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students are not studying

by sanju09 » Fri Jun 18, 2010 1:31 am
Of the 80 students in class, 25 are studying German, 15 French and 13 Spanish. 3 are studying German and French; 4 are studying French and Spanish; 2 are studying German and Spanish; and none is studying all 3 languages at the same time. How many students are not studying any of the three languages?
(A) 18
(B) 27
(C) 36
(D) 53
(E) 62
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by amising6 » Fri Jun 18, 2010 2:23 am
click on the image see the reult in venn diagram Image
Last edited by amising6 on Fri Jun 18, 2010 2:41 am, edited 1 time in total.
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by gmatmachoman » Fri Jun 18, 2010 2:31 am
Total = P(AUBUC) + Neither ---- (eq 1)

P (AUBUC) = P(A) +P(B) + P(C) - P(AnB)-P(BnC)-P(AnC) + P(AnBnC)

=25+15+13-3-4-2+0
=44

So put in equation 1

80 = 44 + Neither of any languages

Neither of any languages = 36

Pick C
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