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

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

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29 Mar 2007, 05:19
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%
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29 Mar 2007, 09:40
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%
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29 Mar 2007, 10:51
i get 5% too. good explanation.
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29 Mar 2007, 19:43
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
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29 Mar 2007, 22:19
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29 Mar 2007, 23:51
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%
29 Mar 2007, 23:51
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