defective

[grandh01]

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%

[eagleeye]

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%

Let's say that the factory produces 100 switches.
Now 1/5 are defective => 1/5*100 = 20 defective switches.
Hence 100-20 = 80 are not defective.
4/5 of defective ones are rejected, the rest are sold => 1/5 of defective are sold = 1/5*20 = 4 switches.
Hence they sell 4 defective switches.
Number of switches rejected by mistake from the nondefective = 1/20*80 = 4 switches.
Hence the factory sells 80-4 = 76 nondefective switches.

Total number of switches sold = defective sold + nondefective sold = 4 + 76 = 80.
% of switches sold that are defective = no. of defective sold/ (total sold) * 100%
= 4/80 * 100% = 5% .

B is correct.

[truplayer256]

Let the total number of light switches be x.
x/5 = defective
(x/5)(4/5) = 4x/25 = rejected defective switches
x - x/5 = 4x/5 = non-defective switches
(4x/5)(1/20) = x/25 = rejected non-defective switches
Total switches sold = x - (4x/25 + x/25) = 4x/5
Out of those 4x/5 switches, (x/5)(1/5) = x/25 are defective.
% defective switches sold = (x/25)/(4x/5) * 100 = 5%
Choose B.

[Anurag@Gurome]

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%

Picking Numbers Approach:

Let us assume that the no. of light switches produced = 100
Then defective light switches = (1/5) * 100 = 20
Non-defective light switches = 100 -20 = 80
Defective light switches that are rejected = (4/5) * 20 = 4 * 4 = 16
No. of non-defective switches that are rejected = (1/20) * 80 = 4
Defective Switches that are sold = 20 - 16 = 4
Non-defective Switches that are sold = 80 - 4 = 76

Total light switches sold = 4 + 76 = 80
Therefore, % of defective switches sold = (4/80) * 100 = [spoiler]5%[/spoiler]

The correct answer is B.

[vikramaditya234]

Answer is B
Used the same method as eagleeye