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?
Answers
A) 144	B) 119	C) 113	D) 88	E) 31

Rationale: "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 can not 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 = 88 . answer : d ."
Answer: D