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

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Senior Manager
Joined: 21 Aug 2003
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Location: Bangalore
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One-fifth of the light switches produced by a certain [#permalink]  25 Sep 2003, 04:45
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%

ps: Question is not tough but what is more important is how u solve. Such questions throw lot of data and a small mistake can be fatal. Faster u neatly organize data, faster u will get the answer.
SVP
Joined: 03 Feb 2003
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X is the total number

X/5 is defective, and 4X/5 is OK
Four-fifths of the defective switches are rejected = 4X/25
So, one-fifth of the defective switches is not rejected = X/25

1/20 of the nondefective switches are rejected by mistake=4X/100

All the rejected=4X/100+4X/25=X/5
The sold = 4X/5

[X/25]/[4X/5]=1/20 or 5%

Last edited by stolyar on 25 Sep 2003, 21:10, edited 1 time in total.
Senior Manager
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Another way you could solve this:

Say 100(divisible by all the denominators mentioned) light switches are produced.
1/5 * 100 = 20 defective leaving 80 non-defective
4/5 * 20 defective = 16 rejected leaving 4 non-rejects defectives
1/20 * 80 non-defective = 4 rejected non-defectives
so 80 non-rejects are sold and 4 are defective
4/80 = 0.05 = 5%
SVP
Joined: 03 Feb 2003
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a nice approach; sometimes it helps a lot.
Senior Manager
Joined: 21 Aug 2003
Posts: 258
Location: Bangalore
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yes, thats true. When fractions and percentage are involved its better to start with a number thats divisible (or LCM) of the denominators.
Secondly, i think such questions can be solved much faster if a 2X2 table is drawn. It help a lot in organizing info and avoiding silly mistakes.
CEO
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Re: Defective [#permalink]  30 May 2007, 23:11
Makky07 wrote:
Another way you could solve this:

Say 100(divisible by all the denominators mentioned) light switches are produced.
1/5 * 100 = 20 defective leaving 80 non-defective
4/5 * 20 defective = 16 rejected leaving 4 non-rejects defectives
1/20 * 80 non-defective = 4 rejected non-defectives
so 80 non-rejects are sold and 4 are defective
4/80 = 0.05 = 5%

small elaboration. i was slightly confused by the wording and took the total defective amount rather than the defective amount of the units sold.

If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

4 / (4 + 76)
4/80
1/20
5%
B
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Re: Defective [#permalink]  30 May 2007, 23:54
B.

1/5 of the total are defective,
4/5 of the total are non-defective,

Of the 1/5 defective, 4/5 are rejected: No. of defective and rejected = [1/5 * 4/5] = 4/25 (of the total)

Of the 4/5 non-defective, 1/20 are rejected: No. of non-defective and rejected = [4/5 * 1/20] = 1/25 (of the total)

No. of rejected = 4/25 + 1/25 = 1/5

"All the switches not rejected are sold", therefore No. of sold = 4/5

"Of the 1/5 defective, 4/5 are rejected", therefore 1/5 of the defective are sold, or [1/5 * 1/5] = 1/25 of the total are defective and sold.

The fraction of [defective and sold] over the [sold] is now [1/25] / [4/5] = 1/20 = 5%
Re: Defective   [#permalink] 30 May 2007, 23:54
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