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

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Manager
Joined: 05 Sep 2007
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Location: New York
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One-fifth of the light switches produced by a certain [#permalink]  27 Mar 2008, 18:29
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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 non defective 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%
Director
Joined: 10 Sep 2007
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Re: PS: Light swt [#permalink]  27 Mar 2008, 19:37
Assume total bulbs are 100.
Out of these 1/5th are defective = 100/5 = 20
In defective 4/5 are rejected = 20*4/5 = 16
So remaining bulbs are selected and sold = 20 - 16 = 4

Non-defective bulbs = 100 - 20 = 80
Wrongly rejected = 80/20 = 4
Remaining bulbs for selling = 80 - 4 = 76

So total bulbs available for selling = 4 (defective bulbs) + 76 (non-defective) = 80 Bulbs

Percentage = 4*100/80 = 5%

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Joined: 29 Aug 2007
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Re: PS: Light swt [#permalink]  27 Mar 2008, 19:38
el1981 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 non defective 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%

d= defective
nd= not defective
r = rejected
s = sold

d = 1/5
r(d) = (4/5) (1/5) = 4/25
r(nd) = 1/20 (4/5) = 1/25
Total r = 4/25 + 1/25 = 5/25 = 1/5
sold = 1 - 1/5 = 4/5
s(d) = 1/5 - 4/25 = 1/25

the percent of the defective switches sold by the factory = (1/25)/(4/5) = 1/20 = 5%. so B.

Assigning values also help solve the problem easily.
t = 100
d = 1/5 x 100 = 20
r(d) = 4/5 x 20 = 16
r(nd) = 1/20 x 80 = 4
r = 16+ 4 = 20
s = t - r = 100 - 20 = 80
s(d) = not r(d) = d - r(d) = 20 - 16 = 4
% of defective sold = 4/80 = 5%
_________________
Re: PS: Light swt   [#permalink] 27 Mar 2008, 19:38
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