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

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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:

41% (04:17) correct 59% (03:47) wrong based on 305 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 5017 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 Followers: 1 Kudos [?]: 10 [0], given: 9 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: 58 Location: United States (NY) GMAT 1: 780 Q51 V47 GPA: 3.89 Followers: 16 Kudos [?]: 62 [11] , given: 13 Re: There are 100 freshmen at a particular college, all of whom [#permalink] ### Show Tags 12 Jan 2013, 22:57 11 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: 6686 Location: Pune, India Followers: 1838 Kudos [?]: 11183 [1] , given: 219 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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Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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21 Nov 2013, 18:55
Where are u Bunnel? ...please suggest any easy way....
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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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23 Nov 2013, 12:46
Thanks a lot Karishma .......kudos to this explanation !!!!!!
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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....
Re: There are 100 freshmen at a particular college, all of whom   [#permalink] 30 Jun 2016, 08:21
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