XAT 2016 — QA & DI Question 4
In an amusement park along with the entry pass a visitor gets two of the three available rides (A, B and C) free. On a particular day 77 opted for ride A, 55 opted for B and 50 opted for C; 25 visitors opted for both A and C, 22 opted for both A and B, while no visitor opted for both B and C. 40 visitors did not opt for ride A and B, or both. How many visited with the entry pass on that day?
Answer & solution
- A
102
- B
115
- C
130
- D
135
150
Let the Venn diagram be as shown in the figure,
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No one can take all three rides, hence g = 0.
22 people take rides A and B,
∴ d = 22
25 people take rides A and C,
∴ f = 25
50 people take ride C,
∴ c = 50 – 25 = 25.
40 people don’t take A or B or both,
∴ 40 = c + h
⇒ h = 40 – 25 = 15
∴ Total number of people visiting the park = (77 + 55 + 50 – 25 – 22) + 15 = 150.
Hence, option (e).