Analytical Ability - Problem Solving: Series, Codes, Relations, Arrangements, Logic and Counting
Series and codes
Number series favour constant or increasing differences, ratios, alternating operations, squares or cubes with a small offset, and two interleaved series. Letter series work on position numbers (A = 1 … Z = 26) and reverse pairs (A with Z sums to 27). Coding–decoding uses a fixed shift, reversal, position sums or symbol substitution; verify the rule on every letter of the sample word before applying it to the target.
Relations and arrangements
For blood relations, draw a tree with a consistent notation (vertical = generation, horizontal = sibling or spouse) and mark gender only where the question needs it. In seating, fix one anchor, then branch; for circular arrangements facing the centre, left is anticlockwise, and it flips when people face outward.
Logic and counting
Syllogisms need Venn diagrams: 'All A are B' does not give 'All B are A'; 'Some A are B' converts to 'Some B are A'; 'No A is B' converts both ways. Clock angle = |30H − 5.5M|, reduced to the smaller angle. Calendar odd days: an ordinary year has 1, a leap year 2. A cube cut into n³ unit cubes has 8 with three painted faces, 12(n − 2) with two, 6(n − 2)² with one, and (n − 2)³ with none.
Worked example
Angle between the hands at 3:40 is |30 × 3 − 5.5 × 40| = |90 − 220| = 130°. Since 130° is not more than 180°, the answer stays 130°.
Traps
- Assuming 'some' reverses in syllogism conclusions.
- Mixing facing directions in circular seating.
- Forgetting that a clock angle above 180° must be subtracted from 360°.
- Applying a coding rule without checking every letter of the sample.