All the alphabets in the word ‘DICTIONARY’ are arranged in the alphabetical order. How many alphabets are there in the English alphabetical series between the alphabet which is fourth from the left end and the one which is second from the right end in the newly formed letter-cluster?

Correct — D. Sort the ten letters of DICTIONARY: A, C, D, I, I, N, O, R, T, Y. Both I's stay in.

Fourth from the left end is I — A, C, D, then I.
Second from the right end is T — the last two are T, Y.

I is the 9th letter and T is the 20th.
Letters lying strictly between them: 20 − 9 − 1 = 10, namely J K L M N O P Q R S → option (d).

Why the others are wrong

• (a)
  12 — 12 counts both endpoints. 20 − 9 + 1 includes I and T themselves, and the question asks only for what lies between them.
• (b)
  9 — 9 is one short. The run J to S holds ten letters, not nine.
• (c)
  11 — 11 keeps one endpoint in the tally. 20 − 9 is the gap between the positions, one more than the letters inside it.

Two mechanics, and candidates slip on both. First, alphabetising a word keeps every repeated letter — DICTIONARY has two I's and the sorted cluster is still ten letters long.

Second, counting between two letters is a strictly-between count. For positions m and n with n the larger, the answer is n − m − 1. Fix that formula rather than counting on your fingers under the clock.

Key facts

• Sorting DICTIONARY alphabetically gives A, C, D, I, I, N, O, R, T, Y, with both I's retained.
• I is the 9th letter of the alphabet and T is the 20th.
• The count of letters strictly between positions m and n is n − m − 1.

Common traps

• Dropping the repeated I and sorting only nine letters
• Taking Y as the second letter from the right instead of the first
• Answering with the position gap 20 − 9 rather than the letters inside it

No directly related past PYQ was found.