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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 units digit of 7^23?

    Answer: 3

    Powers of 7 cycle 7,9,3,1 with period 4; 23 mod 4 = 3, giving units digit 3.

  2. If n is an integer, which expression is always even?

    Answer: n^2 + n

    n^2 + n = n(n+1) is a product of two consecutive integers, so it is always even.

  3. What is the greatest common divisor (GCD) of 84 and 120?

    Answer: 12

    84 = 2^2·3·7 and 120 = 2^3·3·5, so the GCD is 2^2·3 = 12.

  4. How many distinct prime factors does 360 have?

    Answer: 3

    360 = 2^3·3^2·5, which has the three distinct primes 2, 3, and 5.

  5. If the remainder when x is divided by 5 is 3, what is the remainder when 2x is divided by 5?

    Answer: 1

    2x ≡ 2·3 = 6 ≡ 1 (mod 5), so the remainder is 1.

  6. Which of the following is the least common multiple (LCM) of 6, 8, and 9?

    Answer: 72

    Taking highest prime powers 2^3·3^2 = 72.

  7. If a positive integer has exactly 3 divisors, it must be which of the following?

    Answer: The square of a prime

    A number with exactly 3 divisors is p^2 for a prime p, giving divisors 1, p, and p^2.