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
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: 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
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
Smallest Possible Number taken both should be given byVincen wrote: ↑Fri Jun 19, 2020 2:49 amIn 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
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 \(11931 = 88\)
So the correct answer is D
GMAT/MBA Expert
 Scott@TargetTestPrep
 GMAT Instructor
 Posts: 5170
 Joined: 25 Apr 2015
 Location: Los Angeles, CA
 Thanked: 43 times
 Followed by:23 members
Solution:Vincen wrote: ↑Fri Jun 19, 2020 2:49 amIn 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]
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 WoodburyStewart
Founder and CEO
scott@targettestprep.com
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews