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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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blitzkriegxX
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After a fisherman sold 1/4 of the fish he had caught and gave away 2/3 [#permalink] New post   17 Jan 2019, 06:28
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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
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Loser94
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Re: After a fisherman sold 1/4 of the fish he had caught and gave away 2/3 [#permalink] New post   17 Jan 2019, 11:30
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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.
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blitzkriegxX
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After a fisherman sold 1/4 of the fish he had caught and gave away 2/3 [#permalink] New post   17 Jan 2019, 21:27
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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] New post   10 Jul 2019, 17:31
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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

Answer: B
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Re: After a fisherman sold 1/4 of the fish he had caught and gave away 2/3 [#permalink] New post   31 Jan 2023, 07:33
Fastest way:

Let total be 100%
100-(100*1/4)
=100-25= 75%

75- (75*2/3)= 75-50= 25

25% of fish left.
25%= 4
100%= 4/25 *100= 16

ANSWER :B

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Re: After a fisherman sold 1/4 of the fish he had caught and gave away 2/3 [#permalink]
31 Jan 2023, 07:33
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