A pie (circle) graph shows how a single total is divided into shares, so every slice is a percent of one whole and all slices sum to 100% (or, in angle terms, 360°). Two conversions unlock every pie question. To turn a slice into a real quantity, multiply its percent by the grand total: a 35% slice of $80,000 is 0.35 × 80,000 = $28,000. To move between a slice’s angle and its percent, use percent = (angle/360) × 100 — a 90° slice is a quarter, i.e. 25%. The most common GRE trap is comparing two different pies: a bigger slice of a smaller pie can represent fewer actual units than a smaller slice of a larger pie, because percentages are relative to different totals. Never compare slice sizes across two charts without first converting each to an absolute number using its own total.
✅ Solved examples
1. A household budget pie: Rent 40%, Food 25%, Transport 15%, Savings 20%. If total monthly income is $3,200, how much goes to Food?
Food = 25% of 3,200 = 0.25 × 3,200 = $800.
2. In the same budget, how many degrees does the Rent slice span?
Rent is 40%, so its angle = (40/100) × 360 = 144°.
3. A pie of 1,200 survey respondents shows "Prefer tea" as a 30% slice and "Prefer coffee" as a 45% slice. How many more chose coffee than tea?
4. Quantitative Comparison. Company X has 5,000 employees; 20% work in Sales. Company Y has 3,000 employees; 40% work in Sales. Quantity A: Sales staff at X. Quantity B: Sales staff at Y. Which is greater?
X: 0.20 × 5000 = 1000. Y: 0.40 × 3000 = 1200. 1000 < 1200, so Quantity B is greater — the smaller percent of the larger company still trails, illustrating why you must convert to absolute numbers.
✏️ Practice — try these, take hints as needed
1. A pie: Category A 50%, B 30%, C 20%, of a total of 600. How many units are in Category B?
Multiply the percent by the total.
0.30 × 600.
Compute the product.
180
2. A slice spans 72°. What percent of the whole is it?
percent = (angle/360) × 100.
72/360 = 1/5.
One-fifth as a percent.
20%
3. A budget pie has Savings at 15% of $4,000 monthly income. Annual savings?
Find monthly savings first.
0.15 × 4000 = 600.
Multiply by 12 months.
$7,200
4. A 25% slice equals 90 units. What is the grand total?
25% is one quarter.
90 is a quarter of the total.
Multiply by 4.
360
5. Pie X (total 2,000) shows Marketing at 10%. Pie Y (total 800) shows Marketing at 30%. Which has more Marketing staff?
Convert each to a real count.
X: 0.10 × 2000 = 200.
Y: 0.30 × 800 = 240.
Pie Y (240 vs 200)
📝 Topic test — 8 questions
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GRE reference
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