QUANTITATIVE REASONING · GMAT-Q-AR-01

Successive Percentage Changes

One skill · Separate practice and exam questions · Linked analysis

Original training content. Unofficial prototype; not an official GMAT mock examination.

SKILL GMAT-Q-AR-01

Discover the concept

A 20% increase followed by a 20% decrease does not restore the original value, because the second percentage is calculated from a different base.

1 · Why successive changes are multiplicative

Final = Initial \times (1 + r_{1}) (1 + r_{2})

2 · Choose the correct multiplier

Increase by p % : 1 + \frac{p}{100} Decrease by p % : 1 - \frac{p}{100}

3 · Worked example: unequal percentage changes

A company has 200 customers. Its customer count increases by 20% in the first month, then decreases by 20% in the second month. How many customers remain after the second month?

200 (1 + 0.20) (1 - 0.20) = 200 (1.2) (0.8) = 192

4 · Why equal rise and fall do not cancel

(1 + r) (1 - r) = 1 - r^{2} Net loss = r^{2}

5 · Reverse percentages: recover the original

0.80 x = 96 ⟹ x = \frac{96}{0.80} = 120

6 · Changes across multiple stages

V_{n} = V_{0} \prod_{k = 1}^{n} (1 + r_{k})

7 · GMAT strategy: test with a convenient base

100 + 10% 110 + 20% 132 \Rightarrow + 32%

First, convert each percentage change into a multiplier. Then multiply the factors and compare the result with 1.00.

Think Like a GMAT Test-Taker

Identify the base quantity, then translate each percentage into a multiplier before computing.

The faster method

For successive +a% and +b% changes, the overall increase is a + b + ab/100 percent. For +p% then -p%, the overall loss is p²/100 percent.

Decision rule

When the original value is missing, divide the final value by the product of the multipliers; never reverse a discount by simply adding the percentage.

Common GMAT Traps

Adding consecutive percentage changes instead of multiplying factors.
Assuming +20% followed by -20% gives zero net change.
Applying a discount to the original base after an earlier increase.
Confusing a percentage-point change with a percentage change.