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

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NandishSS: Master | Next Rank: 500 Posts; Posts: 366; Joined: Fri Jun 05, 2015 3:35 amFollowed by: 2 members; Thanked: 3 times

by NandishSS » Fri Jul 19, 2019 5:42 am

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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: Beat The GMAT — Problem Solving | Fri Jul 19, 2019 5:42 am

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Fri Jul 19, 2019 10:18 am

Let the number of fishes caught $= x$

Number of fishes sold $= \frac{1}{4}x$

Number of fishes UNsold $= x−\frac{1}{4}x=\frac{3}{4}x$

Gave away $\frac{2}{3}$ of the remaining fish $=\frac{2}{3}\cdot \frac{3}{4}x = \frac{1}{2}x$

After all the above he had 4 fish left. Therefore, __B__ is the correct option.

Darkknightreturning: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Mon Jul 01, 2019 8:40 am

by Darkknightreturning » Sat Jul 20, 2019 11:30 pm

Let the No. of fishes be X
After selling 1/4x fishes, fishes left = 3/4x.
He gave away 2/3rd of fishes left. Thus, he now has 1/3rd of fishes left = 1/3 * 3/4x = 1/4x
This 1/4x is equal to 4. Thus, x = 16
Answer is B

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Jul 30, 2019 8:44 am

NandishSS 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

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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