All of the letters in the word ‘FROWNED’ are arranged in alphabetical order. How many letters are there in the English alphabetical series between the letter which is fourth from the left end and the one which is second from the right end in the new letter- cluster thus formed?

Correct — C. Sort the letters of FROWNED before you count anything.

F, R, O, W, N, E, D in alphabetical order is D E F N O R W.

Fourth from the left end is N. Second from the right end is R, because W is first from the right.

Between N (14) and R (18) lie O, P and Q — three letters, option (c).

Why the others are wrong

• (a)
  Five — Five would need the two letters six places apart. N is 14 and R is 18, a gap of four, so at most three letters can stand between them.
• (b)
  Two — Two undercounts by one. The letters lying strictly between N and R are O, P and Q, and P is easy to lose when counting on the fingers.
• (d)
  Four — Four is the gap itself, R − N = 18 − 14 = 4. The number of letters in between is always one less than the gap.

Three separate steps sit inside one sentence, and each has to be finished before the next begins. Sort the word, locate the two named positions in the sorted cluster, then count the letters strictly between them.

The last step is where the arithmetic bites. Letters strictly between two letters number one less than the difference of their alphabet positions, so a gap of 4 gives 3.

Key facts

• FROWNED sorted alphabetically is DEFNORW, a seven-letter cluster.
• Second from the right end of DEFNORW is R, not W.
• N is the 14th letter and R the 18th, so exactly three letters lie between them.

Common traps

• Counting positions in the original word instead of in the sorted cluster.
• Reading second from the right end as the last letter.
• Answering with the gap of 4 rather than the count of 3.

No directly related past PYQ was found.