In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number W and the smallest possible number of students that could have taken both geometry and biology?	Pick
A) 144	B) 119	C) 113	D) 88	E) 31
OFFICIAL SOLUTION:   First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.   {Total} = {geometry} + {biology} - {both} + {neither};   232 = 144 + 119 - {both} + {neither};   {both} = 31 + {neither}.   {both} is minimized when {neither} is 0. In this case {both} = 31.   The greatest possible number W of students that could have taken both geometry and biology, is 119.   Thus, the answer is 119 - 31= 
<gadget id="calculator">119 - 31</gadget>
<output>88</output>
88.   Answer: 88.
<result>D</result>
In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number W and the smallest possible number of students that could have taken both geometry and biology?