hi guys , here is a problem i couldn't solve..
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
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Brent@GMATPrepNow
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One option is to TEST the answer choices. I'll leave that to you.souma730 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
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 dies, 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
Cheers,
Brent
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Hi souma730,
As Brent mentioned, this question can be solved by TESTing THE ANSWERS. Here's how:
We're given 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.
Let's TEST Answer B:
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!
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
As Brent mentioned, this question can be solved by TESTing THE ANSWERS. Here's how:
We're given 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.
Let's TEST Answer B:
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!
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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GMATGuruNY
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Alternate approach:souma730 wrote:hi guys , here is a problem i couldn't solve..
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
Original ratio of males to females = 3x/2x.
After 90 males are lost to disease, the new number of males = 3x-90.
Since the resulting ratio of males to females is 2 to 3, we get:
(3x-90)/2x = 2/3
9x-270 = 4x
5x = 270
x = 54.
Since the original number of males = 3x and original number of females = 2x, the total number of rabbits before the onset of disease = 5x = 5*54 = 270.
The correct answer is B.
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The posted problem is no different from the following:
Of the total number of rabbits last year, the percentage that were males = 2/5 = 40%.
Of the total number of rabbits added this year -- since no females were added -- the percentage that were males = 100%.
In the MIXTURE of old rabbits and new rabbits, the percentage that are males = 3/5 = 60%.
We can solve with ALLIGATION -- a great way to handle mixture problems.
Let O = original rabbits and A = added rabbits.
Step 1: Plot the 3 percentages on a number line, with the percentages for the original rabbits and the added rabbits on the ends and the percentage for the mixture of rabbits in the middle.
O 40------------60------------100 A
Step 2: Calculate the distances between the percentages.
O 40-----20-----60-----40----- 100 A
Step 3: Determine the ratio in the mixture.
The ratio of O to A in the mixture of rabbits is equal to the RECIPROCAL of the distances in red.
O:A = 40:20 = 2:1.
Since O:A = 2:1 = 180:90, there are 180 original rabbits for the 90 added rabbits, implying that the current number of rabbits = 180+90 = 270.
The correct answer is B.
More alligation problems:
https://www.beatthegmat.com/mixture-prob ... 90121.html
This can be treated as a MIXTURE problem:Last year, the ratio of male alpine rabbits to female alpine rabbits at the Tzatzek nature reserve was 2 to 3. Since the beginning of this year, the number of male alpine rabbits has increased by 90, while the number of female alpine rabbits has remained the same. If the current ratio of male alpine rabbits to female alpine rabbits is 3 to 2, what is the total number of rabbits currently at the Tzatzek nature reserve?
A. 180
B. 270
C. 360
D. 450
E. 540
Of the total number of rabbits last year, the percentage that were males = 2/5 = 40%.
Of the total number of rabbits added this year -- since no females were added -- the percentage that were males = 100%.
In the MIXTURE of old rabbits and new rabbits, the percentage that are males = 3/5 = 60%.
We can solve with ALLIGATION -- a great way to handle mixture problems.
Let O = original rabbits and A = added rabbits.
Step 1: Plot the 3 percentages on a number line, with the percentages for the original rabbits and the added rabbits on the ends and the percentage for the mixture of rabbits in the middle.
O 40------------60------------100 A
Step 2: Calculate the distances between the percentages.
O 40-----20-----60-----40----- 100 A
Step 3: Determine the ratio in the mixture.
The ratio of O to A in the mixture of rabbits is equal to the RECIPROCAL of the distances in red.
O:A = 40:20 = 2:1.
Since O:A = 2:1 = 180:90, there are 180 original rabbits for the 90 added rabbits, implying that the current number of rabbits = 180+90 = 270.
The correct answer is B.
More alligation problems:
https://www.beatthegmat.com/mixture-prob ... 90121.html
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Let's change the Female part in both ratio such that it remains constantsouma730 wrote:hi guys , here is a problem i couldn't solve..
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
First Ratio of Male : Female = 3:2 = 9:6
Second Ratio of Male : Female = 2:3 = 4:6
here we understand that Female part is constant and male part has changed from 9 point to 4 point
i.e. Decrease of (9-4) = 5 points = 90 rabbits
i.e. 1 point = 18 Rabbits
i.e. Total Rabbits are represented by (9+6) = 15 points [From First ratio 9:6]
i.e. 15 points = 270 Rabbits
Answer: Option B
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