GMAT Quantitative: Profit, Revenue, and Cost Problems

Mastering financial word problems isn't just about passing the GMAT; it's about building the quantitative literacy required to make sound business decisions. These questions test your ability to translate real-world business scenarios—from pricing strategies to investment returns—into precise mathematical relationships. Success here requires fluency in core financial formulas and the strategic reasoning to avoid common conceptual traps.

Foundational Relationships: Cost, Revenue, and Profit

Every business transaction starts with these three pillars. Cost is the amount a business pays to acquire or produce a good. Revenue (or Sales) is the total money received from selling goods, calculated as Selling Price × Quantity Sold. Profit is what remains after costs are subtracted from revenue.

The fundamental equations are: $$\text{Profit}=\text{Revenue}-\text{Total Cost}$$ $$\text{Profit Percentage}=\left(\frac{\text{Profit}}{\text{Cost}}\right)\times 100\%\text{or}\left(\frac{\text{Profit}}{\text{Revenue}}\right)\times 100\%$$

Crucially, you must always note which base (cost or revenue) a profit percentage uses, as the GMAT will test this distinction. If a store buys a shirt for \$20 (cost) and sells it for \$30 (revenue), the profit is \$10. The profit on cost is (\10 / \$20) \times 100\% = 50\% $.Theprofiton\ast revenue\ast (oftencalled\ast \ast profitmargin\ast \ast )is$ (\$10 / \$30) \times 100\% \approx 33\% $.

Markup vs. Margin and Successive Discounts

Markup is the percentage increase added to the cost price to arrive at the selling price. Using the shirt example, a 50% markup on the \$20 cost gives a selling price of \20 \times (1 + 0.50) = \$30 $.

Margin (or profit margin), as defined above, is the percentage of profit relative to the selling price. Confusing these two is a major trap. Remember: Markup is on cost; margin is on revenue.

Discount problems follow a similar logic but in reverse. A price discounted by $d\%$ means you pay $(100-d)\%$ of the original price. For successive discounts, you cannot simply add the percentages. A 20% discount followed by a 10% discount on the new price is not a 30% total discount. Instead, you multiply the remaining percentages: $(1-0.20)\times (1-0.10)=0.80\times 0.90=0.72$. This means you pay 72% of the original, equivalent to a single discount of 28%.

Break-Even Analysis

The break-even point is where total revenue equals total costs, resulting in zero profit. This is a critical concept for evaluating a business's viability. Costs are often split into fixed costs (rent, salaries) that do not change with production volume and variable costs (materials) that do.

The break-even formula in terms of units is: $$\text{Break-Even Units}=\frac{\text{Fixed Costs}}{\text{Selling Price per Unit}-\text{Variable Cost per Unit}}$$ The denominator $(\text{Selling Price}-\text{Variable Cost})$ is the contribution margin per unit—the amount each sale contributes to covering fixed costs. For example, if fixed costs are \$10,000, you sell a product for \$50, and the variable cost is \$30, the contribution margin is \$20. You must sell \frac{\10,000}{\$20} = 500 $ units to break even.

Interest Calculations: Simple vs. Compound

Simple interest is calculated only on the principal amount. The formula is $I=P\times r\times t$, where $P$ is principal, $r$ is the annual interest rate, and $t$ is time in years. The total value $A$ is $A=P+I=P(1+rt)$.

Compound interest is calculated on the principal and accumulated interest from previous periods, making it more powerful over time. The standard formula is: $$A=P{\left(1+\frac{r}{n}\right)}^{nt}$$ where $n$ is the number of times interest is compounded per year. For annual compounding, $n=1$. A key GMAT shortcut is knowing that for compound interest, the total value grows by a factor of $(1+r{)}^t$ each year. If \$1,000 is invested at 10% compounded annually for 2 years, the value is \1,000 \times (1.10)^2 = \$1,000 \times 1.21 = \$1,210 $.

Installment Payments and Tax Calculations

Installment problems often involve loans repaid in equal monthly payments. A common GMAT setup is a simple interest loan where interest is applied to the principal, and payments first cover the interest, then the principal. You might be asked: "A \$12,000 car loan at 10% annual simple interest is repaid in 12 equal monthly installments. What is the approximate monthly payment?" First, calculate total interest: I = \12,000 \times 0.10 \times 1 = \$1,200 $.Totaltorepayis$ \$12,000 + \$1,200 = \$13,200 $.Monthlypaymentis$ \frac{\$13,200}{12} = \$1,100 $.

Tax-related problems typically involve adding a percentage-based sales tax to a price or calculating income tax in brackets. The key is the order of operations with discounts and taxes. Usually, discount (if any) is applied first to the merchandise, then tax is applied to the discounted price. For example, a \$100 item with a 20% discount and an 8% sales tax has a final price of \100 \times 0.80 = \$80 $,then$ \$80 \times 1.08 = \$86.40 $.

Common Pitfalls

1. Confusing Markup and Margin: As detailed, a 50% markup is not the same as a 50% margin. Always identify the base of the percentage. If the problem says "profit of 25%," check the context to see if it's on cost or sales.
2. Adding Successive Percent Changes: You cannot add percentages that act on different bases. A 50% increase followed by a 50% decrease does not return you to the original value. Always convert to multipliers: $1.50\times 0.50=0.75$, a 25% net loss.
3. Misapplying the Profit Formula: Ensure you're using the correct cost figure. In multi-step production or wholesale/retail chains, "cost" may refer to the seller's acquisition cost, not the original manufacturing cost. Read carefully.
4. Overcomplicating Break-Even: The core concept is simple: Revenue = Cost. Set up the equation clearly, separating fixed and variable components. Don't let wordy scenarios obscure this straightforward equality.

Summary

• The core triad is Profit = Revenue - Cost, with profit percentage defined relative to either cost (markup) or revenue (margin).
• Successive discounts require multiplying the remaining percentage factors (e.g., 0.80 * 0.90), not adding the discounts.
• Break-even analysis hinges on the formula: Fixed Costs / (Selling Price - Variable Cost per Unit). It’s the point where total contribution margin equals fixed costs.
• Simple interest is linear ($I=Prt$), while compound interest grows exponentially ($A=P(1+r/n{)}^{nt}$).
• For installments on a simple interest loan, calculate total interest over the full term first, add it to the principal, then divide by the number of payments.
• In problems with both discounts and taxes, the standard sequence is to apply the discount first, then apply the tax to the discounted price.