DRILL 4

Question 1

If xaybzc equals the product of 154 and 56, z > y > x, and a > b > c, then what is the value of axbycz?

      1,024

      2,048

      8,624

    22,528

    It cannot be determined from the information given.

Question 2

If |–3x + 1| < 7, then which of the following represents all possible values of x?

    −2 < x

    −2 < x <

    –2 ≤ x

    x < −2, or x >

    x ≤ –2, or x

Question 3

What is the smallest common multiple of 160 and 240?

Question 4

When x is divided by 3, the remainder is 1. When x is divided by 7, the remainder is 2. How many positive integers less than 100 could be values for x?

Question 5

If j is a multiple of 12, and k is a multiple of 21, then jk must be a multiple of which of the following?

      8

    15

    22

    28

    35

Question 6

In the equation above, x is an integer with 3 distinct prime factors, and y is a positive integer with no prime factors. If z is a positive, non-prime number, what is the greatest possible value of z?

Question 7

If w is a non-positive integer, which of the following must be positive?

Indicate all such expressions.

    −3w

       2w + 10

       w4

       w0

    −w + 0.5

Question 8

Integers a and b are consecutive multiples of 6. Integers x and y are consecutive multiples of 8. In terms of a, b, x, and y, what is the ­ratio of the average of a and b and the average of x and y?

    

    

    

    

    

Question 9

If |x2y| = |(–w)z|, then which of the following could be true?

Indicate all such expressions.

    x2 = wz

    |x2y| = |(–w)z|

    −(wz) = wz

    |–x2| = |(–w)z|

    −w = z

    x2 = –|y|

Question 10

If p and x are non-negative numbers and y is a non-positive number, then which of the following must be true?

Indicate all such expressions.

    px > xy

    px > 0

    pxy > –1

    pxy ≤ 0

    pxy

    xpy

Question 11

If , what is the least integer value of x?

    No such least value exists.

    101

    100

        5

        4

Question 12

If x is divisible by 78, which of the following must be divisible by x?

Indicate all such expressions.

    

    x

    x + 78

    

    78 − x

    78x

    78x + 78

Question 13