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# One-fifth of the light switches produced by a certain

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Senior Manager
Joined: 13 Mar 2007
Posts: 294
Location: Russia, Moscow
One-fifth of the light switches produced by a certain [#permalink]

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29 Mar 2007, 06:19
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%
Manager
Joined: 02 Jan 2007
Posts: 208

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29 Mar 2007, 10:40
Nice Question Vlad77.
I go with B.

let the total no. of switches = 100
so defective (or lets say d) = 20
of these 4/5 get rejected, so
& nrd (non-rejected defectives) =4 (20-16 ie 4/5 of 20)..........i

Total Non-defective switches (or n) = 80
1/20 of these are rejected by mistake, thats
mr (mistakenly rejected) = 4
so good switches sold = 76........................ii

With this we now we need to find out how many switches sold
and how many rejectes sold.

Total sold = 80 (adding i & ii)
of these defective = 4 ......from i

4/80*100 = 5%
Intern
Joined: 11 Feb 2007
Posts: 30

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29 Mar 2007, 11:51
i get 5% too. good explanation.
Manager
Joined: 28 Feb 2007
Posts: 197
Location: California
Re: Please, help to solve not concise question!!! [#permalink]

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29 Mar 2007, 20:43
Vlad77 wrote:
One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

Rejected defective switches = 1/5 x 4/5 = 4/25
Accepted defective swicthes = 1/5 x 1/5 = 1/25

Rejected good switches = 4/5 x 1/20 = 1/25
Accepted good switched = 4/5 x 19/20 = 19/25

Since all accepted switches are sold so total switches sold = 1/25 + 19/25 = 4/5

required answer = 1/25 / 4/5 = 1/20 = 5%
Senior Manager
Joined: 13 Mar 2007
Posts: 294
Location: Russia, Moscow

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29 Mar 2007, 23:19
Many thanks for your prompt answers !!!
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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30 Mar 2007, 00:51
Assume total 100 switches produced.

(100)*(1/5) = 20 switches are defective

4/5*(20) = 16 swtitches are rejected

1/20*(80) = 4 switches are rejected by mistake.

# of switches sold = 76 + 4 = 80
# of defects sold = 4
% = 4/80 * 100% = 5%
30 Mar 2007, 00:51
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# One-fifth of the light switches produced by a certain

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