Percentages • Topic 5 of 5

Percent Applications

Most GRE percent questions are applications wearing a costume: profit and discount, simple and compound interest, growth and depreciation, mixtures and concentrations, and Data Interpretation. Three reliable moves cover almost all of them. (1) Turn every percent into a multiplier and chain them: a $200 item marked up 50% then discounted 20% sells for 200 × 1.5 × 0.8 = $240. (2) For interest, simple interest adds the same amount each period while compound interest multiplies — over 2 years at r%, compound exceeds simple by exactly the cross term (r²/100 % of the principal). (3) For "percent of a total" in Data Interpretation, always anchor to the correct whole — a common trap gives a percent of one category when the question wants a percent of the grand total. Read the base carefully; the arithmetic is easy, the base is where points are lost.

✅ Solved examples

1. An item costing $80 is marked up 25%, then sold at a 10% discount. Selling price?
80 × 1.25 × 0.90 = 80 × 1.125 = $90.
2. $1,000 at 10% simple interest for 2 years earns how much interest?
SI = 1000 × 10% × 2 = $200.
3. $1,000 at 10% compounded annually for 2 years — total interest?
1000 × 1.1² = 1210 ⇒ interest = $210 (the extra $10 is the r²/100 cross term).
4. In a class, 60% are women; 25% of the women study physics. What percent of the class are women studying physics?
60% × 25% = 0.60 × 0.25 = 15%.

✏️ Practice — try these, take hints as needed

1. A $150 item is discounted 20%, then 5% tax is added. Final price?
× 0.8 then × 1.05.
150 × 0.8 = 120.
120 × 1.05.
$126
2. Simple interest on $500 at 8% for 3 years?
P × r × t.
500 × 0.08 × 3.
= 120.
$120
3. $2,000 compounded annually at 10% for 2 years — final amount?
× 1.1².
2000 × 1.21.
= 2420.
$2,420
4. A shirt marked up 40% is sold at a 30% discount. Overall profit/loss %?
× 1.4 × 0.7.
= 0.98.
Net multiplier < 1.
2% loss
5. 30% of a survey chose tea; of those, 40% also chose biscuits. Percent choosing both?
0.30 × 0.40.
Multiply the fractions.
= 0.12.
12%

📝 Topic test — 8 questions

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