SOLUTION

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.

You can draw a Venn diagram or make a matrix to solve this question.

Note that statement (1) says that "of those companies surveyed that required computer skills, half required writing skills" --> if \(y\) required computer skills, then of those \(y\) who required computer skills, \(\frac{y}{2}\) also required writing skills (# of companies required computer and writing skills is \(\frac{y}{2}=20\)).
Answer: C.
_________________

Answer - C

Strategy: Find out both "JUST" computer skills and "JUST" writing skills, SUM them. Take that SUM and subtract from 100% (Total possible) to reach the "neither" of those 2 possibilities.

From stem: 20% require both computer skills and writing skills (helps us ascertain "JUST" computer skills" in statement 1.
From (1): 2 * 20% require JUST computer skills -> 40% for JUST computer skills but don't know about writing skills - N.S.
From (2): 45% require JUST writing skills -> 45% for JUST writing skills but don't know about computer skills - N.S
(1 + 2) Now know both "JUST" computer skills & writing skills. If you add these up you get 85% with no overlap. Subtract this from 100% (total possible) to reach 15% as neither. Sufficient.

Answer - C

Think of the Venn Diagram. You are given that the overlap area has 20 companies (assuming total 100 companies) in the question stem.

(1) Of those companies surveyed that required computer skills, half required writing skills.
So half of the companies that required computer skills, required writing skills too. Hence this 20 forms half of the companies that required computer skills. So total 40 companies required computer skills. The info given in red is obtained by using statement 1. We don't know how many required only writing skills yet so we cannot find none. Not sufficient.

(2) 45 percent of the companies surveyed required writing skills but not computer skills.
Now we know that 45 required only writing skills. The info in green is obtained by statement 2. But we don't know how many required only computer skills so not sufficient.


Using both, we have all the data.

None = 100 - 20 - 20 - 45 = 15

Answer (C)
_________________

Here is a visual that should help.

_________________

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

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
_________________

VeritasKarishma

I have a small doubt. Since, we are talking about skills it is possible that there were other skills also considered besides writing and computer and this possibility is not ruled out by the 2 statements. How do we ensure that these are the only skills to be considered?

Pls help

Sure, the companies could require n number of skills. Our question deals with only these two - writing skills and computer skills.

The question very clearly asks us: "What percent of the companies surveyed required neither computer skills nor writing skills?"
It does not ask "What percent of companies required no skills?" or something like that.
_________________

Total = 100
Both= 20
Computer =x
Neither = N


(1) 100=x+1/2*x-20+N

120=x+1/2*x+N; Insufficient.

(2) Don't about writing skills.

Considering both;
100=90+45-20+N Sufficeint

The answer is C
_________________

My approach to solve this problem was as follows:

Let total be 1 and it is given that 20% percent required both Writing (W) and Computer (C). W&C=0.2

So for Calculating Neither (W&C)=1 - (W + C - W&C)......(a)

Statement 1 provides C=0.5 W.....(b)

Statement 2 provides W= 0.45.....(c)

Using eqn. (a), (b) & (c), we can calculate the required answer thus 1 &2 together sufficient.

Please correct me if this approach is wrong.

Thank You,
Regards,
Shashank

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


Writing

		Not writing	Total
Computer skills	20%
Not computer skills		x=?
Total

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

Writing

		Not writing	Total
Computer skills	20%	20%	40%
Not computer skills		x=?	60%
Total			100%

Not sufficient

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

Writing

		Not writing	Total
Computer skills	20%
Not computer skills	45%	x=?
Total	65%	35%	100%

Not sufficient

(1) + (2)
(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.

Writing

		Not writing	Total
Computer skills	20%	20%	40%
Not computer skills	45%	x=15%	60%
Total	65%	35%	100%

The percent of the companies surveyed required neither computer skills nor writing skills = 15%
Sufficient

IMO C
_________________