Hi there,

I'm using one of the Princeton review GMAT books and I don't understand one of its solutions for a plug-in problem solving problem. I'm getting a different answer and would like it if someone can explain to me the correct answer or justify that I am indeed correct.

The problem states: "Half the graduating class of a college was accepted by a business school. One-third of the class was accepted by a law school. If one-fifth of the class was accepted to both types of school, what fraction of the class was accepted only by a law school?

A. 1/60
B. 2/15
C. 1/3
D. 1/2
E. 4/5"

If you plug in 30 for the total class you get 15 who are accepted to biz school, 10 who are accepted to law school, and 6 who are accepted to both schools, which leave you with 4 who were accepted only to law school. So the fraction would be 4/30 or 2/15. The correct answer is B, which I get.

But the side note says to try solving the problem as if it were a ratio problem. But instead asks, "What is the ratio of students accepted to only biz school to those accepted to both?"

I got 15 minus 6 equals 9, those who were accepted to business school only. So 9:6 reduces to 3:2, option "C," but the book says that the correct ratio is 5:2 or in this case "B."

A. 5:3
B. 5:2
C. 3:2
D. 3:1
E. 2:1

My question is, is this a typo in the Princeton review book? If you use the same logic as they did in the original problem, the correct answer should be C and not B when you compare ratios because the question states "only to business school." I would understand "5:2" if it asked for the ratio of those accepted to business school to both schools. But it didn't. Am I missing something here? Or did Princeton goof up?