Problem Solving

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%

say you have 100 total light bulbs. 1/5, or 20 are defective. That means 80 are non-defective. 4/5 of the defective ones are rejected, so 4/5*(20) = 16 defective + rejected. 1/20 of non-defective ones are rejected, or 1/20*(80) = 4 nondefective + rejected.

Total rejected = 16 + 4 = 20, total non-rejected that are sold = 100 - 20 = 80.

Nondefective that are rejected / Total non-rejected that are sold = 4 / 80 = 5%. Choice B.

mp2437 wrote:say you have 100 total light bulbs. 1/5, or 20 are defective. That means 80 are non-defective. 4/5 of the defective ones are rejected, so 4/5*(20) = 16 defective + rejected. 1/20 of non-defective ones are rejected, or 1/20*(80) = 4 nondefective + rejected.

Total rejected = 16 + 4 = 20, total non-rejected that are sold = 100 - 20 = 80.

Nondefective that are rejected / Total non-rejected that are sold = 4 / 80 = 5%. Choice B.

Before i post, I did the same calculations. I do not understand the last sentence ? I get 20/80 = 1/4 because total defective is 20 and the sold ones are 80

Why you chose 4/80 ? 4 is rejected non defective. the question wants: defective/80

could someone help ?

heshamelaziry 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%

B is the answer.

Check the attachment .. It's easier to use the double sets chart.

heshamelaziry wrote:

mp2437 wrote:say you have 100 total light bulbs. 1/5, or 20 are defective. That means 80 are non-defective. 4/5 of the defective ones are rejected, so 4/5*(20) = 16 defective + rejected. 1/20 of non-defective ones are rejected, or 1/20*(80) = 4 nondefective + rejected.

Total rejected = 16 + 4 = 20, total non-rejected that are sold = 100 - 20 = 80.

Nondefective that are rejected / Total non-rejected that are sold = 4 / 80 = 5%. Choice B.

Before i post, I did the same calculations. I do not understand the last sentence ? I get 20/80 = 1/4 because total defective is 20 and the sold ones are 80

Why you chose 4/80 ? 4 is rejected non defective. the question wants: defective/80

20 is the total rejected count. The question only asks what percentage of non-defective switches were rejected. Doesn't asks or talks about rejected items in the question.
So as shown by mp2437, its 4 / 80. where 4 is the non-defective switches that are rejected and 80 is the total non-rejected items sold.
Therefore 5% should be the answer.

Thank you guys. I understand now.

Could you guys give your assessment about how challenging this question to each of you ? for example, not at all, somewhat, fairly, more than average, very


Thanks all.

Is this correct ?

1) 100 * 1/5 = 20 defective

2) 20 * 4/5 = 16 defective and rejected --------> leaves 4 defective, but not rejected------> 4 ( available for sale)

3) 80 * 1/20 = 4 not defective, but rejected -------> leaves 76 not defective, and not rejected ( available for sale )

So, total available for sale = all - rejected --------> 100- 20 = 80

% defective = (4/80 ) * 100 = 5%

heshamelaziry wrote:Is this correct ?

1) 100 * 1/5 = 20 defective

2) 20 * 4/5 = 16 defective and rejected --------> leaves 4 defective, but not rejected------> 4 ( available for sale)

3) 80 * 1/20 = 4 not defective, but rejected -------> leaves 76 not defective, and not rejected ( available for sale )

So, total available for sale = all - rejected --------> 100- 20 = 80

% defective = (4/80 ) * 100 = 5%

Correct.