CAT 2003 Slot 1 — QA Question 46
Geometric ProgressionEasy
In a certain examination paper, there are n questions. For j = 1, 2, ..., n, there are 2(n − j) students who answered j or more questions wrongly. If the total number of wrong answers is 4095, then the value of n is
Answer & solution
Correct answer: 12
12
- B
11
- C
10
- D
9
Solution
For j = n, 2(n - n) = 1 student has answered wrongly
j = n - 1, 2[n - (n - 1)] = 2 students have answered wrongly
.
.
j = 1, 2(n - 1) students have answered wrongly
∴ 1 + 2 + ... + 2(n – 1) = 4095
The series is in G.P. with common ratio r = 2
∴ 1 × (2n − 1)/(2 − 1) = 4095
∴ 2n − 1 = 4095
∴ 2n = 4096
∴ n = 12
Hence, option (a).