Eggs - Princeton Review

[sparkles3144]

In a certain egg-processing plant, every egg must be inspected, and is either accepted for processing or is rejected. For every 96 eggs accepted for processing or is rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but overall number of eggs inspected remained the same, the rato of those accepted to those rejected would be 99 to 1. How many eggs does the plant process per day?

A. 100
B. 300
C. 400
D. 3,000
E. 4,000

This question is so confusing.
Please explain. Thanks!

[GMATGuruNY]

In a certain egg-processing plant, every egg must be inspected, and is either accepted for processing or is rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the rato of those accepted to those rejected would be 99 to 1. How many eggs does the plant process per day?

A. 100
B. 300
C. 400
D. 3,000
E. 4,000

We can PLUG IN THE ANSWERS, which represent the total number of eggs.
When the correct answer choice is plugged in, accepting 12 more eggs will yield the following ratio:
accepted/rejected = 99/1.

Answer choice C: 400
Before the change:
Since 4 of every 100 eggs are rejected, 16 of every 400 eggs are rejected.
Thus:
The number of eggs rejected = 16.
The number of eggs accepted = 400-16 = 384.

After the change:
Here, 12 more eggs are accepted, while the total number of eggs remains the same.
Thus:
The number of eggs accepted = 384+12 = 396.
The number of eggs rejected = 400-396 = 4.
Resulting ratio:
accepted/rejected = 396/4 = 99/1.
Success!

The correct answer is C.

[Brent@GMATPrepNow]

In a certain egg-processing plant, every egg must be inspected, and is either accepted for processing or is rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the ratio of those accepted to those rejected would be 99 to 1. How many eggs does the plant process per day?

A. 100
B. 300
C. 400
D. 3,000
E. 4,000

Here's an algebraic approach.
Let T = TOTAL number of eggs inspected each day.
Let A = The number of eggs that are TYPICALLY accepted each day

For every 96 eggs accepted for processing, 4 eggs are rejected
In other words, for every 100 eggs INSPECTED, 96 are accepted.
So, 96% of the T eggs are TYPICALLY accepted.
We can write: 0.96T = A

On a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the ratio of those accepted to those rejected would be 99 to 1
In other words, on this day, for every 100 eggs INSPECTED, 99 were accepted. So, 99% of the T eggs were accepted.
Also, the number of eggs ACCEPTED = A + 12
We can write: 0.99T = A + 12

We now have two equations:
0.99T = A + 12
0.96T = A

SUBTRACT the bottom equation from the top equation to get:
0.03T = 12
Rewrite as (3/100)T = 12
Multiply both sides by 100/3 to get: T = 1200/3 = [spoiler]400 = C[/spoiler]

Cheers,
Brent