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 to answer the question asked.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
• C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient to answer the question asked.
• E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Hint:

For overlapping sets problems, drawing a Venn diagram can be very helpful. Label the two circles "Computer" and "Writing". Fill in the intersection ("Both") with 20%. Statement (1) allows you to find the total for the "Computer" circle. Statement (2) gives you the "Writing only" part, which allows you to find the total for the "Writing" circle. With all parts of the circles filled, you can find the value for "Neither".

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a set theory or Venn diagram problem. Let C be the percentage of companies requiring computer skills, and W be the percentage requiring writing skills. We are given:

Percentage requiring both (C and W) = 20%
We need to find:

Percentage requiring neither (Neither C nor W)
Step 2: Key Formula or Approach:
The formula for the union of two sets is: \[ \text{Total %} = %(\text{C only}) + %(\text{W only}) + %(\text{Both}) + %(\text{Neither}) \] Or, using the principle of inclusion-exclusion: \[ %(\text{C or W}) = %(\text{C}) + %(\text{W}) - %(\text{C and W}) \] And, \[ %(\text{Neither}) = 100% - %(\text{C or W}) \] To solve the problem, we need to find %(C or W), which requires us to find %C and %W.
Step 3: Detailed Explanation:
Analyze Statement (1): Of those companies surveyed that required computer skills, half required writing skills.
This is a conditional probability statement. It means that of the group C, 50% of them are also in group W. \[ 0.50 \times %(\text{C}) = %(\text{C and W}) \] We know %(C and W) = 20%, so: \[ 0.50 \times %(\text{C}) = 20% \] \[ %(\text{C}) = \frac{20%}{0.50} = 40% \] Now we know the total percentage requiring computer skills is 40%. However, we still don't know %(\text{W}). So we can't find %(\text{C or W}). Statement (1) is not sufficient.
Analyze Statement (2): 45 percent of the companies surveyed required writing skills but not computer skills.
This gives us the value for the "W only" region. \[ %(\text{W only}) = 45% \] We know that %(\text{W}) = %(\text{W only}) + %(\text{Both}). \[ %(\text{W}) = 45% + 20% = 65% \] Now we know the total percentage requiring writing skills is 65%. However, we don't know %(\text{C}). So we can't find %(\text{C or W}). Statement (2) is not sufficient.
Analyze Both Statements Together:
From statement (1), we found %(\text{C}) = 40%.
From statement (2), we found %(\text{W}) = 65%.
We were given %(\text{C and W}) = 20%.
Now we can calculate the percentage of companies requiring at least one skill: \[ %(\text{C or W}) = %(\text{C}) + %(\text{W}) - %(\text{C and W}) \] \[ %(\text{C or W}) = 40% + 65% - 20% = 85% \] The percentage requiring neither skill is: \[ %(\text{Neither}) = 100% - %(\text{C or W}) = 100% - 85% = 15% \] Since we can find a unique value, the statements together are sufficient.
Step 4: Final Answer:
Combining both statements provides enough information to calculate the required percentage.