It is currently 19 Feb 2018, 23:54

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

The male alpine rabbits of the Tzatzek nature reserve have suffered a

  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: 43828
The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

Show Tags

New post 20 Jan 2015, 05:49
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

73% (01:21) correct 27% (01:36) wrong based on 125 sessions

HideShow timer Statistics

The male alpine rabbits of the Tzatzek nature reserve have suffered a disease that killed 90 of them, causing the male to female ratio to drop from 3:2 to 2:3. How many alpine rabbits lived in the reserve before the disease struck?

A. 180
B. 270
C. 360
D. 450
E. 540

Kudos for a correct solution.
[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

2 KUDOS received
Manager
Manager
User avatar
Joined: 04 Oct 2013
Posts: 176
Concentration: Finance, Leadership
GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

Show Tags

New post 20 Jan 2015, 08:47
2
This post received
KUDOS
1
This post was
BOOKMARKED
ratio before the disease 3/2; disease kills 90 males --> 3x-90/2x=2/3 --> x=54. total number of rabbits before the disease 5x=270.

Answer B.
_________________

learn the rules of the game, then play better than anyone else.

Manager
Manager
avatar
Joined: 14 Jul 2014
Posts: 96
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

Show Tags

New post 20 Jan 2015, 22:38
straightforward - B

3x-90/2x = 2/3

Find x

Careful - But Question asks 5x. On solving this becomes 270
1 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1839
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

Show Tags

New post 22 Jan 2015, 20:34
1
This post received
KUDOS
Answer = B. 270

.............................. Male ......................... Female ........................ Total

Initial ........................ 3x ............................... 2x ............................ 5x (This has to be calculated)

After deaths ............... 3x-90 .......................... 2x .......................... Ratio = 2:3

Setting up the equation

\(\frac{3x-90}{2x} = \frac{2}{3}\)

4x = 9x - 270

5x = 270
_________________

Kindly press "+1 Kudos" to appreciate :)

Manager
Manager
User avatar
Joined: 16 Jan 2015
Posts: 52
Location: United States
Schools: Kellogg '17, ISB '17
GMAT Date: 05-20-2015
GPA: 3.06
WE: Business Development (Commercial Banking)
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

Show Tags

New post 22 Jan 2015, 20:46
The male alpine rabbits of the Tzatzek nature reserve have suffered a disease that killed 90 of them, causing the male to female ratio to drop from 3:2 to 2:3. How many alpine rabbits lived in the reserve before the disease struck?

A. 180
B. 270
C. 360
D. 450
E. 540

Ans : 270

Initial M/ F = 3:2

After M is reduced by 90

(M-90)/F = 2:3

solving : 3M-270=2F , but M=3F/2

So , F=108 and M=162

M+F= 270

Kudos if this helps :)
Senior Manager
Senior Manager
avatar
S
Joined: 18 Aug 2014
Posts: 300
GMAT ToolKit User Reviews Badge
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

Show Tags

New post 01 Mar 2016, 19:52
PareshGmat wrote:
Answer = B. 270

.............................. Male ......................... Female ........................ Total

Initial ........................ 3x ............................... 2x ............................ 5x (This has to be calculated)

After deaths ............... 3x-90 .......................... 2x .......................... Ratio = 2:3

Setting up the equation

\(\frac{3x-90}{2x} = \frac{2}{3}\)

4x = 9x - 270

5x = 270


So why is the first ratio the number to "x" (i.e 3x) but not the second ratio? First ratio is 3 times some number over 2 times some number, 90 of the male rabbits die, and now we have 2 over 3. Why is it not 2 times some number over 3 times some number? It seems from a logic standpoint like you treat one as a ratio representing the whole and then the second ratio specifically as a 2/3rds fraction if that makes sense.

I'm sure it's a pretty rudimentary understanding of ratios I'm just trying to figure out from the meaning stand point why you get rid of the x's on the right hand side.
_________________

Please help me find my lost Kudo's bird

Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7941
Location: Pune, India
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

Show Tags

New post 01 Mar 2016, 23:08
2
This post received
KUDOS
Expert's post
redfield wrote:
PareshGmat wrote:
Answer = B. 270

.............................. Male ......................... Female ........................ Total

Initial ........................ 3x ............................... 2x ............................ 5x (This has to be calculated)

After deaths ............... 3x-90 .......................... 2x .......................... Ratio = 2:3

Setting up the equation

\(\frac{3x-90}{2x} = \frac{2}{3}\)

4x = 9x - 270

5x = 270


So why is the first ratio the number to "x" (i.e 3x) but not the second ratio? First ratio is 3 times some number over 2 times some number, 90 of the male rabbits die, and now we have 2 over 3. Why is it not 2 times some number over 3 times some number? It seems from a logic standpoint like you treat one as a ratio representing the whole and then the second ratio specifically as a 2/3rds fraction if that makes sense.

I'm sure it's a pretty rudimentary understanding of ratios I'm just trying to figure out from the meaning stand point why you get rid of the x's on the right hand side.


You can do it that way too.

.............................. Male ......................... Female ........................ Total

Initial ........................ 3x ............................... 2x ............................ 5x

After deaths ............... 2y ...............................3y ............................. 5y

And you know the relation between them:

3x - 90 = 2y
2x = 3y

Now you solve them to get the answer. But this is a little more tedious.

If you want to stick to one variable, you can use the method given above. In that case, we don't need to assume the variable y.

Number of males after death => 3x - 90 = 2y (in our case)
Number of females stay the same => 2x = 3y (in our case)

Divide the two equations:

(3x - 90)/2x = 2y/3y = 2/3

That is why in this case, there is no need to take the variable y.

Both methods will give the same answer, of course.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Manager
Manager
avatar
Joined: 25 Dec 2012
Posts: 134
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

Show Tags

New post 02 Mar 2016, 09:08
Given:

Before Death: M:F = 3:2 --> eqn1
After Death: M:F = 2:3 --> eqn2

Merge eqn1 & 2 = i.e Before Death:After Death = 9:6:4
BM:F:AM (Before Death Male:Female:After Death Male)

5X difference caused a reduction of 90. Hence X = 90/5 = 18.

So on substituting in ration we get = 9(18):6(18):4(18) = 162:108:72
= 162 + 108 =270
Intern
Intern
avatar
Joined: 08 May 2016
Posts: 6
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

Show Tags

New post 08 May 2016, 13:52
Hello,

I encountered a similar question and I was wondering how to solve it...

Suppose that instead of telling you specifically that the 90 dead rabbits are male, they just told you that 90 rabbits died overall.

How would you solve the problem then?

Thanks!
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7941
Location: Pune, India
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

Show Tags

New post 08 May 2016, 21:59
1
This post received
KUDOS
Expert's post
inak wrote:
Hello,

I encountered a similar question and I was wondering how to solve it...

Suppose that instead of telling you specifically that the 90 dead rabbits are male, they just told you that 90 rabbits died overall.

How would you solve the problem then?

Thanks!


There would be no unique answer in that case.

Before:
Male:Female = 3:2
Male = 3a, Female = 2a, Total = 5a

After:
Male:Female = 2:3
Male = 2b, Female = 3b, Total = 5b

5a - 5b = 90
a - b = 18

Under this constraint, a and b can take any value.
Say, a = 20, b = 2
Before: Male = 60, Female = 40, Total = 100
After: Male = 4, Female = 6, Total = 10

Say, a = 21, b = 3
Before: Male = 63, Female = 42, Total = 105
After: Male = 6, Female = 9, Total = 15

and so on...
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Manager
Manager
User avatar
B
Joined: 17 Nov 2014
Posts: 51
Location: India
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

Show Tags

New post 10 May 2016, 08:41
.............................. Male ......................... Female ........................ Total

Initial ........................ 3x ............................... 2x ............................ 5x (This has to be calculated)

After deaths ............... 3x-90 .......................... 2x .......................... Ratio = 2:3



3x−90 : 2x = 2:3

4x = 9x - 270

5x = 270

IMHO B
Expert Post
Top Contributor
SVP
SVP
User avatar
P
Joined: 11 Sep 2015
Posts: 2051
Location: Canada
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

Show Tags

New post 19 Jan 2018, 07:32
Expert's post
Top Contributor
Bunuel wrote:
The male alpine rabbits of the Tzatzek nature reserve have suffered a disease that killed 90 of them, causing the male to female ratio to drop from 3:2 to 2:3. How many alpine rabbits lived in the reserve before the disease struck?

A. 180
B. 270
C. 360
D. 450
E. 540

Kudos for a correct solution.


Here's an algebraic solution.

Let M = the # of male rabbits BEFORE the disease struck.
Let F = the # of female rabbits BEFORE the disease struck.

We're told that the male/female ratio was 3:2 BEFORE the disease.
So, we can write: M/F = 3/2
Cross multiply to get: 2M = 3F
--------------------------
When the disease hits, 90 male rabbits die.
So, M - 90 = the # of male rabbits AFTER the disease struck.
Since no females die, F = the # of female rabbits AFTER the disease struck.
We're told that the male/female ratio was 2:3 AFTER the disease.
So, we can write: (M - 90)/F = 2/3
Cross multiply to get: 3(M - 90) = 2F
Simplify, to get: 3M - 270 = 2F
--------------------------
We now have two equations:
2M = 3F
3M - 270 = 2F

Multiply the top equation by 2 to get: 4M = 6F
Multiply the bottom equation by 3 to get: 9M - 810 = 6F

Since both equations are set equal to 6F, we can conclude that 4M = 9M - 810
Subtract 9M from both sides to get: -5M = -810
Solve, M = 162
To solve for F, we can use one of the equations we created earlier.
Take 2M = 3F and replace M with 162 to get 2(162) = 3F
Simplify: 324 = 3F
Solve: F = 108

How many alpine rabbits lived in the reserve BEFORE the disease struck?
So, M + F = 162 + 108
= 270
= B

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a   [#permalink] 19 Jan 2018, 07:32
Display posts from previous: Sort by

The male alpine rabbits of the Tzatzek nature reserve have suffered a

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


cron

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®.