GATE2016 EC-2: GA-6

Question

The Venn diagram shows the preference of the student population for leisure activities.

From the data given, the number of students who like to read books or play sports is _______.

• A. $44$
• B. $51$
• C. $79$
• D. $108$

Comments

possible silly mistake that to not considering "or" in the given question .This might look like dumbest thing to do but actually that exam pressure makes us to do these type of mistakes like here choosing option B

Answer 1

The number of students who like to read books or play sports will be the sum of students who belong to both sets $\quad =13+12+44+7+17+15 = 108.$

Answer will be D

Answer 2

Read books = n(R) = 12 + 44 + 7 + 13 = 76

Play sports = n(s) = 44 + 7 + 17 +15 = 83

n (R $\bigcap_{}^{}$ S) = 44 + 7 = 51

n (R $\bigcup$ S) = n (R) + n (S) – n (R $\bigcap_{}^{}$ S) = 76 + 83 – 51 = 108

ANSWER : (d)

Answer 3

According to the given Venn diagram number of students who like to read books are.

13 + 12 + 44 + 7 = 76

Number of students who like to play sports are,

44 + 7 + 15 + 17 = 83

But the number of students who like both to read books and play sports are,

44 + 7 = 51

Hence the number of students who like to read books or play sports are,

76 + 83 – 51 = 108.

Here formula used is:

(No. of students Read books ⋃ no. of students play sports) ⋂ No of students read books or play sports