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
Which of the following is a perfect square?
Answer: 196
196 = 14², making it a perfect square, while the others are not.
If an integer n is divided by 9 and leaves remainder 4, what is the remainder when n + 11 is divided by 9?
Answer: 6
n ≡ 4 (mod 9), so n + 11 ≡ 15 ≡ 6 (mod 9).
The number 360 has how many distinct prime factors?
Answer: 3
360 = 2³·3²·5, giving the three distinct primes 2, 3, and 5.
If a is odd and b is even, which expression is always odd?
Answer: a + b
Odd plus even is always odd, so a + b must be odd.
What is the smallest positive integer divisible by 2, 3, 4, 5, and 6?
Answer: 60
The LCM of 2,3,4,5,6 is 60, the smallest number divisible by all of them.
How many factors of 2 are in the prime factorization of 48?
Answer: 4
48 = 2⁴·3, so there are four factors of 2.
If the product of two integers is odd, which must be true about both integers?
Answer: Both are odd
A product is odd only when both factors are odd.