Problem Solving

Hi,

The correct answer is B) ..can anyone explain? thx!

One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 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%

dunkin77 wrote:Hi,

The correct answer is B) ..can anyone explain? thx!

One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 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%

the darkened sentence is incomplete ... chk it out ...

Oops - sorry! here you go - thanks!

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%

I did not get the same answer, I got 4%.

For my setup, please look at the attachment. I thought I had a good grasp of this. Am I missing something?

Let total number of switches produced be y. Therefore y/5 are defective. 4/5 of y/5 = 4y/25 are rejected.

y/5 - 4y/25 = y/25 of switches which are defective (but not rejected) are sold.

Total number of non-defective switches = 4y/5. Ones rejected = 1/20 of 4y/5 = 4y/100 = y/25 are rejected

Total rejected = 4y/25 + y/25 = 5y/25 = y/5. Therefore total sold = 4y/5

Therefore percent of the switches sold by the factory that are defective =( (y/25) / (4y/5) ) * 100

= 5%