there are 100 freshmen at a particular college , all of whom must take at least one of the 3 core classes : art , biology , and calculus . of these freshmen , 17 take only biology , 10 take only calculus , 9 take all 3 classes , and 20 take art and exactly one of the other two core classes . if the number of freshmen who take only art is 3 times the number of freshmen who take every core class except art , how many freshmen take art ? Choose the correct answer:
A) 25	B) 32	C) 36	D) 48	E) 62

Rationale: make a venn diagram to get a clear picture . look at the diagram : each letter represents only one color . b represents the people who take only art . d represents people who take only art and bio etc . d + f = 20 ( people who take art and one other class ) b = 3 e ( people who take only art is 3 times the people who take bio and calculus ) 17 + 10 + 9 + b + d + e + f = 100 ( total people ) b + b / 3 = 44 b = 33 number of freshmen who take art = 33 + 20 + 9 = 62 answer e
Answer: E