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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
Joined: 28 Jun 2018
Posts: 129
Location: Bouvet Island
GMAT 1: 490 Q39 V18
GMAT 2: 640 Q47 V30
GMAT 3: 670 Q50 V31
GMAT 4: 700 Q49 V36
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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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17 Jan 2019, 06:28
1
4
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:24) correct 21% (01:32) wrong based on 61 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
Intern
Joined: 14 Jan 2018
Posts: 49
Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 660 Q50 V29
GPA: 3.8
WE: Engineering (Manufacturing)
Re: After a fisherman sold 1/4 of the fish he had caught and gave away 2/3  [#permalink]

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17 Jan 2019, 11:30
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

Manager
Joined: 28 Jun 2018
Posts: 129
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
After a fisherman sold 1/4 of the fish he had caught and gave away 2/3  [#permalink]

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17 Jan 2019, 21:27
1
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 $$x = 16$$.
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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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10 Jul 2019, 17:31
blitzkriegxX 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

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

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Re: After a fisherman sold 1/4 of the fish he had caught and gave away 2/3   [#permalink] 10 Jul 2019, 17:31
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