Logical Reasoning and Statistics: Data Interpretation and Probability
Domain 5, Logical Reasoning and Statistics, combines data interpretation with elementary probability and logical constraints. Expect tables, percentage changes, set-based counting, classical probability and simple conditional probability without replacement.
Core rules
- Percentage change = (new − old)/old × 100%; the base is the old value. Percentage points compare two percentages directly.
- For two events, P(A or B) = P(A) + P(B) − P(A and B). Subtract the overlap unless the events are mutually exclusive.
- For independent events, P(A and B) = P(A)×P(B). For sampling without replacement, update both numerator and denominator after each draw.
- In data interpretation, read the units and totals first; a “share” is part/total, not part/other part.
Worked example
In a class, 60% pass Mathematics, 50% pass Statistics and 30% pass both. The probability a randomly chosen student passes at least one subject is 0.60 + 0.50 − 0.30 = 0.80, or 80%. If a bag has 3 red and 2 blue balls and two are drawn without replacement, P(both red) = (3/5)×(2/4) = 6/20 = 0.30.
Traps
Do not add 60% and 50% without subtracting the 30% overlap. Do not treat “without replacement” draws as independent. In DI, a rise from 20% to 25% is 5 percentage points but a 25% relative increase. Check whether a table gives values in thousands or lakhs before computing.