GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Aug 2019, 23:39

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# There are 816 students in enrolled at a certain high school. Each of

Author Message
TAGS:

### Hide Tags

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

### Show Tags

Updated on: 08 Jun 2018, 02:54
14
00:00

Difficulty:

55% (hard)

Question Stats:

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

### HideShow timer Statistics

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

_________________
"Please hit +1 Kudos if you like this post"

_________________
Manish

"Only I can change my life. No one can do it for me"

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
Joined: 14 Dec 2017
Posts: 517
Location: India
Re: There are 816 students in enrolled at a certain high school. Each of  [#permalink]

### Show Tags

07 Jun 2018, 12:19
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.

Thanks,
GyM
_________________
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1031
WE: Supply Chain Management (Energy and Utilities)
Re: There are 816 students in enrolled at a certain high school. Each of  [#permalink]

### Show Tags

07 Jun 2018, 22:23
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
Attachments

EBG.JPG [ 26.91 KiB | Viewed 1676 times ]

_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Intern
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]

### Show Tags

22 Dec 2018, 02:58
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
Display posts from previous: Sort by