Arithmetic: Number Properties, Percents, Ratios, and Exponents
What you must know
Arithmetic on the GRE is number-property reasoning more than long computation. Be fluent with divisibility rules (3 and 9 by digit sum, 4 by the last two digits, 8 by the last three), prime factorization, greatest common factor and least common multiple, remainders, even/odd and sign rules, fraction–decimal–percent conversions, ratios and proportions, exponent laws, roots, absolute value, and order of operations. Memorize common fraction–percent equivalents (1/6 ≈ 16.7%, 1/8 = 12.5%, 1/7 ≈ 14.3%) to save time under the clock.
Traps that cost points
- Percent change is always measured against the base. A 25% increase followed by a 20% decrease returns to the original value; successive percents multiply, they never add.
- Distinguish percent of from percent more than, and percent from percentage points.
- Never divide both sides by a quantity that could be zero - it silently destroys a case.
- Convert units before comparing, and honor any integer constraint the question states.
- For huge powers, only the units digit matters; digit cycles repeat with period 1, 2, or 4.
Worked example
A jacket costs $80. Its price is raised 25%, then the new price is discounted 20%. Final price = 80 × 1.25 × 0.80 = 80 × 1.00 = $80 - unchanged. Rule of thumb: chain percent changes by multiplying factors of the form (1 + r), never by adding percentages.