Complete reference for HCS CSAT Paper II — Numerical Ability, Logical Reasoning & Data Interpretation
| Shape | Area | Perimeter / Volume |
|---|---|---|
| Square (side a) | a² | P = 4a |
| Rectangle (l×b) | l × b | P = 2(l+b) |
| Triangle (b, h) | ½ × b × h | Sum of sides |
| Circle (r) | πr² | C = 2πr |
| Cylinder (r, h) | 2πr(r+h) | V = πr²h |
| Cone (r, h, l) | πr(r+l) | V = ⅓πr²h |
| Sphere (r) | 4πr² | V = 4/3 πr³ |
| Cuboid (l,b,h) | 2(lb+bh+hl) | V = l×b×h |
| Type | Pattern | HCS Example |
|---|---|---|
| Arithmetic Series | Common difference (d) between terms | 2, 5, 8, 11, … (d=3) |
| Geometric Series | Common ratio (r) between terms | 3, 9, 27, 81, … (r=3) |
| Square Series | Terms are perfect squares | 1, 4, 9, 16, 25, … |
| Fibonacci | Each term = sum of previous two | 1, 1, 2, 3, 5, 8, 13, … |
| Prime Number | 2, 3, 5, 7, 11, 13, 17, … | Next prime after 17? |
| Difference Series | Differences form another pattern | Check 1st, 2nd order diff. |
| Mixed/Alternating | Two separate interleaved series | Odd/even positions separately |
| Relation | Symbol / Key |
|---|---|
| Brother of Father | Uncle (Paternal) |
| Sister of Father | Aunt (Paternal) |
| Son of Uncle | Cousin |
| Father's Father | Grandfather (Paternal) |
| Mother's Brother | Maternal Uncle |
| A is the only son of B | A and B are parent–child (no siblings) |
| Statement Type | Conclusion Rule |
|---|---|
| All A are B + All B are C | All A are C ✓ |
| All A are B + Some B are C | Some A are C ✗ (not definite) |
| No A is B + All C are A | No C is B ✓ |
| Some A are B + No B is C | Some A are not C ✓ |
| All A are B | Some B are A ✓ (reverse: some) |
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.500 | 50% |
| 1/3 | 0.333 | 33.33% |
| 2/3 | 0.667 | 66.67% |
| 1/4 | 0.250 | 25% |
| 3/4 | 0.750 | 75% |
| 1/5 | 0.200 | 20% |
| 2/5 | 0.400 | 40% |
| 3/5 | 0.600 | 60% |
| 4/5 | 0.800 | 80% |
| 1/6 | 0.167 | 16.67% |
| 1/7 | 0.143 | 14.29% |
| 1/8 | 0.125 | 12.5% |
| Question Type | What to Look For | Common Trap |
|---|---|---|
| Main Idea | Central theme of entire passage | Specific detail that's only part of passage |
| Author's Tone | Adjectives, adverbs, word choice | Mistaking neutral for critical |
| Inference | What's implied but not stated | Going too far beyond the passage |
| Vocabulary in Context | Surrounding sentences, not dictionary meaning | Using the literal/common meaning |
| "According to passage" | Direct statement in passage | Correct fact but not stated in passage |
| Purpose/Function | Why the author includes something | What it says vs. why it's there |
| Trick | Rule | Example |
|---|---|---|
| Multiply by 5 | Divide by 2, multiply by 10 | 48 × 5 = 480/2 = 240 |
| Multiply by 11 | Sum adjacent digits in middle | 72 × 11: 7_(7+2)_2 = 792 |
| Multiply by 25 | Divide by 4, multiply by 100 | 48 × 25 = 1200 |
| Square ending in 5 | (a5)² = a(a+1) followed by 25 | 75² = 7×8 = 56, so 5625 |
| % shortcut | x% of y = y% of x | 35% of 60 = 60% of 35 = 21 |
| Average of consecutive | Middle term = average | Avg of 3,4,5,6,7 = 5 |
| Fractions: which is larger? | Cross-multiply to compare | 3/7 vs 4/9: 27 vs 28 → 4/9 larger |
| Sum 1 to n (quick) | n(n+1)/2 | 1 to 50 = 50×51/2 = 1275 |
| Section | Questions | Ideal Time | Strategy |
|---|---|---|---|
| Reading Comprehension | ~15-20 | 25 min | Read questions first, answer directly from passage |
| Numerical Ability | ~15-20 | 25 min | Use approximation, skip difficult, come back |
| Logical Reasoning | ~15-20 | 20 min | Draw diagrams, don't do in head |
| Data Interpretation | ~8-12 | 20 min | Scan chart first, answer easy questions first |
| Decision Making | ~5-8 | 10 min | Use given guidelines only, not personal judgment |
| Buffer / Review | — | 20 min | Mark difficult, attempt last |