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

A) Of those companies surveyed that required computer skills, half required writing skills
B) 45% of the companies surveyed required writing skills but not computer skills

This is an EITHER/OR group problem.
Every company EITHER requires computer skills OR does not.
Every company EITHER requires writing skills OR does not.
For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data.

Let C = computer skills, NC = not computer skills, W = writing skills, NW = not writing skills.
In the grids below, the entries in any given row or column must add up to the TOTAL of that row or column.
Let the total number of companies = 100.

20% required both computer skills and writing skills:

The question stem asks for the value of the middle box: the number that require NEITHER type of skill.

Statement 1: Of those companies surveyed that required computer skills, half required writing skills.
Thus, the 20 companies in the top left corner of the grid represent half the total number of companies that require computer skills.
The following grid is yielded:

No way to determine the value of the middle box.
INSUFFICIENT.

Statement 2: 45% of the companies surveyed required writing skills but not computer skills.
The following grid is yielded:

No way to determine the value of the middle box.
INSUFFICIENT.

Statements combined:
The following grid is yielded:

Middle box = 15.
SUFFICIENT.

The correct answer is C.

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

A) Of those companies surveyed that required computer skills, half required writing skills
B) 45% of the companies surveyed required writing skills but not computer skills

We can use the formula:

Total = Computer + Writing - Both + Neither

So in terms of percentage, we have:

100 = Computer + Writing - 20 + Neither

120 = Computer + Writing + Neither

We need to determine Neither, so we need to know Computer and Writing.

Statement One Only:

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

This means computer skills must be 40 since half of it is 20, which is both computer and writing skills. Therefore, we have:

120 = 40 + Writing + Neither

However, without knowing the value of Writing, we can't determine Neither. Statement one alone is not sufficient.

Statement Two Only:

45% of the companies surveyed required writing skills but not computer skills.

Notice writing skills only = Writing - Both, so 45 = Writing - 20 or Writing = 65. So we have:

120 = Computer + 65 + Neither

However, without knowing the value of Computer, we can't determine Neither. Statement two alone is not sufficient.

Statements One and Two Together:

With both statements, we have:

120 = 40 + 65 + Neither

15 = Neither

Answer: C