Question

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.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are not sufficient

Hint:

When solving problems with percentages, set up equations based on the given relationships to find the unknowns.

Answer 1

The Correct Option is C

Step 1: Analyze statement (1).
Statement (1) tells us that half of the companies that required computer skills also required writing skills. However, this information does not give us enough information to find how many companies required neither skill.
Step 2: Analyze statement (2).
Statement (2) tells us that 45 percent of the companies required writing skills but not computer skills, but this information alone does not give us the percentage of companies that required neither skill.
Step 3: Combine both statements.
Combining both statements:
- Let \( x \) represent the total percent of companies that required computer skills, and let \( y \) represent the total percent that required writing skills.
- From statement (1), half of the companies that required computer skills also required writing skills, so the percentage of companies that required both skills is \( 0.5x \).
- From statement (2), we know that 45 percent required writing skills but not computer skills, so \( y - 0.5x = 45 \).
- We now have enough information to solve for the percentage of companies that required neither skill.
\[ \boxed{C} \]