After a fisherman sold 1/4 of the fish he had caught and

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

After a fisherman sold 1/4 of the fish he had caught and

by BTGmoderatorDC » Mon Jun 17, 2019 9:41 pm

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After a fisherman sold 1/4 of the fish he had caught and gave away 2/3 of the remaining fish, he had 4 fish left. What was the total number of fish he had caught?

(A) 8
(B) 16
(C) 20
(D) 32
(E) 40

OA B

Source: GMAT Prep

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Source: Beat The GMAT — Problem Solving | Mon Jun 17, 2019 9:41 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Mon Jun 17, 2019 11:30 pm

BTGmoderatorDC wrote:After a fisherman sold 1/4 of the fish he had caught and gave away 2/3 of the remaining fish, he had 4 fish left. What was the total number of fish he had caught?

(A) 8
(B) 16
(C) 20
(D) 32
(E) 40

OA B

Source: GMAT Prep

Say the fisherman caught x numbers of fish.

Thus,

he sold = x/4 numbers of fish; remaining = x - x/4 = 3x/4
number of fish donated = 2/3 of 3x/4 = x/2; remaining = 3x/4 - x/2 = x/4

We are given that x /4 = 4; thus, x = 4*4 = 16

The correct answer: B

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Jul 10, 2019 4:22 pm

BTGmoderatorDC wrote:After a fisherman sold 1/4 of the fish he had caught and gave away 2/3 of the remaining fish, he had 4 fish left. What was the total number of fish he had caught?

(A) 8
(B) 16
(C) 20
(D) 32
(E) 40

OA B

Source: GMAT Prep

We can let n = the number of fish the fisherman caught and create the equation:

n - (1/4)n - (2/3)(3/4)n = 4

n - (1/4)n - (1/2)n = 4

Multiplying the equation by 4, we have:

4n - n - 2n = 16

n = 16

Answer: B

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