All the alphabets in the word ‘CARDBOARD’ 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 cluster of nine letters?

Correct — A. Sort all nine letters of CARDBOARD, keeping every repeat:

A A B C D D O R R

Fourth from the left is C. Second from the right is R.

C is the 3rd letter of the alphabet and R the 18th.
Letters lying strictly between them = 18 - 3 - 1 = 14 -> option (a).

Why the others are wrong

• (b)
  16 — 16 is the inclusive count, C to R counting both ends. The stem asks how many letters lie between the two, so C and R themselves drop out.
• (c)
  12 — The two letters the stem fixes are C and R, and 14 letters sit between them. 12 would need the far letter to be P.
• (d)
  10 — 10 is what the six distinct letters A, B, C, D, O, R give - fourth from left D, second from right O. The sorted cluster keeps all nine letters, both As, both Ds and both Rs.

This item chains two small operations, and the marks are lost in the first one.

Step one is a sort of the whole word, repeats included. CARDBOARD holds nine letters, not six, so every position shifts if you quietly drop a duplicate.

Step two is a gap count in the alphabet, which is always higher position minus lower position minus one. Nothing about the word matters once the two letters are fixed.

Key facts

• CARDBOARD sorted alphabetically is A A B C D D O R R, nine letters.
• C is the 3rd letter of the English alphabet and R the 18th.
• Letters strictly between two letters = higher position - lower position - 1.

Common traps

• Dropping the repeated letters and sorting only the six distinct ones
• Counting the two endpoint letters themselves into the answer
• Reading fourth from the right instead of fourth from the left

No directly related past PYQ was found.