Number Properties

A computer routine was developed to generate two numbers, ( x,y), the first being a random number between 0 and 100 inclusive, and the second being less than or equal to the square root of the first. Each of the following pairs satisfies this routine EXCEPT:

If a, b, and c are three consecutive odd integers such that 10 < a < b < c < 20 and if b and c are prime numbers, what is the value of a + b?

If x, y, and z are single-digit integers and 100(x) + 1,000(y) + 10(z) = N, what is the units' digit of the number N?

If a sequence of 8 consecutive odd integers with increasing values has 9 as its 7th term, what is the sum of the terms of the sequence?

How many of the integers between 25 and 45 are even?

If x is an even integer, which of the following is an odd integer?

If the positive integer n is added to each of the integers 69, 94, and 121, what is the value of n? (1) 69 + n and 94 + n are the squares of two consecutive integers (2) 94 + n and 121 + n are the squares of two consecutive integers

In the two-digit integers 3 □ ◻ and 2 △ △ ,the symbols □ ◻ and △ △ represent different digits, and the product (3 □ ◻ )(2 △ △ ) is equal to 864. What digit does □ ◻ represent ? (1) The sum of □ ◻ and △ △ is 10. (2) The product of □ ◻ and △ △ is 24

If x is a positive integer, then is x prime? (1) 3x + 1 is prime (2) 5x + 1 is prime

Is the integer x a 3-digit integer? (1) x is the square of an integer. (2) 90 < x < 150

If y ≠2xz, what is the value of (2xz + yz)/(2xz – y)? (1) 2x + y = 3 (2) z = 2

Is the sum of two integers divisible by 10 ? (1) One of the integers is even. (2) One of the integers is a multiple of 5.

If x is a positive integer, what is the value of x + 24 − − − − − √ − x √ x + 24 − x ? (1) x √ x is an integer (2) x + 24 − − − − − √ x + 24 is an integer

If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ ? (1) If r = s, then r θ s = 0. (2) If r ≠ s, then r θ s ≠ s θ r.

Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14

If r and s are positive integers, can the fraction r/s be expressed as a decimal with only a finite number of nonzero digits? (1) s is a factor of 100 (2) r is a factor of 100

Is x an integer? (1) x 3 = 8 x 3 = 8 (2) x = 4 √ x = 4

What is the sum of a certain pair of consecutive odd integers? (1) At least one of the integers is negative. (2) At least one of the integers is positive.

The sum of 4 different odd integers is 64. What is the value of the greatest of these integers? (1) The integers are consecutive odd numbers (2) Of these integers, the greatest is 6 more than the least.

If p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers, what is the value of x ? (1) Twice x is equal to the sum of p, r, and s. (2) The sum of p, r, and s is zero.