Problem Solving

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:
$$m+f=162+108=270$$

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

Here's an algebraic solution that uses 2 variables:

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

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