GRE Arithmetic and Number Properties 2

Question 1

What is the units digit of 7^23?

Accepted Answer

3

Answer

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

Question 2

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

Accepted Answer

n^2 + n

Answer

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

Question 3

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

Accepted Answer

12

Answer

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

Question 4

How many distinct prime factors does 360 have?

Accepted Answer

3

Answer

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

Question 5

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

Accepted Answer

1

Answer

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

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