Problem Solving

Hi AAPL,

We're told that in a class of 200 students, 120 study Spanish and 100 study French and each student must study AT LEAST one of these two languages. We're asked for the percent of the students that study French but NOT Spanish. This question is a variation on a standard Overlapping Sets question, so we can use the Overlapping Sets Formula:

Total = (1st group) + (2nd group) - (Both) + (Neither)

200 = 120 + 100 - (Both) + (0)
200 = 220 - (Both)
Both = 20

Thus, those that study JUST French is 100 - 20 = 80 and the answer to the question is 80/200 = 8/20 = 4/10 = 40%

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

AAPL wrote:In a class of 200 students, 120 study Spanish and 100 study French. If a student must study at least one of these two languages, what percent of the students study French but NOT Spanish?

A. 80%
B. 40%
C. 30%
D. 20%
E. 10%

We can create the equation:

Total = Spanish + French - both + neither

200 = 120 + 100 - both + 0

both = 20

So the number who study French but not Spanish is 100 - 20 = 80.

So 80/200 = 40/100 = 40% of the students study French but not Spanish.

Answer: B