Reasoning: patterns, codes and relations
Reasoning / Mental Ability in PECE tests pattern recognition rather than memorised facts: series, analogies, coding–decoding, blood relations, direction sense, syllogism, clocks and calendars, seating and mirror images. Practise drawing small diagrams; most errors come from holding too much in your head.
Core rules
- Number series: check differences first, then ratios, then squares/cubes, then alternating patterns.
- Alphabet: A = 1 … Z = 26; reverse position = 27 − forward position; EJOTY (E = 5, J = 10, O = 15, T = 20, Y = 25) speeds up coding.
- Coding–decoding: write the alphabet above the word and mark the shift; check whether the shift is +1, −1 or alternating.
- Blood relations: use a tree with symbols for male/female and vertical links for generations; never assume gender from a name.
- Direction sense: fix north at the top, mark turns, and compute net displacement with Pythagoras if needed.
- Syllogism: draw Venn diagrams; ‘some’ does not imply ‘all’, and ‘no’ statements create disjoint sets.
Worked example
Find the next term: 2, 6, 12, 20, 30, ? Reasoning: differences are 4, 6, 8, 10 - an arithmetic progression increasing by 2. The next difference is 12, so the next term is 30 + 12 = 42. Equivalently, the terms are 1×2, 2×3, 3×4, 4×5, 5×6, so the next is 6×7 = 42.
Traps
Locking onto the first pattern you see; counting positions from 0 instead of 1; confusing left and right after a turn; treating ‘some A are B’ as ‘all A are B’; and ignoring the possibility of a two-step coding shift.