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 Post subject: Arithmetic QuestionPosted: Thu Aug 05, 2010 8:16 pm

Joined: Wed Aug 04, 2010 6:03 am
Posts: 2
A student of mine asked me this question yesterday. I am posting it here for everyone to try out.

At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japanese, do more students at the school study French or Japanese?

1) 16 students at the school study both French and Japanese.

2) 10 percent of the students at the schoool who study Japanese also study French.

Sol.

We know that at least 100 students study Japanese.
Number of students who study French and Japanese n(F and J) = 4% of F

Stmnt. 1: Given n(F and J) = 16. This implies that 4% of F = 16.
Therefore, F = 400 students. Number of students who study French = 400 but we do not know anything about the number of students who study Japanese. Hence statement 1 is not sufficient.

Stmnt. 2: Given 10% of J = n(F and J)
n(F and J) = 4% of F (Given in the question stem)
Hence 10% of J = 4% of F which implies that F must be greater than J.
If you are unsure of this, think of it this way: Lets say J = 100. Then 10% of J = 10. If 4% of F = 10, then F = 250.
Therefore statement 2 is sufficient.

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