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There are 100 freshmen at a particular college, all of whom [#permalink]
10 Jan 2013, 16:44

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Difficulty:

95% (hard)

Question Stats:

40% (04:20) correct
60% (03:33) wrong based on 224 sessions

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?

Re: Overlapping Sets - Freshman at a College [#permalink]
10 Jan 2013, 20:53

5

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Expert's post

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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 3300 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 _________________

Re: Overlapping Sets - Freshman at a College [#permalink]
12 Jan 2013, 15:36

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?

Re: Overlapping Sets - Freshman at a College [#permalink]
13 Jan 2013, 22:15

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.

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