When the number of people in an office is divided by 12, the remainder is 0. If 
times the number of people in the office is divided by 12, and the remainder resulting from this operation is greater than 0, the remainder must be
When the number of people in an office is divided by 12, the remainder is 0. If times the number of people in the office is divided by 12, and the remainder resulting from this operation is greater than 0, the remainder must be
1
2
3
5
6
Question 2
a, b, and c are multiples of 15 and a < b < c
| Quantity A | Quantity B |
|
The remainder when b is divided by c |
The remainder when (b + c) is divided by a |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question 3
Emma is 3 years older than Merrick, who is 8 years younger than Aliza. If Aliza is at least 25, which of the following could be Emma’s age?
Indicate all such values.
12
15
17
20
25
29
Question 4
If each letter on the number line above is the number that corresponds to the point below it, then which of the following is closest to D ÷ A?
A
B
C
D
E
Question 5
Set X consists of all the even integers from 1 to 100, inclusive, and set Y consists of all the integers divisible by 5 from 1 to 100, exclusive. How many members of set X are not members of set Y?
If negative integer a is multiplied by b and the result is greater than 0 but less than |a|, then which of the following must be true of b?
b > 1
0 < b < 1
−1 < b < 0
b < a
|b| < a
A number divisible by a positive even prime number must be
prime
odd
even
the square of a prime
the square of an odd number
Question 8
What are the greatest and smallest positive differences between any of the factors of 210?
103 and 1
209 and 0
210 and 1
103 and 11
209 and 1
Question 9
On Monday, Janice started training for a marathon and ran one mile that day. On Tuesday, Janice ran one mile more than she did on Monday. She continues this training process for 12 days. The sum of the total number of miles Janice ran has how many distinct prime factors?
Question 10
Last year, Melania had a total of $20,000 invested in two mutual funds, Capital Growth Fund and Venture Index Fund. At the end of the year, she analyzed her investments and found that her earnings on her shares of Capital Growth Fund were three times half of her earnings on her investment in Venture Index Fund. If she earned a total of $1,250 on her investments in the two funds, and had three times as much money invested in Capital Growth Fund as in Venture
Index Fund, what percent interest did Melania earn on her investment in Venture Index Fund? (percent interest = 
× 100)
.075
.01
7.5
10
500
a is the product of 3 and the square root of 2, b is the product of 2 and the square root of 3, and c is the product of 2 and the square root of 6. If x is the square of the sum of a and b, y is the product of 6 and the difference of 5 and c, and z is the product of 2 squared and 3 squared, what is 
?
1
36
64
Question 12
The integer m is a multiple of 154, 250, and 264. Which of the following do NOT have to be factors of m?
Indicate all such values.
176
242
275
924
2,500
7,000
Question 13
If when x is divided by z, the result is y remainder q, then which of the following must be true?
z(y + q) = x
xz − q = y
