A car manufacturer organised a test drive of two of its...

[TommH]

I'm struggling with understanding how they arrived at the answer for this DS question. I've read 2 approaches on the GMATclub forum and I'm still a little lost. Any help in simplifying and ultimately making me understand would be greatly appreciated!

Many thanks in advance!


QUESTION:

A car manufacturer organised a test drive of two of its prototypes. Each driver tested both prototypes and was asked if he or she liked the prototype. If a driver did not like a prototype, he or she was asked if the prototype's performance was the main reason. A driver did not like a prototype because of its performance 180 times, whereas only half as often a driver did not like a prototype because of some other major reason. How many test drivers were there?

(1) 120 people liked both prototypes.
(2) As many people liked neither prototype a liked both of them

[MichaelO788]

I draw a Matrix table and set like not like on the x axis and performance not performance on the y-axis with a total column in each

Statement 1: Insufficient.

Statement 2: Insufficient. It is only sufficient to find the total that did not like the cars

Statement 1 and 2 Sufficient . 180+90 = total not likes and 120 is the total likes so sufficient to find total. GMATClub thinks otherwise. Beat the Gmat tends to agree.

MGMAT instructors should join on this one

[Sage Pearce-Higgins]

This looks like an overlapping sets problem, but it's not obvious how to draw up the set matrix. MichaelO788, your set matrix would yield some strange results: what does the box "not performance / not like" represent in your scheme?

Since all the drivers tried both cars, we could set up a matrix with 'Prototype 1: like or dislike' and then 'Prototype 2: like or dislike' as the two axes. Try out this method of solving the problem.

However, I think that it's simpler to think about it in this way. The information in the question stem tells us that we have a total of 270 dislikes among the drivers. We need to find the total number of likes, and from that we can calculate the number of drivers. Statement 1 alone isn't sufficient as we don't know how many people liked just 1 prototype (you can prove this by testing cases). Statement 2 alone isn't sufficient. The two statements together are sufficient as we can see that 120 people liked neither (that's 240 dislikes in total) and 120 liked both, meaning that 30 (from the information in the question stem) people liked one prototype. Answer C.

However, the wording in this question is vague: what if some people didn't decide? And the quality of the writing isn't great, especially the phrase "only half as often a driver did not like a prototype". For that reason, I don't think that this is a problem from GMAT Prep resources and you shouldn't spend any more time on it.