It is currently 23 Jan 2018, 22:04

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If positive integer y is a perfect square and is the product of r, s,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43380
If positive integer y is a perfect square and is the product of r, s, [#permalink]

Show Tags

New post 27 Apr 2016, 10:22
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

77% (00:57) correct 23% (01:30) wrong based on 129 sessions

HideShow timer Statistics

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
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

4 KUDOS received
Manager
Manager
avatar
Joined: 13 Apr 2016
Posts: 60
Location: India
GMAT 1: 640 Q50 V27
GPA: 3
WE: Operations (Hospitality and Tourism)
Re: If positive integer y is a perfect square and is the product of r, s, [#permalink]

Show Tags

New post 27 Apr 2016, 11:15
4
This post received
KUDOS
1
This post was
BOOKMARKED
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

ans to this question is B. answer explained in attachment.
Attachments

ans.jpg
ans.jpg [ 207.78 KiB | Viewed 1301 times ]

1 KUDOS received
Manager
Manager
User avatar
G
Joined: 13 Aug 2015
Posts: 207
GMAT 1: 710 Q49 V38
GPA: 3.82
WE: Corporate Finance (Retail Banking)
GMAT ToolKit User Reviews Badge
If positive integer y is a perfect square and is the product of r, s, [#permalink]

Show Tags

New post 05 Jul 2017, 18:18
1
This post received
KUDOS
2
This post was
BOOKMARKED
Bunuel wrote:
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



Theory:
A perfect square has an even power of a number.
eg. 9=\(3^2\)
100=\(10^2\)

Since, y is a perfect square its factor must have an even power.
y=r.s.8.9.11
y=r.s.\(2^3\).\(3^2\).11
Thus, r and s must be 2.11=22
Ans: B
_________________

If you like my posts, please give kudos. Help me unlock gmatclub tests.

Intern
Intern
avatar
B
Joined: 22 Oct 2017
Posts: 31
Re: If positive integer y is a perfect square and is the product of r, s, [#permalink]

Show Tags

New post 24 Nov 2017, 05:41
I don't understand the solution. Because stated this way we get 2^4 * 3^2*11^2
So there are two "2" to much?

Because for a perfect square every factor should have the same exponent?
In that case I would say we have to multiply by 11^2 and 3, so rs=11^2*3 and we get 3 in every exponent.
Can anybody explain please?
1 KUDOS received
VP
VP
avatar
P
Joined: 22 May 2016
Posts: 1261
Premium Member CAT Tests
If positive integer y is a perfect square and is the product of r, s, [#permalink]

Show Tags

New post 25 Nov 2017, 16:19
1
This post received
KUDOS
Bunuel wrote:
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

Dokami wrote:
I don't understand the solution. Because stated this way we get 2^4 * 3^2*11^2
So there are two "2" to much?

Because for a perfect square every factor should have the same exponent?
In that case I would say we have to multiply by 11^2 and 3, so rs=11^2*3 and we get 3 in every exponent.
Can anybody explain please?

Dokami This material can get confusing . . . No -- There are not enough 2s. We need one more, to make pairs. We need four 2s, not three 2s. There are not enough 11s either. There is only one 11. We need one more 11, so that 11s will be in pairs.

And, no: a perfect square's factors do not have the same exponent. The prime factors must have an even exponent (e.g., 2, 6, 222). A perfect square always has an even number of powers of prime factors.

That rule (perfect squares must have prime factors with even powers) is often easier to remember this way: all prime factors must come in pairs. Couplets.

There are no single "copies" of a prime factor in a perfect square. If there is only one "copy" of a prime factor, the number is not a perfect square.

\(y\) "is a perfect square. and is the product of r, s, 8, 9, and 11." So

\(y = 8 * 9 * 11 * r * s\)

Break just the numbers down into prime factors:

\(8 = (2 * 2 * 2) = 2^3\)
\(9 = (3 * 3) = 3^2\)
\(11 = (11 * 1) = 11^1\)

\(y = 2^3 * 3^2 * 11^1 * r * s\)

Looking at just the numbers, this situation will not make a perfect square. There are three 2s. The twos are not in pairs. (There is one pair of twos, but a third 2 is by itself.) The 11 is not in a pair. There is only one 11. We have to make pairs.

In order to make pairs, we need one more 2, and one more 11. Both numbers need one more "copy" of themselves.

That's what \(r\) and \(s\) are for, to make up for the "missing" 2 and the "missing" 11.

\((r * s) = (2^1 * 11^1) = 22\):
(r*s) IS 22, so (r*s) must be divisible by 22.

y WAS \((2^3 * 3^2 * 11^1 * r * s)\). We added one factor of 2 and one factor of 11 (using r and s).

y NOW is \(2^4 * 3^2 * 11^2\). The factors' exponents are even numbers. We used r and s to make sure the factors came in pairs. There are two pairs of 2s. There is one pair of 3s. And there is one pair of 11s.

Hope that helps.
_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

1 KUDOS received
Intern
Intern
avatar
B
Joined: 22 Oct 2017
Posts: 31
Re: If positive integer y is a perfect square and is the product of r, s, [#permalink]

Show Tags

New post 26 Nov 2017, 09:07
1
This post received
KUDOS
Got it thank you :-)
Expert Post
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10763
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If positive integer y is a perfect square and is the product of r, s, [#permalink]

Show Tags

New post 23 Jan 2018, 14:12
Hi All,

This question is based on a specific Number Property rule involving perfect squares: 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:
[Reveal] Spoiler:
B


GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: If positive integer y is a perfect square and is the product of r, s,   [#permalink] 23 Jan 2018, 14:12
Display posts from previous: Sort by

If positive integer y is a perfect square and is the product of r, s,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.