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

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Intern
Joined: 02 Feb 2017
Posts: 15
Concentration: Entrepreneurship, Strategy
A car manufacturer organized a test drive of two of its prototypes  [#permalink]

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09 Apr 2017, 07:50
3
14
00:00

Difficulty:

95% (hard)

Question Stats:

21% (02:13) correct 79% (02:41) wrong based on 154 sessions

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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 itmes, 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 protototypes.
(2) As many people liked neither prototype a liked both of them
Math Expert
Joined: 02 Aug 2009
Posts: 8299
Re: A car manufacturer organized a test drive of two of its prototypes  [#permalink]

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09 Apr 2017, 17:51
3
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RUSDI wrote:
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 itmes, 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 protototypes.
(2) As many people liked neither prototype a liked both of them

Hi..
180 did not like because of the performance and half of it or 180/2 that is 90 did not like for some other reason.
Total who did not like = 180+90-b where b is the number of people who did not like BOTH..

Total number of test drivers = 270-b+x where x is the number of people who like both.

So we require to know value of b and x.

Let's see the statements..
1) 120 like both.
So we know x but b is still not known
Insufficient

2) b=x.
Number = 270-b+x=270-x+x=270
Sufficient

B
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##### General Discussion
Intern
Joined: 08 Jul 2013
Posts: 13
Re: A car manufacturer organized a test drive of two of its prototypes  [#permalink]

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11 Apr 2017, 02:02
Can someone please post a nice detailed solution to this? Thanks
Senior Manager
Joined: 24 Apr 2016
Posts: 316
Re: A car manufacturer organized a test drive of two of its prototypes  [#permalink]

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07 Jul 2017, 00:21
2
rt9 hope this helps

Let,

A = Drivers who liked the Prototype 1, but did not like Prototype 2 either for Performance issue or some other Reason
C = Drivers who liked the Prototype 2, but did not like Prototype 1 either for Performance issue or some other Reason
B = Drivers who liked both the Prototype 1 & 2
D = Drivers who did not like both Prototype 1 & 2

Total Number of Drivers = A + B + C + D

Given in question Stem

A Driver did not like a prototype because of it's performance 180 times, whereas did not like it for some other reason 90 times.

This means,

'A' No. of drivers who did not like Prototype 2 for either Performance/other reason + 'C' No. of drivers who did not like Prototype 1 for either Performance/other reason + 2 * 'D' the number of drivers who did not like both Prototype 1 & 2 = 180 + 90 = 270

Therefore, A+B+2D = 270

[Since D no. of drivers once tested prototype 1 and, 2 then protototype 2, each of the D drivers would have two opinions each. Since Both Opinions were negative, Hence we are taking twice D.]

Statement 1: 120 people liked both prototypes.

This just gives us the value of C, but nothing about A, B and D. Hence this statement is not sufficient.

Statement 2: As many people liked neither prototype as liked both of them

This tells us that C = D, which means

A+B+2D = A+B+C+D = 270

As we can find the total number of drivers, this statement is sufficient.

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Re: A car manufacturer organized a test drive of two of its prototypes  [#permalink]

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07 Aug 2019, 00:59
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Re: A car manufacturer organized a test drive of two of its prototypes   [#permalink] 07 Aug 2019, 00:59
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