GMAT Quantitative: Number Properties 2

Question 1

If n is a positive integer, which of the following must be even?

Accepted Answer

n(n+1)

Answer

The product of two consecutive integers is always even because one of them must be even.

Question 2

What is the units digit of 7^23?

Accepted Answer

3

Answer

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

Question 3

How many positive divisors does 36 have?

Accepted Answer

9

Answer

Since 36 = 2^2 * 3^2, the divisor count is (2+1)(2+1) = 9.

Question 4

If x is an odd integer, which expression is always odd?

Accepted Answer

3x

Answer

An odd number times an odd number is odd, so 3x stays odd.

Question 5

What is the remainder when 47 is divided by 6?

Accepted Answer

5

Answer

Since 6 * 7 = 42, the remainder is 47 - 42 = 5.

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