Number Series, Coding and Decoding, Odd Man Out for CA Foundation
Number series, letter and word coding, and odd-man-out questions: quick marks in the Logical Reasoning part of Paper 3.
Quantitative AptitudePaper 3, Logical Reasoning14 MCQs2 lessons2 flashcards3 memory tricks
Practise Number Series, Coding and Decoding, Odd Man Out free
What you'll learn
- Number and letter series
Spot the common patterns in number and letter series. - Coding–decoding and odd man out
Decode letter and number codes and find the odd item.
Key formulas
| Opposite letter | position of opposite = 27 − position |
|---|---|
| EJOTY | E = 5, J = 10, O = 15, T = 20, Y = 25 |
Concepts explained
Number series patterns
Most number series follow one of a few patterns: constant or growing differences, a constant ratio, squares and cubes, primes, Fibonacci, or two series alternating.
What it means
- Check differences first, then ratios.
- Learn squares to 30, cubes to 20 and primes to 100.
- n(n + 1): 2, 6, 12, 20, 30, 42. n² + 1: 2, 5, 10, 17, 26.
- Alternating series: split odd and even positions.
- 7, 10, 14, 19, 25: differences 3, 4, 5, 6
Answer: Next 32
- 3, 9, 27, 81: ×3
Answer: Next 243
Related terms
- Second differences: differences of the differences
- Mixed series: alternate operations such as ×2, +1
Exam tip: If differences don't settle in two rounds, try ratios or alternate terms.
Coding and decoding
A code applies one rule to every letter: a fixed shift, alphabet positions, reversal, or opposite letters.
What it means
- Shift: each letter moves forward or back by the same number (CAT → DBU).
- Positions: A = 1 … Z = 26; anchors E 5, J 10, O 15, T 20, Y 25.
- Reversal: PEN → NEP.
- Opposite letters: positions add to 27 (A↔Z, M↔N).
- TABLE → UBCMF (+1)
Answer: CHAIR → DIBJS
- APPLE → 1-16-16-12-5
Answer: BALL → 2-1-12-12
Related terms
- Mixed coding: different shifts for alternate letters
Exam tip: Test the rule on at least two letters before applying it.
Odd man out
Find the property shared by all but one item: prime/composite, even/odd, squares, a category of words, or letter patterns.
What it means
- Numbers: primes, squares, cubes, multiples, even/odd.
- Words: category (animals, fruits), wild/domestic, function.
- Letters: vowels, positions, symmetry.
- 3, 5, 7, 9, 11
Answer: 9 (not prime)
- Lion, Tiger, Leopard, Cow
Answer: Cow (domestic herbivore)
Related terms
- Classification: same skill under another name
Exam tip: If two different odd ones seem possible, choose the one based on the stronger, more obvious property.
Memory tricks
E = 5, J = 10, O = 15, T = 20, Y = 25.
Position of opposite letter = 27 − position.
Check differences, ratios, squares/cubes, primes and Fibonacci in that order.
Try 3 CA Foundation-style questions
Q1. If APPLE is coded as 1-16-16-12-5, then BALL is coded as
- 2-1-11-11
- 1-2-12-12
- 2-2-12-12
- 2-1-12-12
Show answer
Answer: (4) 2-1-12-12
Each letter is replaced by its position in the alphabet: B = 2, A = 1, L = 12.
Q2. Find the odd one out: 3, 5, 7, 9, 11
- 3
- 9
- 7
- 11
Show answer
Answer: (2) 9
All are prime except 9 (= 3 × 3).
Q3. Find the next number: 1, 1, 2, 3, 5, 8, ?
- 13
- 11
- 12
- 16
Show answer
Answer: (1) 13
Each term is the sum of the previous two (Fibonacci): 5 + 8 = 13.
Practise all 14 questions Free · explanations for every option · see where you go wrong