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CAT (Common Admission Test) · Data Interpretation & Logical Puzzles

Pie Charts

Interpreting proportions, angles and shares represented in circular charts.

A pie chart is a circle that stands for a total. Every CAT DI question on one is the same three moves: turn a sector into a percentage (or leave it as a fraction of 360), multiply by that pie's own total, and — when two pies appear — refuse to compare angles until both sides are absolute values.

  • CAT (Common Admission Test)
  • Easy level
  • 5 concepts
  • 17 practice questions

1Angle to percentage: 360° is 100%

The whole pie is a circle of 360°, and that circle is defined to be 100% of the quantity the chart is about. So each degree is 100/360 = 5/18 of a percent, and the useful shortcut is the other way round: 1\% = 3.6°. A sector of \theta degrees is (\theta/360)\times 100 percent of the total.

Convert the angle before you chase rupees or headcounts. Most wrong answers on pie questions start from treating the degree reading as if it were already a percentage — reading 72° as "about 72%" instead of 20%.

Figure. The pie is gone on purpose: the load-bearing claim is the ratio of central angles. Food's 72 deg bar is one-fifth of the 360 deg full-circle bar, so the sector is 20%.

How to convert

  1. Write the fraction of the circleSector angle over 360 — keep it as a fraction when it cancels cleanly (90/360 = 1/4).
  2. Turn the fraction into a percentMultiply by 100, or divide the angle by 3.6. Same number either route.
  3. Sanity-check against 3.6A 36° sector must be 10%; a 180° sector must be 50%. If your percent is near the degree reading, you skipped the conversion.

A 72° sector as a percent

In a pie chart of monthly expenditure, the Food sector measures 72°. What percentage of the total is spent on food?

  • Fraction of the circle = 72/3601/5
  • (1/5) × 10020%
  • Shortcut check: 72 ÷ 3.620
  • Food share of the pie20%

Pro tip. When the angle is a multiple of 18 or 36, the percent is a clean multiple of 5 or 10 — write the fraction of 360 first and the arithmetic usually collapses.

A sector measures 108°. As a percentage of the pie it is
  1. 108%
  2. 30%
  3. 36%

108/360 × 100 = 30%, or 108 ÷ 3.6 = 30. Reading the degree mark as the percent gives 108%; dividing by 3 instead of 3.6 gives 36%. Both are the "forgot the circle is 360" family of errors.

2From a sector to an absolute value

A percentage (or a fraction of the circle) is still only a share. The absolute value is that share multiplied by the pie's total: actual value = (\text{percentage}/100)\times\text{total}, or equivalently (\text{sector angle}/360)\times\text{total}.

You need the total — or one known absolute value that lets you recover it — before any sector becomes a rupee figure. The chart alone never hands you rupees; it hands you proportions of a total the question must supply.

Figure. A 90 deg sector is one-quarter of the rim, so Rent takes Rs 18,000 of the Rs 72,000 total. The remaining three-quarters stay as the Other segment.

How to read a sector

  1. Get the shareConvert the sector angle to a fraction of 360, or take the percentage as given.
  2. Name the totalFind the total this pie stands for — a stated sum, a previous year's figure, or a value recovered from one known sector.
  3. Multiply onceShare × total. Do not convert the same sector twice by different routes and average the answers.

Angle to actual value

In a pie chart of total expenditure Rs 72,000, the Rent sector measures 90°. What is the rent amount?

  • Fraction of the circle = 90/3601/4
  • As a percentage, (1/4) × 10025%
  • Rent = (1/4) × 72,000Rs 18,000
  • Rent amountRs 18,000

Pro tip. Turn the sector angle into a fraction of 360 first, then multiply by the total. The percent form (25%) is optional bookkeeping — the fraction already is the multiplier.

A pie of total Rs 85,000 has a Transport sector of 40%. Transport expenditure is
  1. Rs 34,000
  2. Rs 21,250
  3. Rs 40,000

0.40 × 85,000 = 34,000. Dividing by 4 instead of taking 40% gives 21,250; reading the percent as a thousands figure gives 40,000. The total is the only base the percentage may sit on.

3Combined categories: add, then convert once

When a question asks for two (or more) categories together — Food and Rent, or all non-salary heads — add their percentages, or add their sector angles, and convert the sum once. Combined share = sum of the individual percentages (or angles).

Adding the absolute values after separate conversions gives the same rupee total, but costs an extra multiply per sector. The trap is converting one sector, forgetting the other, or adding a percentage to an angle without translating units first.

Figure. Add the angles first (72 + 90 = 162), convert once (45%), then scale the total. Food and Rent together are the two highlighted segments summing to Rs 32,400.

How to group sectors

  1. Stay in one unitAdd angles to angles, or percents to percents — never 72° + 25%.
  2. Sum the sharesFood 72° + Rent 90° = 162°, or 20% + 25% = 45%.
  3. Convert the sum onceOne multiplication by the total finishes the combined absolute value.

Food and Rent together

In a pie chart of total expenditure Rs 72,000, Food is 72° and Rent is 90°. What is spent on Food and Rent combined?

  • Combined angle = 72° + 90°162°
  • Combined share = 162/3600.45 (= 45%)
  • Combined value = 0.45 × 72,000Rs 32,400
  • Food + RentRs 32,400

Pro tip. Check by the slow route: Food = 0.20 × 72,000 = 14,400 and Rent = 18,000, sum 32,400. If the two routes disagree, the angle sum or the total is wrong — not the method.

In a pie of total Rs 48,000, Food is 15% and Clothing is 25%. Food and Clothing together are
  1. Rs 7,200
  2. Rs 19,200
  3. Rs 12,000

15% + 25% = 40%, and 0.40 × 48,000 = 19,200. Taking only Food gives 7,200; taking only Clothing gives 12,000. The question asked for the combined share.

4One known absolute unlocks the pie

If the question withholds the total but gives one category in absolute units — "Rent is Rs 18,000 and is 90°" — that one sector recovers the total: total = absolute ÷ share. Every other sector then scales from the total you just found.

This is the same multiplication as reading a sector, run backwards. The mistake is to treat the known absolute as if it belonged to a different pie, or to divide by the angle in degrees instead of by the fraction of the circle.

Figure. Food's absolute and its 72 deg share unlock the whole pie: 14,400 / 0.20 = 72,000. Transport at 54 deg is then 15% of that total, Rs 10,800.

How to unlock

  1. Convert the known sector to a shareAngle over 360, or percent over 100 — a pure fraction.
  2. Divide to get the totalKnown absolute ÷ share. Rs 14,400 at 20% means the pie is Rs 72,000.
  3. Scale every other sectorEach remaining category is its own share times the total you recovered.

Total from Food, then Transport

In a pie chart, Food is Rs 14,400 and measures 72°. Transport measures 54°. Find the Transport amount.

  • Food share = 72/3600.20
  • Total = 14,400 ÷ 0.20Rs 72,000
  • Transport share = 54/3600.15
  • Transport = 0.15 × 72,000Rs 10,800

Pro tip. Find one absolute value first (here Food was given), recover the total, then scale the others by their percentages — the same order the tricks list gives for a stated total, just with an extra division at the front.

Marketing is Rs 30 crore and is 12% of a company's pie. The company's total is
  1. Rs 250 crore
  2. Rs 360 crore
  3. Rs 42 crore

Total = 30 ÷ 0.12 = 250 crore. Multiplying 30 × 12 gives 360; adding 12 to 30 gives 42. Division by the share is the only move that recovers a total from a part.

5Two pies: equal percentages are not equal values

When two pie charts have different totals, equal percentages do not mean equal absolute values. A smaller angle on a larger pie can exceed a larger angle on a smaller pie. Always multiply each percentage by its own total before comparing.

The common trap is comparing sector sizes across two pie charts by angle (or percent) alone. The eye reads "20% looks bigger than 15%" and stops; the arithmetic has to finish with rupees, tonnes, or headcounts on each side.

Figure. The two pies are gone on purpose: what remains is the comparison the question actually asks — absolute marketing spend. Y's bar is taller (60 cr) even though its sector percentage (15%) is smaller than X's (20%), because Y's total is twice X's.

How to compare two pies

  1. Name each pie's totalWrite the two totals down before reading either sector — they are different bases.
  2. Convert each sector to an absolutePercentage × its own total (or angle/360 × its own total).
  3. Compare the absolutesOnly after both sides are in the same unit may you say which is larger.

Comparing two pie charts

Company X (total Rs 200 cr) spends 20% on marketing; Company Y (total Rs 400 cr) spends 15% on marketing. Which spends more on marketing?

  • X marketing = 20% of 20040 cr
  • Y marketing = 15% of 40060 cr
  • Compare 40 cr vs 60 cr60 > 40
  • Larger marketing spendCompany Y (60 cr)

Pro tip. Never compare percentages across pies with different totals — convert each to an absolute value first. Here the smaller percentage sits on the doubled total and wins by 20 cr.

Pie A totals 120 and shows 25% on tax; pie B totals 180 and shows 20% on tax. Which tax bill is larger?
  1. Pie A (30)
  2. Pie B (36)
  3. They are equal

A: 0.25 × 120 = 30. B: 0.20 × 180 = 36. B is larger despite the smaller percentage. Calling them equal treats the percents as comparable without the totals; picking A trusts the larger percent alone.

Notes

  • Pie Chart - Angle to Percentage: The whole circle is 360 degrees representing 100%, so each 3.6 degrees equals 1%. Convert a sector's angle to a percentage before finding actual values.
  • Percentage to Value: Multiply a category's percentage by the total to get its absolute value; you need the given total (or one known value) to unlock all others.
  • Comparing Two Pies: When two pie charts have different totals, equal percentages do NOT mean equal absolute values; always multiply each percentage by its own total.
  • Combined Categories: To find the share of two categories together, add their percentages (or angles) and then convert once.
  • Common trap: Comparing sector sizes across two pie charts by angle alone when the underlying totals differ - a smaller angle on a larger pie can exceed a larger angle on a smaller pie.

Formulas

  • Percentage of a sector = \dfrac{\text{sector angle}}{360}\times 100.
  • Sector angle = \dfrac{\text{percentage}}{100}\times 360 degrees.
  • Actual value = \dfrac{\text{percentage}}{100}\times \text{total}.
  • 1% corresponds to 3.6 degrees on the circle.
  • Combined share = sum of the individual percentages (or angles).

Exam traps & shortcuts

  • Convert angles to percentages using the 3.6 degrees = 1% shortcut for quick reads.
  • Find one absolute value first (from a given total), then scale others by their percentages.
  • For two-pie comparisons, always multiply each percentage by its own total before comparing.
  • Add angles/percentages of grouped sectors before a single conversion to save steps.

Reference tables

Keep the total attached to its own pie. Every row assumes one circle = one total = 100% = 360°.

Pie-chart conversions
FromToRelation
Sector angle \thetaPercentage(\theta/360)\times 100; also \theta \div 3.6
Percentage pSector angle(p/100)\times 360; also p \times 3.6
Percentage p, total TAbsolute value(p/100)\times T
Angle \theta, total TAbsolute value(\theta/360)\times T
Absolute A, share sTotalT = A / s
Several sectorsCombined shareSum percentages (or angles), convert once

Recap

Read only this the night before a DI set with pies.

3.6°
360° = 100%, so 1% = 3.6°. Divide the sector angle by 3.6 (or by 360 and × 100) before you touch the total.
Share × total
Absolute value = (percentage/100) × total, or (angle/360) × total. No total means no rupee figure — recover it from one known absolute if needed.
Add, then convert
Grouped categories: sum their percentages or angles in one unit, multiply the sum by the total once.
Two pies
Different totals make equal percentages unequal in absolute value. Multiply each percent by its own total before comparing — a smaller angle on a larger pie can win.

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