Brian spent 1/4 of his paycheck to repair his car, and then paid the

Let the value of paycheck be X.
Brian spent 1/4 of his paycheck value on car repair = x/4
Remaining = X-X/4 = 3X/4
Car registration = car insurance = 1/3 *3X/4 = X/4
Amount left = 3X/4 - X/4 - X/4 (putting X/4 two times because he spent this cost on car registration and car insurance)
Amount left = X/4 = 231
therefore X=231*4 = 924

Hence answer should be C

Key to correctly answering this question is noticing that the 1/3 for the registration and 1/3 for the insurance are not each 1/3 of his paycheck. They are each 1/3 of what remained after he spent 1/4 of the paycheck on repairs.

Question: Brian spent 1/4 of his paycheck to repair his car, and then paid the registration and insurance, which each cost 1/3 of the remainder of his paycheck. If Brian had $0 before he was paid, and he now has $231 left, what was the amount of his paycheck?

Brian spent 1/4 to repair his car.

1 - 1/4 = 3/4

Of what remained, or 3/4, he spent 1/3 on registration and 1/3 on insurance.

We can keep this simple.

1/3 of 3/4 is clearly 1/4.

So, for registration and insurance he spent 1/4 of his paycheck and 1/4 of his paycheck.

3/4 - 1/4 - 1/4 = 1/4

So, of his paycheck, he had left 1/4 = 231.

The whole check must have been 4 x 231 = 924.

The correct answer is (C).

We can let n = the total amount of his paycheck and create the equation:

n/4 + 3n/4(1/3 + 1/3) + 231 = n

n/4 + 3n/4(2/3) + 231 = n

n/4 + n/2 + 231 = n

Multiplying by 4, we have:

n + 2n + 924 = 4n

924 = n

Alternate Solution:

Since Brian spent 1/4 of his paycheck to repair his car, he still had 1 - 1/4 = 3/4 of his paycheck remaining.

Since he paid 1/3 + 1/3 = 2/3 of the remainder for registration and insurance, he was left with 1 - 2/3 = 1/3 of the remainder; which is 3/4 x 1/3 = 1/4 of his paycheck.

Since 1/4 of his paycheck was $231, his entire paycheck was 4 x 231 = $924.

Answer: C

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.