Bunuel wrote:

Tough and Tricky questions: Overlapping Sets.

One-fifth of the batteries produced by an upstart factory are defective and one-quarter of all batteries produced are rejected by the quality control technician. If one-tenth of the nondefective batteries are rejected by mistake, and if all the batteries not rejected are sold, then what percent of the batteries sold by the factory are defective?

A) 4%

B) 5%

C) 6%

D) 8%

E) 12%

We can let the total number of batteries produced = 100.

Thus, 1/5(100) = 20 batteries are defective and thus 80 batteries are not defective.

Also, 1/4(100) = 25 are rejected and thus 75 batteries are not rejected and are sold.

1/10(80) = 8 non-defective batteries are rejected by mistake and thus 72 non-defective batteries are sold. However, since there are a total of 75 batteries sold, among them, thus must be 75 - 72 = 3 defective batteries. Therefore, the percent of the batteries sold that are defective is:

3/75 = 1/25 = 4%

Answer: A

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