GMAT Quantitative Reasoning emphasizes practical business logic over mechanical formula substitution. Building on our foundation in percentage growth, this guided path covers the linear nature of Simple Interest, the compounding factor $(1 + r/100)^n$ across different compounding frequencies, markup-discount chains, and the essential Data Sufficiency traps tested on the GMAT.
Understand simple interest as a constant annual fee for using funds, and master the GMAT shortcut of multiplying Rate × Time directly into a single return percentage.
Interest is simply the payment made for the use of borrowed or deposited funds. When interest is Simple, it is calculated strictly on the original principal every single year.
Simple Interest ($SI$) depends on three key variables:
Assuming Principal P and Rate R remain unchanged, Simple Interest earned in each year is ALWAYS identical.
If total simple interest earned over $n$ years is $x$, then the interest in any single year is simply:
Example: If an account earns $600 in total SI over 3 years, it earned exactly $200 in Year 1, $200 in Year 2, and $200 in Year 3.
Advance from basic 'growth on growth' to the compounding formula A = P(1 + r/100)ⁿ, explore annual vs. semi-annual compounding cycles, and understand the Year-1 invariant.
As introduced in our Percents foundation, compounding means calculating growth on the new, enlarged base. In commercial mathematics, this transforms into repeated multiplication by a Compounding Factor.
Consider a population of 600,000 growing by 10% each year:
Year 1: $600{,}000 \times 1.10 = 660{,}000$
Year 2: $660{,}000 \times 1.10 = 600{,}000 \times 1.10 \times 1.10 = 726{,}000$
Year 3: $600{,}000 \times 1.10 \times 1.10 \times 1.10 = 600{,}000 \times (1.10)^3$
For $n$ years, the value is simply $600{,}000 \times (1.10)^n$.
If an initial value P grows at r% per year for n years:
The factor $\mathbf{(1 + r/100)}$ is the Compounding Multiplier.
Why does Compound Interest exceed Simple Interest?
In Year 1: $SI_1 = CI_1$ (both calculate interest strictly on original principal $P$).
In Year 2: CI adds Year 1 interest to the principal, so Year 2 earns interest on interest.
For the first annual cycle, SI and CI are identical. Divergence begins strictly in cycle 2.
Master the fundamental price anchors: why Profit % is ALWAYS based on Cost Price, while Discount % is ALWAYS calculated on Marked Price, and chain multipliers in seconds.
Commercial word problems on the GMAT involve three primary price points: Cost Price, Marked Price, and Selling Price.
Percent Profit or Loss is ALWAYS calculated on Cost Price (CP) as the denominator, NEVER on Selling Price.
$$ \text{Percent Profit} = \frac{\text{Actual Profit}}{CP} \times 100\% $$
$$ \text{Percent Loss} = \frac{\text{Actual Loss}}{CP} \times 100\% $$
Mark-up Price (MP): Also called the listed price, sticker price, or showroom price.
Percentage Discount is ALWAYS calculated on the Mark-up Price (MP), NEVER on the Cost Price.
$$ \text{Discount Amount} = \text{Discount Rate} \times MP $$
$$ SP = MP - \text{Discount Amount} $$
Deconstruct why consecutive discounts of 25% and 10% do NOT equal 35%, and learn how to multiply remaining percentages to calculate final selling prices effortlessly.
When successive discounts are offered, each subsequent discount is applied strictly to the discounted price so far, never to the initial price.
The mark-up price of an item is $600.
Two successive discounts of 25% and 10% are offered.
What is the final selling price?
Calculate 25% of $600:
Price after 1st discount:
Calculate 10% on the NEW price of $450 (NOT on $600!):
Final Selling Price:
Final Selling Price = $405
Learn how to evaluate Data Sufficiency statements involving profit margins and interest comparisons without calculating actual dollar amounts.
In GMAT Data Sufficiency, questions frequently ask for a percent profit or rate. Recognizing whether a statement provides an absolute dollar amount or a dimensionless ratio is the key to sub-60-second solutions.
What was the percent profit on the sale of a vintage wristwatch?
(1) The selling price was $60 greater than the cost price.
(2) The selling price was 120% of the cost price.
Statement (1) tells us: $\text{Profit} = SP - CP = 60$ (a profit of $60).
Can we find percent profit?
Since we don't know the Cost Price CP, the percent profit could be 60% (if CP = $100) or 6% (if CP = $1,000). Statement (1) is NOT sufficient.
Statement (2) tells us: $SP = 1.20 \times CP$.
The unknown Cost Price cancels out completely! Statement (2) ALONE is sufficient.
A dedicated question set for Interest, Profit & Discount is currently being authored. In the meantime, test your baseline score on the full Diagnostic:
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