CAT 2003 Slot 1 — QA Question 28
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
The 288th term of the series a, b, b, c, c, c, d, d, d, d, e, e, e, e, e, f, f, f, f, f, f... is
Answer & solution
- A
u
- B
v
- C
w
x
In the series a, b, b, c, c, c, d, d, d, d, e, e, e, e, e,...
the first letter of the alphabet is written once, the second is written twice, and the nth letter is written n times.
∴ The number of letters written upto the nth letter is equal to the sum of the first n natural numbers given by, n(n + 1)/2
For n = 23, n(n + 1)/2 = 276 and for n = 24, n(n + 1)/2 = 300
This means the series contains 276 letters in all for the letter corresponding to n = 23 and 300 letters in all for the letter corresponding to n = 24.
∴ The letter corresponding to n = 24 will be the letter occupying the 277th to the 300th place in the series.
But, n = 24 corresponds to letter x.
∴ The 288th letter in the series is x.
Hence, option (d).