Official Guide Explanation:
Data Sufficiency #D34




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Solution and Metadata

Question: D34
Page: 24
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Percents > other
Category 2: Arithmetic > Sets > 2 sets
Category 3: Word Problems > Sets >

Explanation: The best way to think about this question is that there are four possible sets of requirements: computer and writing skills; computer skills only; writing skills only; neither computer nor writing skills. The percentages of companies that require each of those sets of skills will sum to 100. We know that 20 percent require both, so we can set up the following equation:

100 = 20 + cOnly + wOnly + neither

To find neither, we'll need both of the other variables.

Statement (1) is insufficient. The companies that require computer skills fall into one of two categories: computer and writing skills, or computer skills only. If half of those companies require writing skills, those companies are the "both" companies. If 20 percent are both, that means that 20 percent are "computer only." Thus:

100 = 20 + 20 + wOnly + neither

Still not enough.

Statement (2) is also insufficient. This statement gives us "writing only" companies. Again, it's one of the two variables we need, but not both:

100 = 20 + cOnly + 45 + neither

Taken together, the statements are sufficient:

100 = 20 + 20 + 45 + neither

neither = 15

Choice (C) is correct.

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