Bunuel wrote:

Of the companies surveyed about the skills they required in prospective employees, 20 percent required both computer skills and writing skills. What percent of the companies surveyed required neither computer skills nor writing skills?

(1) Of those companies surveyed that required computer skills, half required writing skills.

(2) 45 percent of the companies surveyed required writing skills but not computer skills.

Diagnostic Test

Question: 34

Page: 25

Difficulty: 700

This question asks us if we have enough information to determine what percent of the companies surveyed require neither computer skills nor writing- if we think of this question as a Venn Diagram then circle A can be the percent of companies that require writing skills, circle b can be the percent of companies that require computer skills, the intersection of circle a and b ( circle c if you will) is the percent of companies that require both, and a circle separate from these three circles, circle D, can be the percent of companies that require neither ( see set theory). If we know the percentage of A B and C then we can calculate what the percentage of circle D will be ( Total= A + B - both + neither).

Statement (1) tells us that half of the companies that required computer skills require writing skills; this implies that the percentage of c will be half of b- if the percentage of companies that required computer skills were say 60 percent- then the percentage of companies that require both would be 30 percent according to this statement. However, we cannot calculate the percentage of companies that require writing skills only from this statement and therefore we cannot calculate the percentage that require neither. Insufficient.

Statement (2) gives us the total percentage of companies that require writing skills- if 45 percent require only writing skills then the percentage of A is 65 ( see set theory). However, this leaves us with the same problem as statement (1) - we cannot find out the percentage of "B." Insufficient.

Statement (1) and Statement (2) allow us to calculate the percentage of A, B and C and thus solve for D. Sufficient

Total= 45% + 40% - 20% + D (We can just assume these are values of 100 for the sake of convenience though algebra may be more appropriate in other circumstances)

100= 45+ 40- 20 + D

100= 85-20+D

100=65+D

35=D