The table gives three factors to be considered when choosing GMAT EA

The table gives three factors to be considered when choosing an Internet service provider GMAT EA

The table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,200 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time”, what is the maximum possible number of respondents who cited “bargain prices”, but neither “user-friendly” nor “fast response time”?

A. 312

B. 336

C. 360

D. 384

E. 420

This is a good example of a rather difficult Venn diagram question. However you might notice that at no point do you need actually to draw the circles for the diagram.

For this type of question, it is important to notice where you need to start in order to crack the question open. Focus on what information is provided and what you need: we are given the 30% that are both User Friendly and Fast Response, so this will be the first thing to plug in. How?

The place to start here is to notice the numbers for User Friendly (56%) and Fast Response (48%).

We are then told that 30% are both UF and FR, so that would imply that:

UF: Total UF – both = 56% – 30% = 26% UF only

And likewise, for FR…

FR: Total FR – both = 48%-30% = 18% FR only

This covers the following proportion of the wider total:

Both UF and FR: 30%

UF only   : 26%

FR only   : 18%

——————————-

= 74%

(Ignore what I’m typing here because it’s just to appease the gods of search engines: the table gives three factors to be considered….)

This means that the remaining 26% could be one of three things:

1. Bargain Prices & UF
2. Bargain Prices & FR
3. Bargain Prices alone

In order to maximize the value for Bargain Prices alone, we would have to minimize the first two categories and consider Bargain Prices alone. 

That is: 

1. Bargain Prices & UF = 0%
2. Bargain Prices & FR = 0%
3. Bargain Prices alone = 26%

And we see that 26% of 1200 is:

30% – 4% = 26%

360 – 48 = 312