500 ps

[dunkin77]

Hi,

The answer is B)... but could anyone explain pls? 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%

[santy]

Assume total switches = 100
1/5th of 100 switches are defective = 20
4/5th of these 20 defective switches are rejected = 16
Remaining Defective switches in the lot = (20-16) = 4
1/20th Non Defective switches rejected by mistake = 1/20 * 80 = 4
So, Non defective switches = 76
Total = Non defective + Defective switches not rejected = 76+4 = 80 are sold.
Percentage of defective switches sold = 5% (5% of 80 = 4)

[Cybermusings]

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%

[dunkin77]

very Clear - thanks!

[BTGmoderatorRO]

Assuming 1000 light switches were produced, 200 are detectives (1/5). 160 defective and are rejected . 40 non defective were rejected mistakenly.

Also 40 defective and not rejected.
760 non defective and also not rejected
$$Total\ rejected\ and\ sold=800$$

percentage of the switches sold by the factory which are defective= $$\frac{40}{800}\cdot100=5\%$$

[Scott@TargetTestPrep]

Hi,

The answer is B)... but could anyone explain pls? 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%

We can let the total number of switches = n

So n/5 are defective and 4n/5 are not.

4/5 x n/5 = 4n/25 defective switches are rejected. Thus 1/5 x n/5 = n/25 defective switches are not rejected and are sold.

1/20 x 4n/5 = 4n/100 = n/25 non-defective switches are rejected by mistake.

Thus, a total of 5n/25 = n/5 switches are rejected. So a total of 4n/5 switches are not rejected and are sold.

So the percent of the switches sold that are defective is:

(n/25)/(4n/5) = 5n/(100n) = 1/20 = 5%

Answer: B