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# There are 100 freshmen at a particular college, all of whom

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Intern
Joined: 28 Nov 2012
Posts: 44
There are 100 freshmen at a particular college, all of whom [#permalink]

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10 Jan 2013, 17:44
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Difficulty:

95% (hard)

Question Stats:

43% (04:15) correct 57% (03:48) wrong based on 382 sessions

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There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?

(A) 25
(B) 32
(C) 36
(D) 48
(E) 61
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Jan 2013, 04:20, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Overlapping Sets - Freshman at a College [#permalink]

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10 Jan 2013, 21:53
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skiingforthewknds wrote:
There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?

(A) 25

(B) 32

(C) 36

(D) 48

(E) 61

Make a venn diagram to get a clear picture. Look at the diagram:
Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.

Attachment:

Ques3.jpg [ 18.68 KiB | Viewed 6330 times ]

d + f = 20 (People who take Art and one other class)
b = 3e (people who take only Art is 3 times the people who take Bio and Calculus)
17 + 10 + 5 + b + d + e + f = 100 (Total people)
b + b/3 = 48
b = 36

Number of freshmen who take Art = 36 + 20 + 5 = 61
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 08 Feb 2011 Posts: 11 Re: Overlapping Sets - Freshman at a College [#permalink] ### Show Tags 12 Jan 2013, 16:36 VeritasPrepKarishma wrote: skiingforthewknds wrote: There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art? (A) 25 (B) 32 (C) 36 (D) 48 (E) 61 Make a venn diagram to get a clear picture. Look at the diagram: Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc. Attachment: Ques3.jpg d + f = 20 (People who take Art and one other class) b = 3e (people who take only Art is 3 times the people who take Bio and Calculus) 17 + 10 + 5 + b + d + e + f = 100 (Total people) b + b/3 = 48 b = 36 Number of freshmen who take Art = 36 + 20 + 5 = 61 Hello Karishma, very nice job with this question. I solved by using the formula below and got the same answer. Total = (# in A + # in B + # in C) - (# enrolled in 2 courses) - 2(# enrolled in 3 courses) + (# in 0 courses) Because of all the variables, solving the problem using the formula took me too much time. Your approach is far better! Could you describe a situation when you would be required to use the formula above or will the method you used always be appropriate? Thanks Manager Joined: 12 Jan 2013 Posts: 57 Location: United States (NY) GMAT 1: 780 Q51 V47 GPA: 3.89 Re: There are 100 freshmen at a particular college, all of whom [#permalink] ### Show Tags 12 Jan 2013, 22:57 12 This post received KUDOS 1 This post was BOOKMARKED During an actual exam I would not even introduce any letters. 100 - 17 - 10 - 5 - 20 = 48 students take either only Art or only Biology and Calculus. Dividing 48 in proportion 3:1, we conclude that 48*3/4=36 students take only Art. Thus, we get 36 + 20 + 5 = 61. (Only Art, Art and one course, Art and two courses, respectively.) _________________ Sergey Orshanskiy, Ph.D. I tutor in NYC: http://www.wyzant.com/Tutors/NY/New-York/7948121/#ref=1RKFOZ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7448 Location: Pune, India Re: Overlapping Sets - Freshman at a College [#permalink] ### Show Tags 13 Jan 2013, 23:15 1 This post received KUDOS Expert's post holidayhero wrote: Hello Karishma, very nice job with this question. I solved by using the formula below and got the same answer. Total = (# in A + # in B + # in C) - (# enrolled in 2 courses) - 2(# enrolled in 3 courses) + (# in 0 courses) Because of all the variables, solving the problem using the formula took me too much time. Your approach is far better! Could you describe a situation when you would be required to use the formula above or will the method you used always be appropriate? Thanks I use venn diagrams for most sets questions. It's very easy to see the relation between what is given and what is asked when you see it in a venn diagram. The process becomes completely mechanical and quick. There are various ways to represent the formulas in sets and that can get a little messy hence I avoid them. Check out a post I wrote sometime back on overlapping sets: http://www.veritasprep.com/blog/2012/09 ... ping-sets/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Posts: 52
Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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21 Nov 2013, 19:04
Hey Karishma ,

Could you please explain ,where from b/3 is derive?
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Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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21 Nov 2013, 21:06
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taleesh wrote:
Hey Karishma ,

Could you please explain ,where from b/3 is derive?

The question says:
"If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art"

Freshmen who take every class except art are the freshmen who take Bio and Calculus only.
So b = 3e
or e = b/3

Now, Total = 100 = 17 + 10 + 5 + b + d + e + f
100 - 32 = b + (d + f) + e
68 = b + 20 + b/3

(Note that d + f = 20 and e = b/3)

You get b = 36
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Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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27 Jun 2015, 03:42
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Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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30 Jun 2016, 08:21
Very good Question..

Another Approach:-

3k(k- freshmen who did not opt for Arts at all) + 20(arts+one other) +5 (freshmen who took all) => 3k+25....

Only 61 among all other options is in the form of 3k+25....
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Joined: 18 May 2017
Posts: 12
Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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20 May 2017, 04:51
skiingforthewknds wrote:
There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?

(A) 25
(B) 32
(C) 36
(D) 48
(E) 61

Can someone please provide a more easier approach with detailed explanation?
Thank you!
Intern
Joined: 18 May 2017
Posts: 12
Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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20 May 2017, 04:56
SergeyOrshanskiy wrote:
During an actual exam I would not even introduce any letters.

100 - 17 - 10 - 5 - 20 = 48 students take either only Art or only Biology and Calculus.

Dividing 48 in proportion 3:1, we conclude that 48*3/4=36 students take only Art.

Thus, we get 36 + 20 + 5 = 61.
(Only Art, Art and one course, Art and two courses, respectively.)

Hi Sergey!
How did you derive this one "Dividing 48 in proportion 3:1, we conclude that 48*3/4=36 students take only Art."

Math Expert
Joined: 02 Sep 2009
Posts: 39725
Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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20 May 2017, 05:20
Michaelkalend13 wrote:
skiingforthewknds wrote:
There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?

(A) 25
(B) 32
(C) 36
(D) 48
(E) 61

Can someone please provide a more easier approach with detailed explanation?
Thank you!

My friend, you can find detailed solutions HERE and HERE. You can also find link to the theory HERE. If the question is still unclear please ask more specific question on it.

Hope it helps.
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Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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20 May 2017, 06:10
Bunuel wrote:
Michaelkalend13 wrote:
skiingforthewknds wrote:
There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?

(A) 25
(B) 32
(C) 36
(D) 48
(E) 61

Hi, my friend Bunuel!

Thank you very much for the links. I will study them very carefully.
I've sent you PM, kindly respond at your earliest convenience.

Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 39725
Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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20 May 2017, 06:13
Michaelkalend13 wrote:
I've sent you PM, kindly respond at your earliest convenience.

Thanks!

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Re: There are 100 freshmen at a particular college, all of whom   [#permalink] 20 May 2017, 06:13
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