Solutions

Get detailed explanations to advanced GMAT questions.



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.


 

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

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