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How many students are taking either math or literature class

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How many students are taking either math or literature class

by lenagmat » Fri Oct 28, 2011 2:31 am
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.
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by Amiable Scholar » Fri Oct 28, 2011 3:02 am
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
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by shankar.ashwin » Fri Oct 28, 2011 9:44 pm
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
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by lenagmat » Sat Oct 29, 2011 8:36 am
Native spekers, please, help.
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by GmatMathPro » Sat Oct 29, 2011 8:51 am
"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.
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by lenagmat » Sat Oct 29, 2011 9:47 am
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.
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by GmatMathPro » Sat Oct 29, 2011 9:55 am
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
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