Each of the letters in the word FAMILY is arranged in alphabetical order. How many letters are there in the English alphabetical series between the letter that is second from the left and the one that is third from the right in the new letter-cluster formed?

Correct — D.
Rule: letters between = difference of positions − 1.

FAMILY in alphabetical order: A F I L M Y.
Second from the left: F(6).
Third from the right: Y, M, L(12).

Letters between F and L: G, H, I, J, K → 12 − 6 − 1 = 5 → option (d).

Why the others are wrong

• (a)
  Two — Two counts from the wrong end. The third letter from the left is I, and F to I has only G and H between them. The stem asks for the third from the right, L.
• (b)
  Four — Four leaves out one of G, H, I, J, K. Between F(6) and L(12) sit 12 − 6 − 1 = 5 letters.
• (c)
  Three — Three would fit letters four places apart, like F and J. The third letter from the right is L, two places beyond J.

Two separate counts are in play. First, positions inside the new cluster: second from the left and third from the right depend on the sorted word, A F I L M Y.

Second, the gap in the full alphabet between the two letters found: F(6) and L(12). Sort first; the unsorted FAMILY would hand you A and I instead.

Key facts

• In an n-letter cluster, the r-th letter from the right is the (n − r + 1)-th from the left: 6 − 3 + 1 = 4th, which is L.
• The number of letters strictly between positions p and q is q − p − 1.
• A = 1, F = 6, I = 9, L = 12, M = 13, Y = 25.

Common traps

• Counting the third letter from the left instead of the right, which gives Two
• Picking the letters from the unsorted word FAMILY

No directly related past PYQ was found.