Logical Reasoning
Series, Analogy and Coding–Decoding
In a series, find the rule (difference, ratio, squares, alternation) and extend it. Analogy and classification test a shared 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
If p is true and q is false, then ¬(p ∨ q) is:
p ∨ q is true, so its negation is false.
If p: '5 is odd' and q: '8 is even', then p ∧ q is:
Both p and q are true, so p ∧ q is true.
Direction, Distance and Blood Relations
Direction problems track turns; the straight-line distance 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 or uncle.
Quick recap
- Straight-line gap via Pythagoras.
- Draw a family tree for blood relations.
✓ Quick check
The axis of x² = -16y is:
Parabolas of form x² = 4ay are symmetric about the y-axis.
If f(x) = 5x + 3 for x ≤ 1, and f(x) = 2x² + k for x > 1, find k so that lim(x→1) f(x) exists.
For the limit to exist, LHL = RHL at x = 1. LHL = 5(1) + 3 = 8. RHL = 2(1)² + k = 2 + k. Equating them: 2 + k = 8 → k = 6.
Cubes, Calendars, Clocks and Data Sufficiency
On a standard die opposite faces total 7. The clock minute hand turns 6°/min and the hour hand 0.5°/min. Data sufficiency asks whether the statements are enough — 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.
- Data sufficiency judges adequacy, not the value.
✓ Quick check
The line 5x − 5y + 10 = 0 is equivalent to:
Divide entire equation by 5.
Which measure is most affected by extreme values?
Mean uses every observation and is sensitive to outliers.
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