CAT 1993 — QA Question 23
Geometric ProgressionEasy
Passage / Data
Use the following information:
Eighty five children went to an amusement park where they could ride on the merry – go round, roller coaster, and Ferris wheel. It was known that 20 of them took all three rides, and 55 of them took at least two of the three rides. Each ride cost Re.1, and the total receipt of the amusement park was Rs.145.
Let Un+1 = 2Un + 1 (n = 0, 1, 2, ...) and u0 = 0. Then u10 is nearest to
Answer & solution
1023
- B
2047
- C
4095
- D
8195
Solution
U0 = 0 = 20 – 1 = 0
U1 = 2 × 0 + 1 = 1 = 21 – 1
U2 = 2 × 1 + 1 = 3 = 22 – 1
U3 = 2 × 3 + 1 = 7 = 23 – 1 and so on.
⇒ Un = 2n - 1
∴ U10 = 210 – 1 = 1023.
Hence, option (a).