Number Properties

If n is a positive integer, what is the remainder when n is divided by 7? (1) When n is divided by 14 the remainder is 5. (2) n is less than 20.

Is the product of integers a, b, and c divisible by 8? (1) a, b, c are consecutive even integers. (2) a + b + c = 24.

If x is a positive integer, is x prime? (1) x has exactly 3 positive divisors. (2) x is a multiple of 4.

Is n an integer? (1) n 2 n 2 is an integer (2) √ n n √ is an integer

Of the four numbers represented on the number line above, is r closest to zero? (1) q = –s (2) –t < q

Is n an integer greater than 4? (1) 3n is a positive integer. (2) n/3 is a positive integer.

If x and y are nonzero integers, is x/y an integer? (1) x is the product of 2 and some other integer. (2) There is only one pair of positive integers whose product equals y.

For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b? (1) a/b = 3/5 (2) a and b have no common factors greater than 1

If J, K, L, M, and N and positive integers in ascending order, what is the value of L? (1) The value of K is 3. (2) The value of M is 7.

If a, b, and c are integers, is the number 3(a + b) + c divisible by 3? (1) a + b is not divisible by 3. (2) c is divisible by 3.

If x and y are consecutive odd integers, what is the sum of x and y? (1) The product of x and y is negative. (2) One of the integers is equal to –1.

If S = {2, 3, x, y}, what is the value of x + y? (1) x and y are prime numbers. (2) 3, x, and y are consecutive odd integers in ascending order.

Is x an even integer? (1) x is the square of an integer. (2) x is the cube of an integer.

If b is an integer, is a 2 + b 2 − − − − − − √ 𝑎 2 + 𝑏 2 an integer? (1) a^2 + b^2 is an integer. (2) a^2 – 3b^2 = 0 DS46402.01

Is the integer n odd? (1) n is divisible by 3. (2) n is divisible by 5.

If n is an integer, then n is divisible by how many positive integers? (1) n is the product of two different prime numbers. (2) n and 2^3 are each divisible by the same number of positive integers.

What is the value of the sum of a list of n odd integers? (1) n = 8 (2) The square of the number of integers on the list is 64.

Is the prime number p equal to 37? (1) p = n^2 + 1, where n is an integer. (2) p^2 is greater than 200.

If x, y, and z are three integers, are they consecutive integers? (1) z - x= 2 (2) x < y < z

If p and q are positive integers and pq = 24, what is the value of p ? (1) q/6 is an integer. (2) p/2 is an integer.