Problem Solving

Q1) A survey on a sample of 25 new cars being sold at a local dealer was conducted to see which of the three options - air conditioning, radio and power windows - were already installed. The survey found:
15 had air conditioning
2 had air conditioning and power windows but no radios
12 had radio
6 had air conditioning and radio but no power windows
11 had power windows
4 had radio and power windows
3 had all three options

What is the number of cars that had none of the options?

a) 4
b) 3
c) 1
d) 2
e) 0

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Q2) There are 200 students in a school. Out of these, 100 students play baseball, 50 students play hockey, and 60 students play basketball. 30 students play both baseball and hockey, 35 students play both hockey and basketball, and 45 students play both basketball and baseball.

1) What is the maximum number of students who play at least one game?
a) 90 b) 100 c) 110 d) 120 e) 130

2) What is the maximum number of students who play all the 3 games?
a) 15 b) 30 c) 20 d) 25 e) 10

3) What is the minimum number of students playing at least in one game?
a) 120 b) 85 c) 98 d) 106 e) 105

4) What is the minimum number of students playing all the 3 games?
a) 18 b) 19 c) 20 d) 23 e) 27