Number Properties

If r and t are three-digit positive integers, is r greater than t ? (1) The tens digit of r is greater than each of the three digits of t . (2) The tens digit of r is less than either of the other two digits of r .

If x and y are positive integers, is xy even? (1) x^2 + y^2 − 1 is divisible by 4. (2) x + y is odd.

Is w + h 4 w + h 4 positive? (1) h is positive (2) w is positive

The 9 squares above are to be filled with x's and o's, with only one symbol in each square. How many of the squares will contain an x ? (1) More than 1/2 of the number of squares will contain an o. (2) Each of the 4 corner squares will contain an x.

On the number line, point R has coordinate r and point T has coordinate t. Is t < 0? (1) -1 < r < 0 (2) The distance between R and T is equal to r^2

Is the product of two positive integers x and y divisible by the sum of x and of y ? (1) x=y (2) x=2

If a and b are integers, is a + b + 3 an odd integer? (1) ab is an odd integer. (2) a − b is an even integer.

Is the sum of four particular integers even? (1) Two of the integers are odd and two are even. (2) The average (arithmetic mean) of the four integers is an integer.

If a is a 3-digit integer and b is a 3-digit integer, is the units digit of the product of a and b greater than 5? (1) The units digit of a is 4. (2) The units digit of b is 7.

Is n equal to zero? (1) The product of n and some nonzero number is 0. (2) The sum of n and 0 is 0.

If r and s are positive integers, is r + s even? (1) r is even. (2) s is even.

Does the integer k have at least three different positive prime factors? (1) k/15 is an integer. (2) k/10 is an integer.

What is the value of the integer p ? (1) Each of the integers 2, 3, and 5 is a factor of p. (2) Each of the integers 2, 5, and 7 is a factor of p.

If m and n are positive integers, is ( m − − √ ) n ( m ) n an integer? (1) m − − √ m is an integer. (2) n √ n is an integer.

Is √(x + y) an integer? (1) x^3 = 64 (2) x^2 = y – 3

If x and y are integers, is xy even? (1) x = y + 1. (2) x/y is an even integer.

For any positive integer x, the 2-height of x is defined to be the greatest nonnegative integer n such that 2^n is a factor of x. If k and m are positive integers, is the 2-height of k greater than the 2-height of m? (1) k > m (2) k/m is an even integer.

If A and B are positive integers, is the product AB even? (1) The sum A + B is odd. (2) A is even.

How many integers are there between, but not including, integers r and s ? (1) s-r=10 (2) There are 9 integers between, but not including, r + 1 and s + 1.

If m is an integer, is m odd? (1) m/2 is not an even integer (2) m-3 is an even integer