Percents are the language of business and a cornerstone of the GMAT Quant section. Success requires moving beyond calculation to master the logic of complex word problems, Data Sufficiency, and strategic shortcuts.
Start with the basics. Practice converting between percents, fractions, and decimals to build a solid foundation.
Convert any fraction to a percentage.
Master the fundamental algebraic skill: solving for the Part, the Percent, or the Whole. This is the engine for all word problems.
"20 is what percent of 50?"
"28 is 40% of what number?"
Understand the principle of "growth on growth." This visualizer is the key to mastering compound interest and successive percent change.
Compounding means growth is calculated on the new, larger base, not the original.
Example: Invest $100 at 10% annual growth.
$$ 100 + (10\% \text{ of } 100) = 100 + 10 = \$110 $$
Growth: $10
Now we calculate 10% of the NEW base ($110).
$$ 110 + (10\% \text{ of } 110) = 110 + 11 = \$121 $$
Growth: $11 (More than Year 1!)
This is "Interest on Interest". This same logic applies to successive percent changes in GMAT/GRE problems.
The GMAT loves this trap. See why a +X% and a -X% change don't cancel out, and learn the logic to solve these problems quickly.
+ 20% and - 20%
= 0% change
$100 → +20% → $120.00
$120.00 → -20% → $96.00
The +20% increase adds $20. The -20% decrease is on the NEW, larger value ($120), so it subtracts $24.00. Result < Start.
Now that you understand the trap, learn the specific formulas required to perfectly reverse an initial percent increase or decrease.
Select a scenario to see the exact percentage needed to return to the original value.
Apply your knowledge to the most unique GMAT question type. Learn to analyze percent statements for sufficiency without needing to calculate.
What is the value of x?
(1) x is 20% of y.
(2) y is 30.
We know x in terms of y. But we do not know y
We cannot find a unique value for x. INSUFFICIENT.
Translates to: $$ y = 30 $$
This tells us the value of y, but gives us no information about x. INSUFFICIENT.
Since y was missing in Statement (1) but is provided in Statement (2), we can definitely solve by combining
Note: We could have done: $$ x = 0.20(30) = 6 $$. We find a unique value. But this calculation is NOT NECESSARYHence SUFFICIENT.
Final Answer: (C)
Review the most common percent-to-fraction equivalents, then test your memory with an interactive flashcard quiz to boost your calculation speed.
| Percent Change | Multiplier |
|---|---|
| 50% | $$ 1/2 $$ |
| 33.33% | $$ 1/3 $$ |
| 12.5% | $$ 1/8 $$ |
Memorize the direct fractional multipliers for common percent increases and decreases to solve problems faster than with a calculator.
| Percent Change | Multiplier |
|---|---|
| 16.66% | $$ 7/6 $$ |
| 20% | $$ 6/5 $$ |
| 25% | $$ 5/4 $$ |
| 33.33% | $$ 4/3 $$ |
| 50% | $$ 3/2 $$ |
| 100% | $$ 2 $$ |
Memorize the multipliers for decreases.
| Percent Change | Multiplier |
|---|---|
| 16.66% | $$ 5/6 $$ |
| 20% | $$ 4/5 $$ |
| 25% | $$ 3/4 $$ |
| 33.33% | $$ 2/3 $$ |
| 50% | $$ 1/2 $$ |
Master the powerful 'a% of b = b% of a' rule to simplify complex calculations like "32% of 50" into easy mental math.
$$ A\% \text{ of } B = B\% \text{ of } A $$
You can flip the numbers to make calculation easier.
Calculate: $$ 32\% \text{ of } 50 $$
Hard to do mentally? Flip it!
$$ 50\% \text{ of } 32 = \frac{1}{2} \times 32 = \mathbf{16} $$
Calculate: $$ 160\% \text{ of } 25 $$
Flip it:
$$ 25\% \text{ of } 160 = \frac{1}{4} \times 160 = \mathbf{40} $$
$$ A\% \times B = \frac{A}{100} \times B = \frac{A \times B}{100} $$
$$ B\% \times A = \frac{B}{100} \times A = \frac{B \times A}{100} $$
Since $$ A \times B = B \times A $$, they are identical.
Put your understanding of GMAT Percents: A Guide to Word Problems & Data Sufficiency to the test with our premium, adaptive practice questions. Build pacing efficiency and eliminate knowledge gaps now.
Learn how to use the 'Variance Test' to solve hard GMAT CR questions. We break down a classic 700-level Supply vs. Demand fallacy.
How to use 'Extreme Values' to find the range of a sum without calculating every fraction.
Recursive sequences look scary, but they follow a pattern. Learn how to decode the definition and spot the hidden loop.