In a group of 15, 7 have studied Latin, 8 have studied Greek, and 3 have not studied either. How many of these studied both Latin and Greek?A. 0B. 3C. 4D. 5

B

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Binoy111

  • Apr 22nd, 2009
 

Let A= Latin = 7
B = Greek = 8
Then, A + B = A (UNION) B + A (INTERSECTION) B
          7 + 8 = 15 - 3(3 NOT STUDIED) + ?
           15 = 12 + ?
            15- 12 = A (INTERSECTION) B
               3 = NO. OF STUDENTS WHO STUDIED BOTH

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raj

  • Apr 8th, 2012
 

L=7
G=8
Total number of students(U)=15
Number of students who study neither of them (N)=3
draw a simple diagram representing the above situation.
we need to find out L INTERSECTION G.
Thus we have,
L UNION G + N = 15
L UNION G = L + G - L INTERSECTION G = 7 + 8 - L INTERSECTION G
L INTERSECTION G= 7 + 8 +N-15
= 7+8+3-15
= 3

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Sudipto Sarkar

  • Sep 22nd, 2013
 

total students=15
no of students who dont study=3
no of students who either study Latin or Greek or both=15-3=12 i.e. n(AUB)
no of students who only study latin=7 i.e. n(A) say
no of students who only study greek=8 i.e. n(B) say
so, no of students who study both greek and latin say n(A^B)
applying n(A^B)=n(A)+n(B)-n(AUB)=7+8-12=15-12=3

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suman

  • Dec 17th, 2014
 

A

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anil Shinde

  • Dec 12th, 2015
 

3 is the answer

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Siva

  • Feb 3rd, 2016
 

Ans : 3

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