• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greate

This topic has expert replies
Legendary Member
Posts: 1252
Joined: 07 Sep 2017
Thanked: 6 times
Followed by:3 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?

A. 144
B. 119
C. 113
D. 88
E. 31

[spoiler]OA=D[/spoiler]

Source: GMAT Club Tests

Legendary Member
Posts: 1846
Joined: 02 Mar 2018
Followed by:3 members
Total student => 232
Students that took geometry => 144
Students that took biology => 119


Greatest possible number of students taking both geometry and biology = possibility that all the students that took biology also took geometry


Greatest possible number of students taking both => 119
For the smallest possible number of students doing both:
Total - Neither = A + B - Both
Both = A + B + Neither - Total; where Neither must be equal to 0 in order to get the minimum or smallest value for both
Both = 144 + 119 + 0 - 232 = 31 students


Difference between the greatest and the smallest =>
119 - 31 = 88


Answer = D

Legendary Member
Posts: 1538
Joined: 29 Oct 2017
Followed by:5 members
Vincen wrote:
Fri Jun 19, 2020 2:49 am
In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?

A. 144
B. 119
C. 113
D. 88
E. 31

[spoiler]OA=D[/spoiler]

Source: GMAT Club Tests
Smallest Possible Number taken both should be given by

Total - Neither = A + B - Both

The greatest is between 144 and 119 is: 119.
The Smallest can be calculated by the formula
Both = A+B+Neither - Total (Neither must be 0 to minimize the both)
So, \(144 + 119 + 0 - 232 = 31\)

Greatest - Smallest is \(119-31 = 88\)
So the correct answer is D

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 5170
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:23 members
Vincen wrote:
Fri Jun 19, 2020 2:49 am
In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?

A. 144
B. 119
C. 113
D. 88
E. 31

[spoiler]OA=D[/spoiler]

Solution:

The greatest possible number of students that could have taken both courses is 119, which occurs if all the students who took biology also took geometry. The smallest possible number of students that could have taken both courses is 144 + 119 - 232 = 31, which occurs if we maximize the number of students taking only one course. Therefore, the difference is 119 - 31 = 88.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage