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After a fisherman sold 1/4 of the fish he had caught and gave away 2/3

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Manager
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S
Joined: 28 Jun 2018
Posts: 132
Location: Bouvet Island
GMAT 1: 490 Q39 V18
GMAT 2: 640 Q47 V30
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After a fisherman sold 1/4 of the fish he had caught and gave away 2/3  [#permalink]

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New post 17 Jan 2019, 05:28
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Difficulty:

  25% (medium)

Question Stats:

78% (01:17) correct 22% (00:50) wrong based on 21 sessions

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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
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B
Joined: 14 Jan 2018
Posts: 45
Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 720 Q50 V41
GPA: 3.7
WE: Engineering (Manufacturing)
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Re: After a fisherman sold 1/4 of the fish he had caught and gave away 2/3  [#permalink]

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New post 17 Jan 2019, 10:30
1
Let total fish = F
sold fraction 1/4 , remaining 3/4F
Now gave away 2/3 of reamining , 2/3*3/4F gives 1/4F = 4 fish
so F= 4*4 =16 fishes total he have

Answer B.
Manager
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Joined: 28 Jun 2018
Posts: 132
Location: Bouvet Island
GMAT 1: 490 Q39 V18
GMAT 2: 640 Q47 V30
GMAT 3: 670 Q50 V31
GMAT 4: 700 Q49 V36
GPA: 4
CAT Tests
After a fisherman sold 1/4 of the fish he had caught and gave away 2/3  [#permalink]

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New post 17 Jan 2019, 20:27
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 2/3 of the remaining fish =\(\frac{2}{3} * \frac{3}{4}x\) = \(\frac{1}{2}x\)
After all the above he had 4 fish left.

From here 2 methods can be used -

Method 1 :
Total number of fishes = Number of fishes sold + Number of fishes given away + the 4 he had left
\(x\) = \(\frac{1}{4}x\) + \(\frac{1}{2}x\) + 4

Method 2 : (shorter method as posted by Loser94 )
The UNSOLD fishes = Number of fishes given away + the 4 he had left
\(\frac{3}{4}x\) = \(\frac{1}{2}x\) + 4

Solving either will give you \(x = 16\).
GMAT Club Bot
After a fisherman sold 1/4 of the fish he had caught and gave away 2/3   [#permalink] 17 Jan 2019, 20:27
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After a fisherman sold 1/4 of the fish he had caught and gave away 2/3

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