Number Properties

If n is a positive integer, are n and 1 the only positive divisors of n? (1) n is less than 14. (2) If n is doubled, the result is less than 27

Is n an integer greater than 14? (1) 3 n 3 n is a positive integer. (2) n 3 n 3 is a positive integer.

If x is an integer, is x/2 an even integer (1) x is a multiple of 2 (2) x is a multiple of 4 (1) x is a multiple of 2 (2) x is a multiple of 4

If m, p, and t are positive integers and m<p<t, is the product mpt an even integer? (1) t - p = p - m (2) t - m = 16

If n is a positive integer, is n^3 – n divisible by 4 ? (1) n = 2k + 1, where k is an integer (2) n^2 + n is divisible by 6

The product of the units digit, the tens digit, and the hundreds digit of the positive integer m is 96. What is the units digit of m? (1) m is odd. (2) The hundreds digit of m is 8

(n-x)+(n-y)+(n-z)+(n-k) What is the value of the expression above? (1) The average (arithmetic mean) of x, y, z, and k is n. (2) x, y, z, and k are consecutive integers.

If the integer n is greater than 1, is n equal to 2? (1) n has exactly two positive factors. (2) The difference of any two distinct positive factors of n is odd.

Does the integer k have a factor p such that 1<p<k? (1) k > 4! (2) 13 ! + 2 ≤ k ≤ 13 ! + 13 13 ! + 2 ≤ k ≤ 13 ! + 13

What is the value of the integer x? (1) x is a prime number. (2) 31 ≤ x ≤ 37

If n is a positive integer, is 150/n an integer? (1) n < 7 (2) n is a prime number

Is the integer k a prime number? (1) 2k = 6 (2) 1 < k < 6

If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y? (1) x = 12u, where u is an integer (2) y = 12z, where z is an integer

If r and s are nonzero integers, is r/s an integer ? (1) r - 1 = (s + 1)(s - 1) (2) r - s = 20

Is p^2 an odd integer? (1) p is an odd integer. (2) p √ p is an odd integer.

If n is an integer, is n/7 an integer? (1) 3n/7 is an integer. (2) 5n/7 is an integer

If n is an integer, is ( 100 − n ) n ( 100 − n ) n an integer? (1) n > 4 n > 4 (2) n 2 = 25 n 2 = 25