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

It is currently 23 Jan 2019, 06:29

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 in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • Key Strategies to Master GMAT SC

     January 26, 2019

     January 26, 2019

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
  • Free GMAT Number Properties Webinar

     January 27, 2019

     January 27, 2019

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.

The ratio of dogs to cats at a certain shelter in City X is 2:3 and

  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: 52431
The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

Show Tags

New post 01 May 2017, 01:36
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

66% (03:10) correct 34% (03:24) wrong based on 156 sessions

HideShow timer Statistics

The ratio of dogs to cats at a certain shelter in City X is 2:3 and the ratio of cats to dogs at a different shelter in City Y is 7:3. If there are 300 more cats and dogs at the shelter in City Y than in City X, and the combined ratio of dogs to cats for the two shelters combined is 8:17, how many cats and dogs are at the shelter in City Y?

A. 100
B. 300
C. 350
D. 400
E. 450

_________________

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

Most Helpful Community Reply
Current Student
User avatar
G
Joined: 22 Jun 2016
Posts: 244
Reviews Badge
The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

Show Tags

New post Updated on: 01 May 2017, 06:52
6
4
The ratio of dogs to cats at a certain shelter in City X is 2:3 and the ratio of cats to dogs at a different shelter in City Y is 7:3. If there are 300 more cats and dogs at the shelter in City Y than in City X, and the combined ratio of dogs to cats for the two shelters combined is 8:17, how many cats and dogs are at the shelter in City Y?

At X, dogs: cats = 2:3 or 2x:3x. Total dogs+cats = 2x+3x=5x

At Y, dogs: cats = 3:7 or 3y:7y. Total dogs+cats = 3y+7y=10y

According to 1st condition, 10y-5x=300 ---> 2y-x=60

According to 2nd condition, (2x+3y)/(3x+7y) = 8/17 ---> 34x+51y=24x+56y ---> 2x=y

Solving above 1 eqns, we get x=20 and y=40.

Total cats and dogs at Y = 10y = 400.

Hence, D will be the answer.
_________________

P.S. Don't forget to give Kudos :)


Originally posted by 14101992 on 01 May 2017, 02:45.
Last edited by 14101992 on 01 May 2017, 06:52, edited 1 time in total.
General Discussion
CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2726
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

Show Tags

New post 01 May 2017, 02:58
1
Bunuel wrote:
The ratio of dogs to cats at a certain shelter in City X is 2:3 and the ratio of cats to dogs at a different shelter in City Y is 7:3. If there are 300 more cats and dogs at the shelter in City Y than in City X, and the combined ratio of dogs to cats for the two shelters combined is 8:17, how many cats and dogs are at the shelter in City Y?

A. 100
B. 300
C. 350
D. 400
E. 450


Line to focus at is first ratio is the ratio of Dogs to Cats while second ratio is ratio of Cats to Dogs

In City X
Dog = 2a
Cats = 3a
Total Cats and Dogs = 5a

In City Y
Cat = 7b
Dogs = 3b
Total Cats and Dogs = 10b

Given, 10b = 300 + 5a
i.e. 2b = 60+a

also Cat/Dogs = (3a+7b)/(2a+3b) = 17/8
i.e. 24a + 56b = 34a + 51b
i.e. 5b = 10a
i.e. b = 2a

i.e. 2(2a) = 60+a
i.e. a = 20

i.e. b = 2*20 = 40
Total Animals in Y = 10b = 400

Answer: Option D
_________________

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

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
Premium Member CAT Tests
Re: The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

Show Tags

New post 01 May 2017, 03:53
1
I, Always go by answers for such questions
Condition 1 : There are 300 more cats and dogs at the shelter in City Y
We can strike away A,B

So we start evaluating answer choice C.
If total number of cats & dogs is 350, CityX has 50 and CityY has 350
According to ratios, we will have
CATS:DOGS(City X) 20,30
CATS:DOGS(City Y) 105:245
Adding them doesn't give us our final ratio(8:17)

Next Option D : 400
If total number of cats & dogs is 400, CityX has 100 and CityY has 400
According to ratios, we will have
CATS:DOGS(City X) 40,60
CATS:DOGS(City Y) 120,280
Adding them we get our final ratio(8:17) of cats and dogs. (Option D)
_________________

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

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4612
Location: United States (CA)
Re: The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

Show Tags

New post 06 May 2017, 16:13
Bunuel wrote:
The ratio of dogs to cats at a certain shelter in City X is 2:3 and the ratio of cats to dogs at a different shelter in City Y is 7:3. If there are 300 more cats and dogs at the shelter in City Y than in City X, and the combined ratio of dogs to cats for the two shelters combined is 8:17, how many cats and dogs are at the shelter in City Y?

A. 100
B. 300
C. 350
D. 400
E. 450


We can create the following two ratios:

Ratio of dogs to cats in City X is 2x : 3x

Ratio of cats to dogs in City Y is 7y : 3y, or equivalently, the ratio of dogs to cats in City Y is 3y : 7y

Since there are 300 more cats and dogs at the shelter in City Y than in City X, we can create the following equation:

2x + 3x + 300 = 7y + 3y

5x + 300 = 10y

5x = 10y - 300

x = 2y - 60

Since the combined ratio of dogs to cats for the two shelters combined is 8:17, we can create the following equation:

(2x + 3y)/(3x + 7y) = 8/17

17(2x + 3y) = 8(3x + 7y)

34x + 51y = 24x + 56y

10x = 5y

2x = y

Since y = 2x, we can substitute 2x for y in the equation x = 2y - 60 and we have:

x = 2(2x) - 60

x = 4x - 60

-3x = -60

x = 20

Thus y = 2x = 40, and the number of dogs and cats at the shelter in city Y is 3y + 7y = 10y = 10(40) = 400.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Director
Director
User avatar
V
Joined: 11 Feb 2015
Posts: 681
Premium Member CAT Tests
Re: The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

Show Tags

New post 15 Apr 2018, 07:00
Let "T" be the Total number of Dogs and Cats in City Shelter X. Therefore Total number of Dogs and Cats in City Shelter Y will be "T+300".

From the information develop this equation:-
(2/5)T + (3/10)(T+300)=(8/25)(2T+300)

Solve for T to get "T=100", i.e. Total number of Dogs and Cats in City Shelter X.
Therefore the Total number of Dogs and Cats in City Shelter Y is "T+300"="100+300"=400 - ANS - "D"

PS: Conceptually the equation mentioned above equates the number of Dogs in City shether X & Y with Today number of Dogs in cobined shelters. Please note that for doing so the equation uses "T", i.e. the total number of dogs and cats. Hence we could get to the answer by developing a linear equation in one variable. I hope this was helpful to everyone.
_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

Manager
Manager
avatar
S
Joined: 14 Jul 2014
Posts: 96
Location: India
Concentration: Social Entrepreneurship, Strategy
GMAT 1: 620 Q41 V34
WE: Information Technology (Computer Software)
Re: The ratio of dogs to cats at a certain shelter in City X is 2:3 and  [#permalink]

Show Tags

New post 22 Sep 2018, 11:06
The fastest way to solve this problem is by leveraging the weighted average mapping concept. In the City X shelter, dogs represent 40% (2 out of 5 parts) of the total cats and dogs, in the City Y shelter, dogs represent 30% (3 out of 10 parts) of the total cats and dogs, and in the combined shelter, dogs represent 32% (8 out of 25 parts) of the total cats and dogs. Map this out as you would any weighted average problem:

City Y----------Combined----------------------------------------City X
30% -------------- 32% -----------------------------------------40%

This means the ratio of total pets at City Y to City X is 8 :2 or 4:1 This means y = 4x and you know y = x + 300 so x = 100 and y = 400. Correct answer is D.
GMAT Club Bot
Re: The ratio of dogs to cats at a certain shelter in City X is 2:3 and &nbs [#permalink] 22 Sep 2018, 11:06
Display posts from previous: Sort by

The ratio of dogs to cats at a certain shelter in City X is 2:3 and

  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®.