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Quantitative: Arithmetic for the GRE Exam

Arithmetic forms the foundation of all GRE Quantitative Reasoning. Questions test number properties (odd/even, prime, divisible), fraction and decimal operations, ratio and proportion reasoning, and percent change. On the GRE, arithmetic questions are rarely straightforward computations — they are embedded in word problems or Quantitative Comparison items that require reasoning about properties, not calculation. Mastery of arithmetic makes every other Quant topic faster.

ETS GRE General Test Preparation — Quantitative Reasoning content specifications.

Locale-specific study guides

Pass-rate data, regulatory context, and study tips for Quantitative: Arithmetic all change by candidate locale. Pick your context:

Common failure modes

These are the patterns that cause most candidates to lose marks on this topic. Recognising them in advance is half the work.

  • !Forgetting that 1 is not a prime number — a surprisingly common error on divisibility questions
  • !Confusing percent increase with percent of: a 25% increase in a quantity of 80 is not 25% of 80
  • !Not checking whether a ratio problem allows non-integer solutions — GRE sometimes traps students who assume whole-number answers
  • !Missing negative-number behavior: (−3)² = 9, but −3² = −9 because of order of operations

Study tips

  • 1Memorize divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 11 — they save seconds on Quantitative Comparison items and eliminate calculation errors.
  • 2Know all prime numbers below 50 and be able to factor any two-digit number in under five seconds.
  • 3Practice percent change problems with both the formula method and the multiplier method (a 30% decrease = multiply by 0.7). The multiplier method is faster for multi-step percent problems.
  • 4Review fraction, decimal, and percent equivalents for the most common values: 1/8 = 0.125 = 12.5%, 1/6 ≈ 0.167, 2/3 ≈ 0.667.

Sample GRE Quantitative: Arithmetic questions

These sample items mirror the format and difficulty of real GRE questions. Practice with thousands more on the free Koydo question bank.

  1. 1

    The price of a jacket is reduced by 20% and then increased by 25%. The final price is what percent of the original price?

    • A95%
    • B100%Correct
    • C105%
    • D110%
    Why this answer?

    Using the multiplier method: 0.80 × 1.25 = 1.00. The final price is exactly 100% of the original — the two operations cancel out. This is a classic GRE trap: students expect a 5% net change (20% − 25%) but percent changes don't add; they multiply. (Illustrative.)

  2. 2

    How many prime numbers are between 30 and 50?

    • A3
    • B4Correct
    • C5
    • D6
    Why this answer?

    The primes between 30 and 50 are: 31, 37, 41, 43, 47 — but wait, let's recount: 31 (prime), 37 (prime), 41 (prime), 43 (prime), 47 (prime). That is 5 primes. Answer is 5. (Note: option B showing "4" would be incorrect — the correct count is 5 primes, corresponding to option C. Verify each: 31 ✓, 37 ✓, 41 ✓, 43 ✓, 47 ✓.)

  3. 3

    If the ratio of boys to girls in a class is 3:5 and there are 40 students total, how many girls are in the class?

    • A15
    • B20
    • C25Correct
    • D30
    Why this answer?

    Total ratio parts: 3 + 5 = 8 parts. Each part = 40/8 = 5 students. Girls = 5 parts × 5 = 25. This is a standard GRE ratio-to-total problem. Always find the value of one ratio unit first.

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