Problem Solving

In a school, 10 students are taking math class and 6 are taking literature class. 4 students are taking both classes. How many students are taking either math or literature classes?

A. 8
B. 10
C. 12
D. 14
E. 16

C. Like for me it is a very simple, but why the answer is C. May be I have problems with language, but could you show me where in the question the word BOTH CLASSES. Thanks a lot.

This can be done by simple set rules
Let M is the set of students taking Math class
L is the set of students taking literature

so we have to find out n(M U L)
n(M) = 10
n (L) = 6
n( M ∩ L )= 4
n(M U L )= n(M) + n(L) - n(M ∩ L)
= 10 + 6 - 4
= 12

lenagmat wrote: Like for me it is a very simple, but why the answer is C. May be I have problems with language, but could you show me where in the question the word BOTH CLASSES. Thanks a lot.

I think either math or literature means people who took only math or only literature, NOT BOTH.

If thats the case, Math only = 10-4 = 6
Literature only = 6-4 = 2

So, either Math or Literature = 6+2 = 8

Native spekers, please, help.

"Either math or literature" includes the people who are taking both classes. Mathematically, an "or" statement is true if at least one of the statements is true.

And the answer is 8 or 12?

GmatMathPro wrote:"Either math or literature" includes the people who are taking both classes. Mathematically, an "or" statement is true if at least one of the statements is true.

12.

10 people are taking the math class. This includes 6 people who are taking ONLY the math class and 4 people who are taking both class. 6 people are taking the literature class. This includes 2 people who are taking ONLY literature, and 4 people who are taking both.

10+6=16, but that counts the people who are taking both twice. We only want to count them once, so subtract 4 to get 12.

OR

ONLY Math=6
ONLY Lit=2
BOTH=4

6+2+4=12