DI — Pie Charts

Pie charts show parts of a whole as sectors of a circle. The whole = 100% = 360°, so every value is a share. CAT often pairs two pies (or a pie + table) so you must convert shares to absolutes using a given total. Part of the ~22-question DILR section.

The one identity to internalise

100% ↔ 360°, so 1% = 3.6° and 1° = (5/18)%. A sector's share = its angle ÷ 360. To get an absolute value: share × grand total.

Core conversions

Given	Find	How
Angle	Percentage	angle ÷ 3.6
Percentage	Angle	percentage × 3.6
Percentage + total	Absolute value	(% ÷ 100) × total
Two sectors	Ratio	share₁ : share₂ (angles or %)

Method

1. Confirm whether the pie is labelled in % or degrees (or raw values).
2. Fix the grand total — often given separately; without it you can only find shares, not absolutes.
3. For two pies with different totals, never compare percentages directly — convert both to absolutes first.
4. Use angle↔% (×3.6) freely to switch representations.

Exam Tricks & Tips

• 🎯 1% = 3.6°. Memorise it cold — half of all pie questions are just angle↔percentage conversions.
• 🎯 Percentages only compare within the SAME total. Two pies with different totals: 30% of one can be a smaller absolute than 20% of the other.
• 🎯 Absolute = share × total. You always need the grand total to move from % to a real number.
• 🎯 Quarter/eighth landmarks: 90° = 25%, 45° = 12.5%, 36° = 10%, 60° = 16.67% — read sectors against these anchors.
• 🎯 Ratio of two sectors = ratio of their angles (or %), no total needed.
• ❌ Common mistake: adding or comparing percentages across two pies with different bases as if they were the same currency — always convert to absolutes first.

Expected exam pattern

0–1 pie set, frequently a dual-pie or pie-plus-total combo, in DILR. Questions: sector value, angle↔%, ratio of sectors, and cross-pie absolute comparison. MCQ + TITA. The dual-total conversion is the classic difficulty spike.

Quick recap

Whole = 100% = 360°, so 1% = 3.6°. Convert freely, but to compare across two pies you must move to absolutes (share × each total). Never treat percentages from different totals as directly comparable.

Cover the answer, recall, then check. 12 cards on pie-chart DI.

Q1. What does a pie chart show?
A1. Parts of a whole — sectors summing to 100% (= 360°).

Q2. The key identity for pies?
A2. 100% ↔ 360°, so 1% = 3.6° (and 1° = 5/18 %).

Q3. Convert a 90° sector to a percentage.
A3. 90 ÷ 3.6 = 25%.

Q4. Convert 10% to an angle.
A4. 10 × 3.6 = 36°.

Q5. How do you get an absolute value from a sector?
A5. (share % ÷ 100) × grand total.

Q6. Can you compare percentages across two pies with different totals?
A6. No — convert both to absolutes first; 30% of one may be less than 20% of another.

Q7. Ratio of two sectors — what do you need?
A7. Just their angles or percentages; no total needed.

Q8. Landmark angles for 25%, 12.5%, 10%?
A8. 90°, 45°, 36° respectively (also 60° = 16.67%).

Q9. Without the grand total, what can you NOT find?
A9. Absolute values — only shares/ratios.

Q10. The classic dual-pie difficulty?
A10. Comparing sectors across two pies with different totals — must convert to absolutes.

Q11. First thing to check in a pie set?
A11. Whether sectors are labelled in %, degrees, or raw values.

Q12. Convert 60° to a percentage.
A12. 60 ÷ 3.6 = 16.67%.

Pie charts show parts of a whole — each slice is a percentage of 100%. Their trap is subtle: the pie only gives you proportions, so to get absolute values you need the total, and to compare two pies you must remember their totals may differ. Half of pie-chart DI is really about converting between percentages, degrees, and absolutes without slipping.

What this tests

Proportional reasoning — converting slices (as % or degrees) to values, combining a pie with a given total, and comparing across two pies with different bases.

The method

Beginner — the three currencies of a pie

Every slice can be expressed three ways, all interconvertible:

• Percentage — slice ÷ whole × 100.
• Degrees — percentage × 3.6 (since 100% = 360°, so 1% = 3.6°).
• Absolute value — percentage × total.

Know which the chart gives you (some label percentages, some degrees) and the conversion factor 3.6° per 1%.

Intermediate — you need the total for absolutes

A pie alone tells you shares, not amounts. "Slice A is 25%" means nothing in rupees until you know the total is, say, ₹800 crore → A = ₹200 crore. CAT often supplies the total separately (or in a caption). If comparing slices within one pie, percentages suffice; the moment you compare across two pies or ask "how many units", you must bring in totals.

Advanced — the FAST CAT approach: compare shares directly, convert only when forced

• Within one pie, "which is largest" or "A is what % more than B" needs only the percentages — no total, no absolute conversion.
• Across two pies, a bigger share does not mean a bigger amount: 20% of a ₹1000cr pie (₹200cr) beats 40% of a ₹400cr pie (₹160cr). Always multiply share × total before comparing across pies.
• For degree-labelled pies, convert to % once (÷3.6) and work in %.
• For "combined share" (two slices together), just add the percentages before touching the total.

Worked example

Pie A (total ₹1000 crore) and Pie B (total ₹600 crore) show expense splits. Salaries = 30% in Pie A, 45% in Pie B.
Question: Which company spends more on salaries?
Trap: 45% > 30%, so a hasty reader picks B. But convert to absolutes:

• A: 30% × 1000 = ₹300 crore.
• B: 45% × 600 = ₹270 crore.
  Company A spends more (₹300cr vs ₹270cr) despite the smaller percentage. Answer: A. The larger share (B) is not the larger amount — the different totals decide it.

CAT relevance

Pie-chart DI appears regularly, often paired with a table of totals or a second pie for "compare across companies/years" questions — precisely where the share-vs-absolute trap lives. Mastering the percentage↔degree↔value conversions makes these quick and reliable.

Speed tricks & shortcuts

• 1% = 3.6° — the only conversion you must memorise for degree-based pies.
• Within one pie: work in percentages (no total needed). Across pies: convert to absolutes (total required).
• Combined slices: add percentages first, then apply the total once.
• Mnemonic — "Share within, amount across."
• A larger slice on a smaller pie can be a smaller amount — always check totals when comparing pies.

Key formulas

• Central angle of a sector = (value/total)×360°; value = (angle/360)×total.
• Percentage share = (value/total)×100 = angle/3.6.
• Whole circle = 360° = 100% of the total.
• Compare sectors by their angles or percentages.
• Combine with a given total to get absolute values.

Usage: divide a sector's angle by 3.6 to get its percentage share.

Worked Example

Problem: A family's monthly budget of ₹60,000 is shown as a pie chart: Rent 30%, Food 25%, Transport 15%, Savings 20%, Other 10%.
(a) How much is spent on Food, in rupees? (b) What is the central ANGLE of the Rent sector? (c) If next month Savings rises to 25% while the total stays ₹60,000, and the extra comes entirely from "Other", is "Other" still positive?

Solution:
A pie chart shows parts of a whole; each slice's percentage × total = its value, and its central angle = percentage × 360°.

(a) Food = 25% of ₹60,000 = 0.25 × 60,000 = ₹15,000.

(b) Rent central angle = 30% of 360° = 0.30 × 360 = 108°.
(Cross-check: 360° corresponds to 100%, so 1% = 3.6°; 30 × 3.6 = 108°.)

(c) Savings rising from 20% to 25% is a +5 percentage-point change, i.e. an extra 5% of ₹60,000 = ₹3,000 more into savings. If this ₹3,000 comes entirely from "Other", then Other falls by 5 points: from 10% to 10% − 5% = 5%. In rupees, Other goes from ₹6,000 to ₹3,000. Since 5% > 0, "Other" is still positive (₹3,000). Had Savings needed +12 points instead, Other (only 10%) could not cover it — a useful feasibility check.
Note the standard trap: a "5% increase in savings" here means +5 percentage points of the pie, not a 5% relative increase of the savings amount. Read percentage-point vs percentage carefully.

Answer: (a) Food = 0.25 × 60,000 = ₹15,000. (b) Rent angle = 0.30 × 360° = 108°. (c) Yes — Other drops from 10% (₹6,000) to 5% (₹3,000), still positive, since Savings' +5-point rise is fully absorbed by Other.