A car manufacturer organized a test drive of two of its prototypes.

Question

A car manufacturer organized 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 as liked both of them.

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

chetan2u · Accepted Answer

Hi  ShankSouljaBoi

I am not very fond of the wordings that leave a lot of ambiguity, but if you want to solve it..

Each driver gives a like or dislike for each of the 2 cars, so if you add the number of likes and number of dislikes, then HALF of it will be the number of drivers.

I believe the question means that the main reason/s for disliking car can be ONLY one - Performance or some other reason.

You may not be able to draw a conventional 2*2 matrix, but since you are looking for one, the matrix would be..
Two prototypes A and B... and likes -  A_l,B_l ...dislikes -  A_d,B_d

The matrix would be something like this, and we are looking for the value of  x+a+b+c 
...……... ……...A_l...........A_d....Total 
 B_l.....x............a 
 B_d....b............c. 
Total

We may not know what is the value of a, b, or c, but  (a+c)+(b+c)=270+90=270...a+b+c=270-c

(1) 120 people liked both prototypes....=>x=120

....... .……..A_l...........A_d 
 B_l....120..........a 
 B_d....b............c. 
 Total..120+b......a+c....120+a+b+c=120+270-c 
Nothing much. Insuff

(2) As many people liked neither prototype as liked both of them....=>y=c

....... ……....A_l...........A_d 
 B_l....y..........a 
 B_d....b............c. 
 Total...y+b......a+c....y+a+b+c=y+270-c=c+270-c=270 
Suff

B

Loser94 · Answer

From Statement 2
People who liked both prototype and who liked neither are same.
That means Total no of driver will be equal to 2*270

Anwer will be B

Take an example for 10 driver
if 5 drivers liked the prototypes and 5 liked neither then total drivers will be 10. There will be no driver who liked a single prototype.

ShankSouljaBoi · Answer

Hi  chetan2u  ,

Please help solve this one by double grid method. I am still getting C as the answer.

gerash7 · Answer

So you are assuming a driver gives only one review even though he\she tests two prototypes?

ShankSouljaBoi · Answer

Hi  chetan2u  ,

Good afternoon !!! Could you please help with this this one , as I am still getting C by double grid .

Regards
SSB

Crytiocanalyst · Answer

(1) 120 people liked both prototypes.
It doesn't gives us any definitive number on the total number of people , neither can we deduce based on the same 
therefore out

(2) As many people liked neither prototype as liked both of them.
Let x be the number of people who dislike both the products

Since the total number of people who disliked at least one product = 270 +x
The total number of people = 270+x-x =270 
Clearly sufficient

Therefore IMO B

thakurarun85 · Answer

"A driver did not like a prototype because of its performance 180 times"

What does this means?

GMATGuruNY · Answer

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. Implication: Total number of negative reviews = 180 + (1/2)(180) = 270 Let the two prototypes be A and B. To organize the data, use the following MATRIX: Screen Shot 2023-01-30 at 3.35.05 PM.png In the matrix above, A = people who like A, NA = people who do NOT like A, B = people who like B, NB = people who do NOT like B. Statement 1: 120 people liked both prototypes. Case 1: 120 like both A and B, 120 people like neither A nor B The following matrix is yielded: Screen Shot 2023-01-30 at 3.25.13 PM.png Since the 120 people in the center box give a negative review to A and a negative review to B -- for a total of 240 negative reviews -- 30 people must give a negative review only to A or only to B, bringing the total number of negative reviews to 270. If 10 people don't like A and 20 people don't like B, the following matrix is yielded: Screen Shot 2023-01-30 at 3.24.08 PM.png In this case, the total number of people - 270 Case 2: 120 like both A and B, 100 people like neither A nor B The following matrix is yielded: Screen Shot 2023-01-30 at 3.30.39 PM.png Since the 100 people in the center box give a negative review to A and a negative review to B -- for a total of 200 negative reviews -- 70 people must give a negative review only to A or only to B, bringing the total number of negative reviews to 270. If 50 people don't like A and 20 people don't like B, the following matrix is yielded: Screen Shot 2023-01-30 at 3.30.11 PM.png In this case, the total number of people - 290 Since the total number of people can be different values, INSUFFICIENT. Statement 2: As many people liked neither prototype as liked both of them. Case 1 also satisfies Statement 2. In Case 1, the total number of people = 270 Case 3: 100 people like both A and B, 100 people like neither A nor B The following matrix is yielded: Screen Shot 2023-01-30 at 3.28.35 PM.png Since the 100 people in the center box give a negative review to A and a negative review to B -- for a total of 200 negative reviews -- 70 people must give a negative review only to A or only to B, bringing the total number of negative reviews to 270. If 50 people don't like A and 20 people don't like B, the following matrix is yielded: Screen Shot 2023-01-30 at 3.28.18 PM.png In this case, the total number of people - 270 Since the total number of people in both Case 1 and Case 3 is THE SAME -- 270 -- Statement 2 is SUFFICIENT. B

GMATGuruNY · Answer

Below is the algebra behind Statement 2.

Let:
T = the total number of people
A = people who like A but not B
B = people who like B but not A
AB = people who like both A and B
N = people who like neither A nor B
Resulting equation:
T = A + B + AB + N

Everyone in the A group gives exactly 1 negative review (against B).
Everyone in the B group gives exactly 1 negative review (against A).
Everyone in the N group gives 2 negative reviews (one against A, the other against B).
Since the prompt indicates a total of 270 negative reviews, we get:
A + B + 2N = 270

Statement 2: As many people liked neither prototype as liked both of them.
Substituting AB = N into T = A + B + AB + N, we get:
T = A + B + N + N
T = A + B + 2N

Since A + B + 2N = 270, there are 270 people.

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