Find the missing term in the following alpha-numeric series : C – 24, H – 19, M – 14, ? , W – 4

Correct — B, (b) R – 9. Treat the letters and the numbers as two separate series running side by side; each moves by five, in opposite directions. THE LETTERS. Convert them to their positions in the alphabet: C = 3, H = 8, M = 13, ? , W = 23. The steps are 3 to 8, and 8 to 13 — plus five each time. The next term is 13 + 5 = 18, and the eighteenth letter is R. Check it against the last term: 18 + 5 = 23, which is W, exactly as printed. The letter is R. THE NUMBERS. 24, 19, 14, ? , 4. The steps are minus five each time, so the missing number is 14 − 5 = 9. Check against the last term: 9 − 5 = 4, as printed. The number is 9. The missing term is R – 9. Why checking against the LAST term matters. Two terms are given after the gap in most such series — here just one, W – 4 — and using it as a check catches a miscount in the alphabet immediately. A candidate who thinks the eighteenth letter is S will find that S plus five is X, not W, and will correct the count before committing. The alphabet positions worth having by heart, since almost every letter series depends on them: A 1, E 5, F 6, J 10, K 11, O 15, P 16, T 20, U 21, Y 25, Z 26. From those anchors any letter can be placed in a second or two — R, for instance, is one before S which is three after P, or more simply two before T at 20, so R is 18. A neat check specific to this series. Add each letter's alphabet position to the number beside it: C is 3 and 3 + 24 = 27; H is 8 and 8 + 19 = 27; M is 13 and 13 + 14 = 27; W is 23 and 23 + 4 = 27. The total is constant, because the letters climb by five as the numbers fall by five. The missing term must therefore also sum to 27, and R at 18 with 9 does exactly that — while S at 19 with 7 gives 26, S with 18 gives 37, and R with 17 gives 35. One addition disposes of all three wrong options.

Why the others are wrong

• (a)S – 7 — Both halves are wrong, and each by a familiar route. S is the nineteenth letter, which is what a candidate gets by miscounting the alphabet by one; and 7 does not fit a series falling by five, since 14 − 7 = 7 would need a step of seven. Test it against the printed final term: S plus five is X, not W, so the letter fails immediately.
• (c)S – 18 — Here 18 is the alphabet POSITION of the correct letter, which has been written into the number half of the term by mistake, while the letter half has slipped to S. It is the option for a candidate who has done the alphabet arithmetic correctly and then attached the results to the wrong halves of the pair. Each half of a term in an alpha-numeric series has its own rule and they must be kept apart.
• (d)R – 17 — The letter is right, so the harder half has been done correctly; the number is not. Seventeen does not sit in a sequence descending by five — from 14 the next term must be 9, and 17 is larger than the term before it, which reverses the direction the series has been running in. Having found the letter, check the number against BOTH neighbours: it must be five below 14 and five above 4.

In an alpha-numeric series each term pairs a letter with a number, and the two halves almost always follow independent rules. The standard method is to write the alphabet positions under the letters, look for a constant difference or a simple pattern in each of the two rows, and use any term printed AFTER the gap as a check. The dash inside a term is a joiner, not a minus sign. Common variations are letters advancing by a fixed step while numbers decrease, letters skipping in a pattern such as +1, +2, +3, numbers following squares or multiples, and letters that run backwards from Z. Where a series looks intractable, it is often because the two halves are being read as one relationship.

Key facts

• Alphabet positions: C = 3, H = 8, M = 13, R = 18, W = 23 — a step of five throughout.
• The number half runs 24, 19, 14, 9, 4 — a step of minus five throughout.
• The missing term is therefore R – 9.
• The dash within a term joins its two halves; it is not a minus sign.
• The two halves of an alpha-numeric term follow independent rules and must be worked separately.
• A term printed after the gap is the natural check on any proposed answer.
• Useful anchors for counting the alphabet: E 5, J 10, O 15, T 20, Y 25.
• R is two places before T, which fixes it at 18 without counting from A.

Common traps

• Miscounting the alphabet by one; anchor on E, J, O, T and Y instead of counting from A.
• Reading the joining dash as a minus sign.
• Applying one rule to both halves of the term.
• Not verifying the proposed term against the one printed after the gap.

No directly related past PYQ was found.

• practice — not a real PYQ

  Find the missing term in the series : B – 30, F – 26, J – 22, ? , R – 14

  • (a)M – 18
  • (b)N – 18
  • (c)N – 20
  • (d)M – 20

  Answer(b) N – 18