CLAT Quantitative Techniques — Cheat Sheet

Section anatomy

• 12 questions from 2 DI passages
• Topics: percentages, ratios, averages, profit-loss, simple interest, basic algebra, DI-based charts and tables
• Level: Class 8–9 mathematics

Formula recall

Percentages

• x% of y = xy/100
• % change = (new − old)/old × 100
• Successive % change: net = a + b + ab/100
• Increase by x% then decrease by x%: net = − x²/100 (always a loss)

Ratios & proportions

• a:b = c:d ⇒ ad = bc
• Compound ratio (a:b) & (c:d) → ac:bd
• Split N in ratio a:b → a·N/(a+b), b·N/(a+b)

Averages

• Avg = sum / count
• Weighted avg = Σ(wᵢxᵢ)/Σwᵢ
• Change on add/remove: new avg = (old sum ± value)/(count ± 1)

Profit-loss-discount

• Profit % = (SP − CP)/CP × 100
• Discount % = (MP − SP)/MP × 100
• MP after successive discounts d₁, d₂: SP = MP × (1 − d₁/100)(1 − d₂/100)

Simple interest

• SI = PRT/100
• Amount = P + SI

Compound interest (rare)

• A = P(1 + r/100)ⁿ
• CI − SI (2 yrs) = P(r/100)²

Time-speed-distance

• Speed = distance/time
• Average speed (equal dist): 2v₁v₂/(v₁+v₂)
• Relative speed same dir: v₁ − v₂; opp dir: v₁ + v₂

Time & work

• Together rate = 1/A + 1/B; time = AB/(A+B)

Algebra basics

• (a+b)² = a² + 2ab + b²
• (a−b)² = a² − 2ab + b²
• a² − b² = (a+b)(a−b)
• Quadratic roots: x = (−b ± √(b²−4ac))/(2a)

Geometry mini-set

• Rectangle area = l·w; perimeter = 2(l+w)
• Circle area = πr²; circumference = 2πr
• Triangle area = ½ base × height
• Pythagoras: a² + b² = c²

DI approach

Bar / pie / line chart

1. Read the axis labels, unit and total (if pie chart).
2. Note the ratio between the largest and smallest segments.
3. Answer direct-value questions first.
4. Use ratios for change/percent-change questions.
5. Skip questions requiring multi-step calculations beyond 60 seconds.

Table-based DI

1. Look for row and column totals.
2. Convert percentages to fractions (25% = 1/4, 12.5% = 1/8) to save time.
3. Use rough estimation (round 47 to 50, 96 to 100) before exact math.

Speed multipliers

• 50%, 25%, 10%: instant division/multiplication.
• Complement percentage: 87% ≈ (100 − 13)%; sometimes 13% is easier.
• Ratio comparison: cross multiply.

15-day plan

Days 1–5: One DI set per day + formula recall daily.

Days 6–10: Two DI sets per day. Track time per question.

Days 11–13: Timed sectional tests (12 min for 12 questions).

Days 14–15: Error log review only.

Common traps

• Reading axis unit wrong (thousand vs lakh).
• Percentage of vs percentage change.
• Forgetting that successive % changes are not additive.
• Confusing profit % on CP vs SP (CLAT uses CP unless stated).

Practice MCQs — Quantitative Techniques

Q1. A pie chart shows 25% education spend of ₹80 lakh budget. Education spend = A) ₹15 L B) ₹18 L C) ₹20 L D) ₹25 L

Q2. Ratio 3:5, sum 320. Larger part = A) 120 B) 180 C) 200 D) 220

Q3. CI on ₹10,000 at 10% p.a. for 2 years = A) ₹2000 B) ₹2100 C) ₹2200 D) ₹2500

Q4. If average of 5 numbers is 20 and one is removed to make average 18, removed = A) 24 B) 26 C) 28 D) 30

Q5. A train 120 m long crosses a pole in 6 s. Speed = A) 60 km/h B) 72 km/h C) 80 km/h D) 90 km/h

Answers: 1-C, 2-C, 3-B, 4-C (100−72=28), 5-B.

More Practice MCQs (Q6–Q10)

Q6. 15% of 240 = A) 32 B) 34 C) 36 D) 40

Q7. SP ₹450, loss 10%. CP = A) ₹495 B) ₹500 C) ₹405 D) ₹550

Q8. Simple interest on ₹5000 at 8% for 3 years: A) ₹1000 B) ₹1200 C) ₹1500 D) ₹1800

Q9. If a:b = 2:3, b:c = 4:5, then a:c = A) 8:15 B) 2:5 C) 3:5 D) 4:15

Q10. Bar chart: sales are 30, 45, 60, 75 in Q1–Q4. Average = A) 50 B) 52.5 C) 55 D) 60

Answers: 6-C, 7-B, 8-B, 9-A, 10-B.

MCQ Metadata — Difficulty & Topic Tags

Split: Easy 7 · Medium 3 · Hard 0