XAT 2016QA & DI Question 4

Venn DiagramEasy

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

Solution

Let the Venn diagram be as shown in the figure,

​​​​​​​

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).

XAT 2016 QA & DI Q4: In an amusement park along with the entry pass a visitor gets two of the three available rides (A, B and C) fr — Solution | TheCATExam