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
px ≠ y
x ≥ py
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