Solutions

Question

Of the cans of peaches inspected yesterday at a certain plant, 1.5 percent failed to pass inspection. Of the cans that failed inspection, 5/6 was incorrectly labelled and the rest were dented. If all of the cans that were incorrectly labelled or dented failed inspection, how many of the cans of peaches inspected yesterday at the plant were dented?

I. 450 of the cans of peaches inspected yesterday at the plant failed to pass inspection.

II. 29,550 of the cans of peaches inspected yesterday at the plant passed inspection.

 

Difficulty Level

Easy

Solution

Option D is the correct answer.

Option Analysis

x: total cans of peaches

0.015x: number of cans that failed inspection

0.015x*5/6: number of cans that wrong label

0.015x*1/6: number of cans that dented red

Since all the cans that were incorrectly labelled or dented red, there’s no can that both incorrectly and dented red.

Statement I is sufficient: 450 of the cans of peaches inspected yesterday at the plant failed to pass inspection: number of cans that were dented red = 0.015x/6 = 450/6 = 75 => sufficient

Statement II is sufficient: 29,550 of the cans of peaches inspected yesterday at the plant passed inspection.

Total cans that passed inspection = 1 – 0.015x = 29,550 => x=30,000

Number of cans that were dented red = (0.015*30,000)/6 = 75 => sufficient