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Arithmetic and Number Properties Flashcards

7 cards from real GRE practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. What is the value of (-3)^4 - (-2)^3?

    Answer: 89

    (-3)^4 = 81 and (-2)^3 = -8, so 81 - (-8) = 89.

  2. If x and y are positive integers and xy = 36, what is the greatest possible value of x + y?

    Answer: 37

    The sum is largest when the factors are most spread apart: 1·36 gives 1 + 36 = 37.

  3. What is 0.25 expressed as a fraction in lowest terms?

    Answer: 1/4

    0.25 = 25/100 = 1/4.

  4. If 3^x = 81, what is the value of x?

    Answer: 4

    81 = 3^4, so x = 4.

  5. Which of the following numbers is divisible by 9?

    Answer: 234

    The digits of 234 sum to 9, which is divisible by 9.

  6. The product of two consecutive even integers is 168. What is the smaller integer?

    Answer: 12

    12 × 14 = 168, so the smaller integer is 12.

  7. What is the sum of the first 10 positive even integers?

    Answer: 110

    The sum is 2(1+2+…+10) = 2·55 = 110.