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

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

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New post 05 Feb 2019, 03:45
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Question Stats:

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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?

A. $2772
B. $1622
C. $924
D. $870
E. $693

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

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New post Updated on: 06 Feb 2019, 18:49
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Bunuel wrote:
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?

A. $2772
B. $1622
C. $924
D. $870
E. $693


IMO C

I back solved here, amount of his paycheck

start from C => 924/4 = 231,

Now the remaining 693 was divided 2/3 times(Key word: which each cost 1/3 of the remainder of his paycheck.)

693 * 2/3 = 462

So the remainder is indeed $ 231.

So back solve did help us.
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Originally posted by KanishkM on 05 Feb 2019, 04:29.
Last edited by KanishkM on 06 Feb 2019, 18:49, edited 1 time in total.
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Brian spent 1/4 of his paycheck to repair his car, and then paid the  [#permalink]

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New post Updated on: 06 Feb 2019, 02:23
Bunuel wrote:
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?

A. $2772
B. $1622
C. $924
D. $870
E. $693



total cheque value be x
repair = x/4
left 3x/4
regn + insurance amount spent 1/3 of the paycheck value = 3x/4 * 1/3 = x/4
left 3/4-1/4-1/4 = x.1/4
x/4 = 231
x= 924
IMO C
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Originally posted by Archit3110 on 05 Feb 2019, 04:43.
Last edited by Archit3110 on 06 Feb 2019, 02:23, edited 1 time in total.
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Brian spent 1/4 of his paycheck to repair his car, and then paid the  [#permalink]

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New post 05 Feb 2019, 05:24
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
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Brian spent 1/4 of his paycheck to repair his car, and then paid the  [#permalink]

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New post 05 Feb 2019, 15:58
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).
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Re: Brian spent 1/4 of his paycheck to repair his car, and then paid the  [#permalink]

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New post 07 Feb 2019, 06:46
Bunuel wrote:
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?

A. $2772
B. $1622
C. $924
D. $870
E. $693


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
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Re: Brian spent 1/4 of his paycheck to repair his car, and then paid the   [#permalink] 07 Feb 2019, 06:46
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