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Number Theory and Integer 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.

Read the first 7 Number Theory and Integer Properties flashcards as text

  1. What is the units digit of 3^47?

    Answer: 7

    Units digits of powers of 3 cycle 3,9,7,1 with period 4, and 47 ≡ 3 (mod 4) gives 7.

  2. How many integers between 1 and 100 inclusive are divisible by both 4 and 6?

    Answer: 8

    Divisibility by both means divisibility by LCM(4,6)=12, and there are 8 multiples of 12 up to 100.

  3. If a and b are integers with a·b = 0, which statement must be true?

    Answer: At least one of a or b is 0

    A product of integers is zero only when at least one factor is zero.

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

    Answer: 110

    The sum 2+4+...+20 equals 2(1+2+...+10) = 2·55 = 110.

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

    Answer: 4,572

    The digits of 4,572 sum to 18, which is divisible by 9.

  6. If p is a prime greater than 3, what is the remainder when p² is divided by 12?

    Answer: 1

    Any prime greater than 3 satisfies p² ≡ 1 (mod 12).

  7. How many trailing zeros does the number 25 × 16 × 5 contain?

    Answer: 3

    25×16×5 = 2000, which has 3 trailing zeros from three factors of 10.