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

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Joined: 02 Sep 2009
Posts: 58427
The male alpine rabbits of the Tzatzek nature reserve have suffered a  [#permalink]

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20 Jan 2015, 06:49
00:00

Difficulty:

55% (hard)

Question Stats:

72% (02:14) correct 28% (02:24) wrong based on 146 sessions

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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.

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

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20 Jan 2015, 09:47
2
1
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.

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

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20 Jan 2015, 23:38
straightforward - B

3x-90/2x = 2/3

Find x

Careful - But Question asks 5x. On solving this becomes 270
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Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a  [#permalink]

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22 Jan 2015, 21:34
1

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

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22 Jan 2015, 21:46
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
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Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a  [#permalink]

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01 Mar 2016, 20:52
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.
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Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a  [#permalink]

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02 Mar 2016, 00:08
2
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.
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Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a  [#permalink]

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02 Mar 2016, 10:08
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
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Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a  [#permalink]

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08 May 2016, 14:52
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!
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Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a  [#permalink]

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08 May 2016, 22:59
1
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...
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Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a  [#permalink]

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10 May 2016, 09:41
.............................. 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
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Posts: 4018
Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a  [#permalink]

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19 Jan 2018, 08:32
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

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

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01 Mar 2018, 12:37
Hi All,

The information in the prompt gives us a "starting ratio" of males to females (3:2) and an "ending ratio" (2:3) and we're told that a disease killed off 90 males (which led to this change in ratio). We're asked for the TOTAL number of rabbits BEFORE the disease struck. This question can be solved by TESTing THE ANSWERS.

If…
Total rabbits = 270
The ratio of males to females is 3:2
Males = 162
Females = 108

Killing 90 males leaves us with…
Males = 72
Females = 108
72:108 = 36:54 = 18:27 = 2:3

This is a MATCH for what the question stated about the ending ratio!

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

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