🧮 Aptitude & Reasoning · Chapter 9

Data interpretation: tables and charts under time

A DI set gives you five questions and eight minutes; the toppers finish early because they compute only what the options force them to.

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The basics

Data interpretation (DI) is answering questions from a table or chart — growth, shares, averages, ratios — fast, usually with options to choose from.

The problem it solves: in CAT, bank PO and placement papers, DI sets carry big marks but the arithmetic, done fully, takes longer than the time you have. The skill is reaching the right option without the full calculation.

The mental model: read the chart once for its units and base, then for every question ask "how far apart are the options?" Far apart → approximate hard. Close together → compute, or skip. Comparing two numbers → compare ratios by cross-multiplying instead of dividing.

Everything rests on the percentages chapter: growth is (new − old)/old, and share is part ÷ total.

Explained

"Which brand grew fastest from Q3 to Q4?" Alpha went 150 → 210. Delta went 72 → 108.

Don't divide. Half of 72 is 36, and 72 + 36 = 108: Delta grew exactly 50%. Half of 150 is 75, and 150 + 75 = 225 — Alpha's 210 falls short, so it grew less than 50%.

Delta, in five seconds, with no percentage computed. That's DI: the options tell you how precise you need to be, and usually it's not very.

Monday review at a Pune distributor

Every Monday, the area manager of a biscuit distributor in Pune gets a printout of branch sales (₹ lakh): Pune 40 → 44, Nashik 18 → 15, Kolhapur 12 → 13, Satara 9 → 10.

She doesn't pick up a calculator. In ten seconds she says: "Nashik is the only branch that fell — down a sixth. Everyone else is up about 10%. Call Nashik."

She didn't compute 8.3%, 11.1% or 10% to a decimal. She asked the only question the decision needed — who's different? — and answered it with the nearest friendly fraction.

That's the exam skill. The options are her decision: if they're far apart, a friendly fraction is enough.

The table we'll use

Units sold (thousands), 2025
            Q1    Q2    Q3    Q4   Total
Alpha      120   135   150   210    615
Beta        80    96   104   130    410
Gamma      150   140   168   175    633
Delta       60    75    72   108    315
Total      410   446   494   623   1973

Before any question: the unit is thousands of units, not rupees; the Total row and column are already given — use them, don't re-add. Q2's total (446) is the base for any 'share of Q2' question.

The approximation toolkit

1. Fractions you should see as percentages

1/3 = 33.3%   1/6 = 16.7%   1/7 = 14.3%   1/8 = 12.5%
1/9 = 11.1%   1/11 = 9.1%   1/12 = 8.3%   3/8 = 37.5%   5/8 = 62.5%

2. Compare without dividing. Is 15/45 bigger than 16/56? Cross-multiply: 15 × 56 = 840 vs 16 × 45 = 720 → the first. For "which grew most", compare new/old ratios the same way.

3. Benchmark against ½ or 1. If every fraction is just over ½, compare how far over: the excess over half.

4. Assumed mean. Gamma: 150, 140, 168, 175. Assume 150; deviations 0, −10, +18, +25 sum to 33; average = 150 + 33/4 = 158.25.

5. ×5 for 20%. Is 96 more than 20% of 446? 96 × 5 = 480 > 446 → yes.

When approximation fails: options within about 1–2% of each other, or "cannot be determined" among the options — then check whether the data even answers the question before computing anything.

Solving steps

Step 3 is where the time is won. Most candidates compute to two decimals for options 10 points apart.

A café chart, three questions, ninety seconds

Monthly revenue of a café chain (₹ lakh), Jan–Jun 2026:

 Jan  ██████████████           42
 Feb  ████████████████         48
 Mar  ███████████████          45
 Apr  ████████████████████     60
 May  ███████████████████      56
 Jun  ████████████████████████ 72

(30 s) Highest month-on-month % growth? Only April (+15 on 45) and June (+16 on 56) are serious. 15/45 = 1/3. 16/56 = 2/7, which is less than 1/3. April — even though June had the bigger rupee jump.

(20 s) Average monthly revenue, options 48 / 54 / 58 / 62? Assume 50: deviations −8, −2, −5, +10, +6, +22 sum to +23 → 50 + 23/6 ≈ 54.

(15 s) June vs January, options 41% / 58% / 71% / 85%? 72/42 = 12/7 ≈ 1.71 → +71%.

Two stores, one growth rate

A chain has two stores. The big one did ₹50 lakh last year and grew 10%. The small one did ₹10 lakh and grew 30%.

Traps examiners set

• Wrong base — "growth in Q4" means over Q3 unless it says "over Q1"
• Share vs size — a brand can sell more and still lose share if the total grew faster
• Absolute vs percentage — the biggest jump in rupees is often not the biggest % jump (June vs April above)
• Averaging percentages — combined growth needs raw totals, not the mean of rates
• Units — thousands vs lakh vs crore; a 'per cent' axis vs a value axis
• Percentage points — a share from 20% to 25% is 5 points, a 25% rise
• 'Cannot be determined' — sometimes it's right: a pie chart of shares alone can't give rupee growth without totals

Words to know

In two minutes

• Read units, periods and given totals before the first question; most errors are a wrong base, not wrong arithmetic.
• Growth is (new − old)/old; share is part ÷ total of the same period.
• Check the option spread first: far apart means approximate hard, close together means compute or skip.
• Compare fractions by cross-multiplying, or by their excess over a benchmark like ½.
• Use the fraction–percent table (1/7 = 14.3%, 1/8 = 12.5%, 1/12 = 8.3%) and the assumed-mean trick for averages.
• The biggest absolute jump is often not the biggest percentage jump; a growing item can still lose share.
• Combined growth comes from raw totals, never from averaging the individual percentages.

Test yourself

There are 10 questions, 3 puzzles and 5 recall cards for this lesson in the app — the recall cards come back on later days, just before you would forget.