Logical Reasoning
Series, Analogy and Coding–Decoding
In a series, find the rule (difference, ratio, squares, alternation) and extend it. Analogy and classification ask which item shares — or breaks — a pattern. In coding–decoding, work out the letter or digit shift from the example and apply it.
Example 1: Next term: 2, 6, 12, 20, …?
Gaps 4, 6, 8 grow by 2, so the next gap is 10 → 30.
Example 2: If CAT → DBU, then DOG → ?
Each letter +1: EPH.
Quick recap
- Series: spot the rule and extend.
- Coding: find the shift from the example, then apply.
✓ Quick check
The wheel that travels farther in one revolution is the one with the larger:
Distance per revolution equals the circumference.
Adding a constant to every observation leaves unchanged the:
Shifting all data keeps the spread (range) the same while moving the averages.
Direction, Distance and Blood Relations
Direction problems track turns (left/right relative to facing); the straight-line distance from start to finish comes from Pythagoras. Blood relations are solved by sketching a family tree from the clues.
Example 1: 3 km east then 4 km north — distance from start?
√(9 + 16) = 5 km.
Example 2: A's mother is B's sister — B is A's?
Aunt.
Quick recap
- Sketch directions; straight-line gap via Pythagoras.
- Draw a family tree for blood relations.
✓ Quick check
If a quadratic polynomial has equal zeroes, its graph:
Equal zeroes mean the parabola just touches the x-axis at a single point.
The minute hand of a clock sweeps a full circle in:
The minute hand completes one revolution in 60 minutes.
Cubes, Calendars, Clocks and Data Sufficiency
For a standard die, opposite faces total 7; a painted cube cut into smaller cubes has predictable painted-face counts. Clock: the minute hand turns 6°/min, the hour hand 0.5°/min. Data sufficiency asks whether the given statements are enough to answer — not the answer itself.
Example 1: A die shows 2 on top — bottom face?
Opposite faces total 7, so 5.
Example 2: Angle between the hands at 3:00?
90°.
Quick recap
- Opposite die faces sum to 7; minute hand 6°/min, hour 0.5°/min.
- Data sufficiency judges whether the data is enough, not the value.
✓ Quick check
Which of these is always equal to 1?
sin²θ + cos²θ = 1 for every θ.
Sₙ − Sₙ₋₁ for an AP equals:
Removing the sum of the first (n − 1) terms leaves the nth term.
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