It is currently 19 Feb 2018, 23:54

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43828
The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

### Show Tags

20 Jan 2015, 05:49
Expert's post
1
This post was
BOOKMARKED
00:00

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

_________________
Manager
Joined: 04 Oct 2013
Posts: 176
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

20 Jan 2015, 08:47
2
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.

_________________

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

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

### Show Tags

20 Jan 2015, 22:38
straightforward - B

3x-90/2x = 2/3

Find x

Careful - But Question asks 5x. On solving this becomes 270
SVP
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

22 Jan 2015, 20:34
1
KUDOS

.............................. 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
Joined: 16 Jan 2015
Posts: 52
Location: United States
Schools: Kellogg '17, ISB '17
GMAT Date: 05-20-2015
GPA: 3.06
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

### Show Tags

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
Joined: 18 Aug 2014
Posts: 300
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

### Show Tags

01 Mar 2016, 19:52
PareshGmat wrote:

.............................. 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.
_________________

Veritas Prep GMAT Instructor
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

01 Mar 2016, 23:08
2
KUDOS
Expert's post
redfield wrote:
PareshGmat wrote:

.............................. 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 Joined: 25 Dec 2012 Posts: 134 Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink] ### Show Tags 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 Joined: 08 May 2016 Posts: 6 Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink] ### Show Tags 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! Veritas Prep GMAT Instructor 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 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
Joined: 17 Nov 2014
Posts: 51
Location: India
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

### Show Tags

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
SVP
Joined: 11 Sep 2015
Posts: 2051
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

### Show Tags

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

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