CAT 2003 Slot 2 — QA Question 8
Simple EquationsEasy
A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular 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 and
- 3 had all three options.
What is the number of cars that had none of the options?
Answer & solution
- A
4
- B
3
- C
1
2
Solution
Here, AC – Air Conditioning, R – Radio and PW – Power Windows
From the given conditions, we have the above Venn diagram.
When we add up all the values in the Venn diagram, we get 23 (15 + 5 + 1 + 2) cars.
∴ 2 (i.e. 25 − 23) cars don’t have any of the three options.
Hence, option (d).