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In a group of 80 college students, how many own a car? (1)

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In a group of 80 college students, how many own a car? (1) [#permalink]

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In a group of 80 college students, how many own a car?

(1) Of the students who do not own a car, 14 are male.
(2) Of the students who own a car, 42% are female.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 11 Jun 2013, 07:19, edited 1 time in total.
OA added.

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In a group of 80 college students, how many own a car? (1) [#permalink]

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Hussain15 wrote:
In a group of 80 college students, how many own a car?

(1) Of the students who do not own a car, 14 are male.

(2) Of the students who own a car, 42% are female.


In a group of 80 college students, how many own a car?

(1) Of the students who do not own a car, 14 are male. Clearly insufficient.

(2) Of the students who own a car, 42% are female --> let # of students who own a car be \(x\) --> \(0.42x=\) # of females who own a car. But \(0.42x\) must be an integer, as it represent # of females. \(0.42x=integer\) --> \(\frac{21}{50}x=integer\) --> \(x\) is a multiple of 50: 50, 100, 150, ... But \(x\) (# of students who own car) must also be less than (or equal to) 80. So \(x=50\). sufficient.

Answer: B.
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Re: In a group of 80 college students, how many own a car? (1) [#permalink]

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Bunuel wrote:
Hussain15 wrote:
In a group of 80 college students, how many own a car?

(1) Of the students who do not own a car, 14 are male.

(2) Of the students who own a car, 42% are female.


In a group of 80 college students, how many own a car?

(1) Of the students who do not own a car, 14 are male. Clearly insufficient.

(2) Of the students who own a car, 42% are female --> let # of students who own a car be \(x\) --> \(0.42x=\) # of females who own a car. But \(0.42x\) must be an integer, as it represent # of females. \(0.42x=integer\) --> \(\frac{21}{50}x=integer\) --> \(x\) is a multiple of 50: 50, 100, 150, ... But \(x\) (# of students who own car) must also be less than (or equal to) 80. So \(x=50\). sufficient.

Answer: B.


This is tricky. Thanks for the explanation.
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Re: Good Overlapping Set Problem [#permalink]

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Ans should be E, We do not have enough info to respond.

Consider the following chart:



Attachment:
sets.png
sets.png [ 4 KiB | Viewed 17730 times ]


The question is asking for the value of X. We do not have sufficient info to go forward.

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Re: Good Overlapping Set Problem [#permalink]

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Re: Good Overlapping Set Problem [#permalink]

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New post 30 May 2010, 07:47
My bad !
Well done Bunuel (as always); Hussain15 were is this question from? it seems easy at first sight but is really tricky....

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Re: Good Overlapping Set Problem [#permalink]

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New post 30 May 2010, 09:27
The question is from Magoosh Quant Bank. The bank is a good source of quality GMAT questions.

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Re: Good Overlapping Set Problem [#permalink]

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New post 14 Sep 2010, 00:17
wow !!

Great question. :-D
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Re: Good Overlapping Set Problem [#permalink]

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New post 14 Sep 2010, 07:39
Bunuel wrote:
Hussain15 wrote:
In a group of 80 college students, how many own a car?

(1) Of the students who do not own a car, 14 are male.

(2) Of the students who own a car, 42% are female.


(1) Of the students who do not own a car, 14 are male. Clearly insufficient.

(2) Of the students who own a car, 42% are female --> let # of students who own a car be \(x\) --> \(0.42x=\) # of females who own a car. But \(0.42x\) must be an integer, as it represent # of females. \(0.42x=integer\) --> \(\frac{21}{50}x=integer\) --> \(x\) is a multiple of 50: 50, 100, 150, ... But \(x\) (# of students who own car) must also be less than (or equal to) 80. So \(x=50\). sufficient.

Answer: B.


Wow, nice. I thought it was C.

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Re: Good Overlapping Set Problem [#permalink]

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New post 16 Sep 2010, 11:33
Bunuel wrote:
Hussain15 wrote:
In a group of 80 college students, how many own a car?

(1) Of the students who do not own a car, 14 are male.

(2) Of the students who own a car, 42% are female.


(1) Of the students who do not own a car, 14 are male. Clearly insufficient.

(2) Of the students who own a car, 42% are female --> let # of students who own a car be \(x\) --> \(0.42x=\) # of females who own a car. But \(0.42x\) must be an integer, as it represent # of females. \(0.42x=integer\) --> \(\frac{21}{50}x=integer\) --> \(x\) is a multiple of 50: 50, 100, 150, ... But \(x\) (# of students who own car) must also be less than (or equal to) 80. So \(x=50\). sufficient.

Answer: B.

good strategy Bunuel!!Thanx

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Re: Good Overlapping Set Problem [#permalink]

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New post 16 Sep 2010, 17:33
Awesome question. I too thought the answer is E. That's why it's a good idea to set up equations because these things become plain as day when you write them out. Important to remember that all statements are true.
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Re: Good Overlapping Set Problem [#permalink]

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New post 10 Oct 2010, 22:51
good q. thanks to bunuel for the explanation.
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Re: Good Overlapping Set Problem [#permalink]

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New post 30 Oct 2011, 10:13
I should agree that it is a great question!

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Re: Good Overlapping Set Problem [#permalink]

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New post 31 Oct 2011, 09:45
Bunuel,

Amazing solution!
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New post 31 Oct 2011, 13:35
Bunuel, Nice explanation.

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Re: In a group of 80 college students, how many own a car? (1) [#permalink]

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New post 16 Dec 2011, 11:48
Yep. Clicked on E. Wrong answer. :(
B is the right answer. I wonder why I miss out on such minor details. :(

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Re: In a group of 80 college students, how many own a car? (1) [#permalink]

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Re: In a group of 80 college students, how many own a car? (1) [#permalink]

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New post 31 Dec 2012, 07:51
Hussain15 wrote:
In a group of 80 college students, how many own a car?

(1) Of the students who do not own a car, 14 are male.

(2) Of the students who own a car, 42% are female.


I am confident this question will never be tested in GMAT. There are two parts of my argument. First GMAT does tests 2-D table in a variety of ways. It also tests the two variable one equation where answers can be deduced sometime based on the constraints used, for example a 21c pencil and 23c pen bought for some amount may have only one solution as it has only one such possible combination etc. That leads me to thing why the creator here has combined the two and probably a tried a super trick question. But GMAT is not about such tricks. GMAT tests practical scenario, for example, two variable one equation leading to a unique solution is a well known optimazation problem and there are tons of those tested in high school algebra and in real world.

Second, I have never seen this sort of un-necessay tricks employed in any GMAT questions. Probably filtering mechanism through experimental question will always leads to non-consistent percentile.

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Re: Good Overlapping Set Problem [#permalink]

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New post 01 Jan 2013, 01:53
Bunuel wrote:
Hussain15 wrote:
In a group of 80 college students, how many own a car?

(1) Of the students who do not own a car, 14 are male.

(2) Of the students who own a car, 42% are female.


(1) Of the students who do not own a car, 14 are male. Clearly insufficient.

(2) Of the students who own a car, 42% are female --> let # of students who own a car be \(x\) --> \(0.42x=\) # of females who own a car. But \(0.42x\) must be an integer, as it represent # of females. \(0.42x=integer\) --> \(\frac{21}{50}x=integer\) --> \(x\) is a multiple of 50: 50, 100, 150, ... But \(x\) (# of students who own car) must also be less than (or equal to) 80. So \(x=50\). sufficient.

Answer: B.


I think since the answer is based on a fine point, that the number pf car owners has to be an integer, they need to have covered that angle well. But I think they did not. The integer mentioned above can be 0 and need not be positive. I am pointing this out because in a quantitative test, precision is important.
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Re: In a group of 80 college students, how many own a car? (1) [#permalink]

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New post 03 Jan 2013, 22:25
very good ques had me stumped

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Re: In a group of 80 college students, how many own a car? (1)   [#permalink] 03 Jan 2013, 22:25

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