)(2)(2)(3)(3)(11)(R)(S)

We have TWO 3s, but only THREE 2s and just ONE 11. We need there to be an even number of 2s and an even number of 11s, so the R and S must contain at least a '2' and a '11.' Thus, (R)(S) must be a multiple of 22.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 698
Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members
Location: Noida, India
Thanked: 32 times
GMAT Score:740

by richachampion » Mon Oct 17, 2016 10:37 am
[email protected] wrote:Hi richachampion,

This question is based on the same concept as the other prime-factor question that you posted: when you prime-factor a perfect square, each of the prime factors MUST show up an EVEN number of times...
Correct Sir, I am searching and posting for other guys to practice, expertise and benefit. Thanks!
R I C H A,
My GMAT Journey: 470 → 720 → 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Fri Oct 28, 2016 12:38 am
If we know that

r * s * 8 * 9 * 11 = (something) * (something)

we can start breaking down the numbers we have:

r * s * 2 * 2 * 2 * 3 * 3 * 11 = (something) * (something)

then trying to squeeze them into two identical square roots)

r * s * 2 * 11 = (2 * 3 * other factors) * (2 * 3 * other factors)

Since we've still got a 2 * 11 on the left side, we can put it into one of our roots:

r * s = (2 * 3 * 2 * 11) * (2 * 3 * other factors)

Since the two roots must be the same, we need

(2 * 3 * 2 * 11) = (2 * 3 * other factors)

so the other factors must contain 2 * 11. Since these other factors can only come from r and s, we must have r * s = 22 * whatever, so r * s must be divisible by 22.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Fri Oct 28, 2016 12:39 am
Another approach would be to just try to make the square. Since squares have an EVEN number of each of their prime factors, we'd have to have

r * s * 2 * 2 * 2 * 3 * 3 * 11

become at least

2 * 2 * 2 * 2 * 3 * 3 * 11 * 11

To get there, we need one 2 and one 11. As before, these can only come from r * s, so r * s must contain 2 * 11 and thus be divisible by 22.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1