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Director  V
Joined: 12 Feb 2015
Posts: 886
There are 816 students in enrolled at a certain high school. Each of  [#permalink]

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14 00:00

Difficulty:   55% (hard)

Question Stats: 68% (03:25) correct 32% (03:20) wrong based on 134 sessions

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There are 816 students in enrolled at a certain high school. Each of these students is taking at least one of the subjects economics, geography, and biology. The sum of the number of students taking exactly one of these subjects and the number of students taking all 3 of these subjects is 5 times the number of students taking exactly 2 of these subjects. The ratio of the number of students taking only the two subjects economics and geography to the number of students taking only the two subjects economics and biology to the number of students taking only the two subjects geography and biology is 3:6:8. How many of the students enrolled at this high school are taking only the two subjects geography and biology?

A) 35
B) 42
C) 64
D) 136
E) 240

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Originally posted by CAMANISHPARMAR on 07 Jun 2018, 10:55.
Last edited by Bunuel on 08 Jun 2018, 02:54, edited 1 time in total.
Renamed the topic and edited the question.
Director  P
Joined: 14 Dec 2017
Posts: 517
Location: India
Re: There are 816 students in enrolled at a certain high school. Each of  [#permalink]

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1
CAMANISHPARMAR wrote:
There are 816 students in enrolled at a certain high school. Each of these students is taking at least one of the subjects economics, geography, and biology. The sum of the number of students taking exactly one of these subjects and the number of students taking all 3 of these subjects is 5 times the number of students taking exactly 2 of these subjects. The ratio of the number of students taking only the two subjects economics and geography to the number of students taking only the two subjects economics and biology to the number of students taking only the two subjects geography and biology is 3:6:8. How many of the students enrolled at this high school are taking only the two subjects geography and biology?
A) 35
B) 42
C) 64
D) 136
E) 240

Let,
a = # of students enrolled only in Economics
b = # of students enrolled only in Geography
c = # of students enrolled only in Biology
d = # of students enrolled only in Economics & Geography
e = # of students enrolled only in Economics & Biology
f = # of students enrolled only in Biology & Geography
g = # of students enrolled in all three

Total # of students = 816 = a+b+c+d+e+f+g

Now given that, (a+b+c)+g = 5(d+e+f)

Therefore we get 6(d+e+f) = 816

d+e+f = 136

Now also given that d:e:f = 3:6:8

Hence, d+e+f = 3x+6x+8x = 17x

Therefore, 17x = 136

x = 136/17

Now we need # of students enrolled only in Biology & Geography = 8x = 8*(136/17) = 64.

Answer C.

Thanks,
GyM
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Re: There are 816 students in enrolled at a certain high school. Each of  [#permalink]

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1
CAMANISHPARMAR wrote:
There are 816 students in enrolled at a certain high school. Each of these students is taking at least one of the subjects economics, geography, and biology. The sum of the number of students taking exactly one of these subjects and the number of students taking all 3 of these subjects is 5 times the number of students taking exactly 2 of these subjects. The ratio of the number of students taking only the two subjects economics and geography to the number of students taking only the two subjects economics and biology to the number of students taking only the two subjects geography and biology is 3:6:8. How many of the students enrolled at this high school are taking only the two subjects geography and biology?
A) 35
B) 42
C) 64
D) 136
E) 240

The affixed Venn diagram is drawn as per the given data.
Question stem:- The no of enrolled students who are taking only the two subjects geography and biology at the high school, i. e, 8K=?
From the given data & Venn diagram, we have
E+B+G+ (6K+3K+8K) +All =816 --------- (1)
E+B+G+ All= 5(6K+3K+8K) ------------ (2)
Subtracting (2) from (1), we have,
17K=816-85K
Or, 102K=816
Or, 8K= $$\frac{816}{102}$$ *8=64
So, Answer option (C)
Attachments EBG.JPG [ 26.91 KiB | Viewed 1676 times ]

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Joined: 28 Aug 2018
Posts: 27
Location: India
Schools: LBS '21 (A)
GMAT 1: 650 Q49 V31 GPA: 3.16
There are 816 students in enrolled at a certain high school. Each of  [#permalink]

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1
Easiest way -
Refer the diagram.

Let the sum of all X's be x (the sum of the number of students taking exactly one of these subjects and the number of students taking all 3 of these subjects)
Let the sum of all Y's be y (the number of students taking exactly 2 of these subjects)

Now according to the question x = 5y and there are no students that are taking none of the subjects.

That means x + y = 816
Now as per the question x = 5y. Hence, 6y = 816
y = 136
Divide it into ratio 8/17*136 = 64
Attachments Screen Shot 2018-12-22 at 3.24.35 PM.png [ 65.66 KiB | Viewed 946 times ] There are 816 students in enrolled at a certain high school. Each of   [#permalink] 22 Dec 2018, 02:58
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