Problem Solving

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

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

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