## Venn Diagrams Test 1

Instructions

100 singers participated in a singing competition and were mentored by eminent music directors Rahman, Pritam and Vishal. A spectator had the following observations to make.

Statement 1: Three singers were mentored by all three music directors.

Statement 2: Forty Four singers were mentored by exactly two music directors.

Statement 3: Rahman mentored forty eight singers.

Statement 4: Vishal and Pritam, both mentored, seventeen singers.

Statement 5: The number of singers who were mentored by Vishal alone is five more than the number of singers who were mentored by Rahman alone.

Statement 6: The number of singers who were mentored by Vishal and Rahman is three more than the number of singers who were mentored by Vishal and Pritam

Q 1

What is the total number of singers who were mentored by Pritam?

Q 2

How many singers were coached by Vishal alone?

Q 3

What is the number of singers who were mentored by Rahman and Pritam and not by Vishal?

Instructions

For the following questions answer them individually

Q 4

In an ultimate team there are 7 players. 50 teams $$X_1$$,$$X_2$$ . . . $$X_{50}$$ take part in a tournament with every $$X_i$$ and $$X_{i+1}$$ having a common player for all i<50 (Only teams satisfying the given condition have player common). What is the total number of players playing in the tournament?

Q 5

There are certain number of footballs, volleyballs and tennis balls in a box. Of the different types of balls in the bag, $$\frac{1}{2}$$ are not footballs and $$\frac{2}{3}$$ are not volleyballs. Given that the difference between the number of footballs and tennis balls in the bag is 8 less than thrice the number of volleyballs. Find the number of tennis balls in the bag.