GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Oct 2018, 09:51

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

In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50009
In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages  [#permalink]

Show Tags

New post 29 Jan 2018, 05:44
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

80% (01:11) correct 20% (00:46) wrong based on 73 sessions

HideShow timer Statistics

In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages if the cats must be in the second, fourth, and sixth cages?

A. 12
B. 18
C. 36
D. 72
E. 720

_________________

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

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3191
Location: India
GPA: 3.12
Premium Member CAT Tests
In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages  [#permalink]

Show Tags

New post 29 Jan 2018, 06:08
Bunuel wrote:
In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages if the cats must be in the second, fourth, and sixth cages?

A. 12
B. 18
C. 36
D. 72
E. 720



The arrangement of the cats in the cages will be as follows
D C D C D C

The three cats can be arranged in 3! ways
Similarly, the 3 dogs can be arranged in 3! ways

Therefore, the total ways the pets can be lined up is \(3!*3! = 6*6\) = 36(Option C)
_________________

You've got what it takes, but it will take everything you've got

CEO
CEO
User avatar
P
Joined: 08 Jul 2010
Posts: 2564
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages  [#permalink]

Show Tags

New post 29 Jan 2018, 07:00
Bunuel wrote:
In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages if the cats must be in the second, fourth, and sixth cages?

A. 12
B. 18
C. 36
D. 72
E. 720


The cages for the cats are fixed however the order of cats in those cages may vary in 3! ways

The cages for the Gods are fixed (remaining cages after cats are closed in respective cages) however the order of dogs in those cages may vary in 3! ways

Hence total favorable ways to arrange cats and dogs in cages = 3!*3! = 36

Answer: Option C
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Manager
Manager
User avatar
S
Joined: 28 Jul 2016
Posts: 129
Location: India
GMAT 1: 680 Q50 V32
GPA: 3.97
Re: In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages  [#permalink]

Show Tags

New post 29 Jan 2018, 11:19
Total combinations = 3!*3!
6*6 = 36
_________________

Please give Kudos. Kudos encourage active discussions and help the community grow

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages  [#permalink]

Show Tags

New post 30 Jan 2018, 11:19
Bunuel wrote:
In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages if the cats must be in the second, fourth, and sixth cages?

A. 12
B. 18
C. 36
D. 72
E. 720


Our arrangement must be as follows:

D - C - D - C - D - C

For the first cage, we have 3 possibilities because there are 3 available dogs for the first cage. For the second cage, we have 3 possibilities for the 3 available cats. For the third cage, we have 2 available dogs (because one dog was already placed in the first cage). Similarly, for the fourth cage, we have 2 available cats. Finally, for the fifth cage, we have the one remaining dog, and for the sixth cage, the one remaining cat. .

So, the number of ways to arrange the animals is 3 x 3 x 2 x 2 x 1 x 1 = 36.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Bot
Re: In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages &nbs [#permalink] 30 Jan 2018, 11:19
Display posts from previous: Sort by

In how many ways can a pet shop line up 3 cats and 3 dogs in 6 cages

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.