The male alpine rabbits Tzatsek nature reserve has 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
The OA is B.
Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
The male alpine rabbits of the Tzatsek nature reserve...
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We know that there were originally 3 male rabbits for every 2 female rabbits. We should remember that we can always express ratios as fractions. So if m is the original number of male rabbits and m is the original number of female rabbits:
$$\frac{m}{f}=\frac{3}{2}$$
Then 90 of the male rabbits die, giving us a ratio of 2 male rabbits for every 3 female rabbits. Expressing this using fractions gives us:
$$\frac{m-90}{f}=\frac{2}{3}$$
Now we can combine these equations using substitution:
$$3m-270=2f$$
$$m=\frac{3f}{2}$$
$$3\left(\frac{3f}{2}\right)-270=2f$$
$$9f-540=4f$$
$$5f=540$$
$$f=108$$
Then we can solve for m:
$$\frac{m}{108}=\frac{3}{2}$$ $$m=162$$
Then add m and f together for the original total number of rabbits:
$$m+f=162+108=270$$
$$\frac{m}{f}=\frac{3}{2}$$
Then 90 of the male rabbits die, giving us a ratio of 2 male rabbits for every 3 female rabbits. Expressing this using fractions gives us:
$$\frac{m-90}{f}=\frac{2}{3}$$
Now we can combine these equations using substitution:
$$3m-270=2f$$
$$m=\frac{3f}{2}$$
$$3\left(\frac{3f}{2}\right)-270=2f$$
$$9f-540=4f$$
$$5f=540$$
$$f=108$$
Then we can solve for m:
$$\frac{m}{108}=\frac{3}{2}$$ $$m=162$$
Then add m and f together for the original total number of rabbits:
$$m+f=162+108=270$$
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Here's an algebraic solution that uses 2 variables:swerve wrote:The male alpine rabbits Tzatsek nature reserve has 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
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
Cheers,
Brent
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Hi swerve,
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
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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- Scott@TargetTestPrep
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swerve wrote:The male alpine rabbits Tzatsek nature reserve has 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
We can let the number of male and female rabbits that lived in the reserve before the disease struck be 3x and 2x, respectively, and create the following equation:
(3x - 90)/2x = 2/3
3(3x - 90) = 4x
9x - 270 = 4x
5x = 270
x = 54
The total number of rabbits that originally lived in the reserve was 5x = 5(54) = 270.
Answer: B
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