Numerical Ability & Data Interpretation

General Aptitude is a fixed 15 marks (10 questions) in every GATE paper — the highest-weight single section, and pure scoring if practised. Numerical ability and data interpretation are its quantitative half.

Core numerical topics

GATE numerical ability spans: ratio & proportion, percentages, profit/loss, simple & compound interest, time-speed-distance, time & work, averages, mixtures/alligation, permutations & combinations, probability, and number systems. Most are single-step or two-step; speed and accuracy matter more than depth.

High-yield formulas:

• Percentage change and successive change a + b + ab/100.
• Speed = distance/time; average speed (equal distances) = 2v₁v₂/(v₁+v₂).
• CI amount = P(1 + r/100)ⁿ; SI = PRT/100.
• Work rate: if A does a job in x days, rate = 1/x; combined rate adds.

Data interpretation

Extract answers from tables, bar/line/pie charts, and caselets. Skills: read the correct row/column, compute percentage change/share, ratio comparisons, and averages. Pie chart: each 1% = 3.6°.

Exam Tricks & Tips

• 🎯 Successive percentage change = a + b + ab/100 — turns two-step problems into one line (e.g. +20% then −10% = +8%).
• 🎯 Average speed for equal distances = 2v₁v₂/(v₁+v₂) (harmonic mean) — NOT the arithmetic mean.
• 🎯 Fraction ⇄ percentage table (1/8 = 12.5%, 1/6 = 16.67%…) speeds DI share/percentage work enormously.
• 🎯 In DI, read the question before the data — compute only what's asked; approximate when options are far apart.
• 🎯 Pie chart: 1% = 3.6°; convert between angle and share instantly.
• ❌ Common mistake: averaging two speeds arithmetically for a round trip — use the harmonic mean 2v₁v₂/(v₁+v₂), since equal distances (not equal times) are covered.

Expected exam pattern

Roughly 2–3 of the 10 GA questions are quantitative (one 1-mark, one 2-mark typical), often a data-interpretation set or a percentage/TSD/work word problem. Speed-solving with the fraction–percentage table is the key skill.

Quick recap

GATE numerical ability: percentages, ratio, interest, TSD, time-work, averages, P&C, probability, number systems. Successive % = a+b+ab/100; average speed (equal distance) = 2v₁v₂/(v₁+v₂); CI = P(1+r/100)ⁿ. DI: read charts/tables, 1% = 3.6° on a pie. Approximate when options are spread.

Cover the answer, recall, then check. 11 cards on GATE numerical aptitude.

Q1. Formula for successive percentage change of a% then b%?
A1. Net = a + b + ab/100. E.g. +20% then −10% gives 20 − 10 − 2 = +8%.

Q2. Average speed for a round trip over equal distances at v₁ and v₂?
A2. 2v₁v₂/(v₁ + v₂) — the harmonic mean, not the arithmetic mean.

Q3. Compound interest amount formula.
A3. A = P(1 + r/100)ⁿ; compound interest = A − P.

Q4. Simple interest formula.
A4. SI = P·R·T/100 (principal × rate × time).

Q5. If A finishes a job in x days and B in y days, combined time?
A5. xy/(x + y) days (rates 1/x + 1/y add).

Q6. In a pie chart, how many degrees is 1%?
A6. 3.6° (since 100% = 360°).

Q7. Express 1/8, 1/6, and 1/3 as percentages.
A7. 1/8 = 12.5%, 1/6 = 16.67%, 1/3 = 33.33%.

Q8. Alligation rule for mixing two ingredients?
A8. (Quantity of cheaper)/(Quantity of dearer) = (dearer price − mean)/(mean − cheaper price).

Q9. Profit percentage formula.
A9. Profit% = (Selling price − Cost price)/Cost price × 100.

Q10. Fastest DI strategy when options are far apart?
A10. Approximate/round the numbers and compute only the quantity asked — precision beyond the option gap wastes time.

Q11. A quantity increases 25% then decreases 20%. Net change?
A11. 25 − 20 − 5 = 0% (using a + b + ab/100 with a = 25, b = −20).

General Aptitude carries 15 marks in every GATE paper — the highest-return-per-effort section. Numerical ability and data interpretation reward speed and clean arithmetic, so a systematic toolkit here directly lifts your score with far less study than the technical subjects.

Core concept: most GATE numerical-ability questions reduce to ratios, percentages, averages, and rates; data interpretation is the same arithmetic applied to a table, bar chart or pie chart under time pressure.

Deep explanation

Beginner — the core toolkit

• Percentages: x% of y = xy/100; percentage change = (new − old)/old × 100. A rise of a% then fall of a% gives a net fall of (a²/100)%.
• Ratio & proportion: if a:b = 3:5, treat as 3k and 5k. Direct proportion (both rise) vs inverse (one rises, other falls).
• Averages: average = sum/count; a new item shifts the average by (item − old average)/(new count).

Intermediate — rates and mixtures

• Speed–time–distance: distance = speed × time; average speed for equal distances = harmonic mean = 2v₁v₂/(v₁+v₂), NOT the arithmetic mean.
• Work & time: if A does a job in a days, rate = 1/a per day; combined rate = 1/a + 1/b.
• Mixtures/alligation: ratio of quantities = (mean − cheaper)/(dearer − mean) — a fast lever for weighted averages and dilution.
• Simple vs compound interest: SI = PnR/100; CI amount = P(1 + R/100)ⁿ.

Advanced — data interpretation strategy

• Read the question before the chart — you often need only one number, not the whole table.
• Pie charts: value = (sector angle/360) × total, or (percentage) × total.
• Approximate: round to convenient numbers, compare fractions rather than computing exact decimals.
• Watch units and the axis scale (thousands, %, log). Percentage-of-percentage and growth-rate traps are common.

Worked example

A car covers the first half of a distance at 40 km/h and the second half at 60 km/h. Find the average speed.
Equal distances → average speed = harmonic mean = 2v₁v₂/(v₁ + v₂) = 2(40)(60)/(40 + 60) = 4800/100 = 48 km/h. (Not 50, the arithmetic mean — the car spends more time at the slower speed.)

GATE relevance

Numerical ability and DI are guaranteed in the 15-mark General Aptitude section common to all GATE papers. These are high-yield, low-preparation marks: mastering percentages, ratios, rates and quick chart reading directly raises the aptitude score every candidate must attempt.

Exam tricks & shortcuts

• Equal-distance average speed = harmonic mean 2v₁v₂/(v₁+v₂), never the simple average.
• Successive +a% then −a% → net −(a²/100)% (always a loss).
• Use alligation for mixtures and weighted-average questions — much faster than algebra.
• Mnemonic: "Read the question, then the chart — not the other way round."

Key formulas

• Percentage: x% of N = xN/100; % change = (new − old)/old × 100.
• Average: sum/count; average speed = total distance/total time.
• Ratio & proportion: a:b = c:d ⇒ ad = bc.
• Simple/compound interest: SI = PRT/100; A = P(1 + R/100)ᵀ.
• Mensuration: circle πr², triangle ½bh, cylinder πr²h, sphere (4/3)πr³.
• DI: pie sector = (value/total) × 360°.

Quantitative aptitude relies on percentage, ratio, interest, average and mensuration formulas applied to word/DI problems.

Worked Example

Problem: A shopkeeper marks a product 40% above its cost price and then offers a 10% discount on the marked price. If the cost price is ₹500, find the selling price and the overall profit percentage.

Solution:
Step 1 — Marked price (40% above cost):
MP = 500 × (1 + 0.40) = 500 × 1.40 = ₹700.

Step 2 — Selling price after a 10% discount on the marked price:
SP = MP × (1 − 0.10) = 700 × 0.90 = ₹630.

Step 3 — Profit and profit percentage (always on cost price):
Profit = SP − CP = 630 − 500 = ₹130.
Profit % = (Profit/CP) × 100 = (130/500) × 100 = 26%.

Note: the markup (40%) and discount (10%) do not simply subtract, because they act on different bases (cost vs. marked price).

Answer: Selling price = ₹630 and profit = 26%.