Select the option that can replace the question mark (?) in the following series. AH21, CJ18, EL15, GN12, ?

Correct — B. Rule: first letter +2, second letter +2, number −3.

First letters: A, C, E, G, so the next is I.
Second letters: H, J, L, N, so the next is P.
Numbers: 21, 18, 15, 12, so the next is 9.

The three strands together give IP9, option (b).

Why the others are wrong

• (a)
  HR11 — HR11 breaks all three strands at once: H is one step past G rather than two, R is four past N, and 11 is one less than 12 instead of three less.
• (c)
  J8 — J8 carries a single letter where every printed term carries two, so it cannot continue a two-letter series whatever its number does.
• (d)
  HQ10 — HQ10 moves the first letter forward one and the second forward three. This series moves both letters by exactly two.

A letter-plus-number term hides three independent series in one, and each has to be read down its own column.

Split AH21 into first letter, second letter and number, then read the column. Every column here is arithmetic: +2 on both letters, −3 on the number.

Knowing alphabet positions makes the letter columns as easy as the number one. A1 C3 E5 G7 is simply the odd positions in order, and H8 J10 L12 N14 the even positions from 8.

Key facts

• A=1, C=3, E=5, G=7, I=9 — the first letters are the odd alphabet positions in order.
• H=8, J=10, L=12, N=14, P=16 — the second letters are the even positions from 8.
• The number strand falls by 3 each term: 21, 18, 15, 12, 9.

Common traps

• Assuming the number moves in the same direction as the letters
• Reading a falling number strand as a ratio when it is a plain subtraction

No directly related past PYQ was found.