1. When the positive integer   is divided by  , the remainder is   and when   is divided by  , the remainder is  . What is the least possible value of  ?

2.   is a positive integer that is divisible by  .

 Quantity A Quantity B The remainder when   is divided by  The remainder when   is divided by 

3.

 Quantity A Quantity B The least number divisible by  , and  The least number that is a multiple of  and 

4.  Which of the following could be the units digit of  where   is a positive integer?
Indicate all such digits. 

(A)  
(B) 
(C) 
(D) 
(E) 
(F)  
(G) 
(H) 
(I) 
(J) 

5.

 Quantity A Quantity B The last digit in the number  The last digit in the number 

6.   The last digit of the positive even number  equals the last digit of  . Which one of the following could be   ?

(A) 
(B) 
(C) 
(D) 
(E) 

7.  The number  divides  with a result of  and a remainder of  . The number  divides  with a result of  and a remainder of  . What is the value of  ?

(A) 
(B) 
(C) 
(D) 
(E) 

8. The remainder when the positive integer  is divided by  is  . The remainder when  is divided by  is  . Which one of the following could  equal?

(A) 
(B) 
(C) 
(D) 
(E) 

9.  Each of the two positive integers  and  ends with the digit  . With which one of the following numbers does  end?

(A) 
(B) 
(C) 
(D) 
(E) 

10.   If each of the three nonzero numbers  , and  is divisible by  , then  must be divisible by which one of the following the numbers?

(A) 
(B) 
(C) 
(D) 
(E) 

11.  If  is a positive integer, which one of the following numbers must have a remainder of  when divided by any of the numbers  and  ?

(A) 
(B) 
(C) 
(D) 
(E) 

12.    and  are both positive integers. When x is divided by  , the quotient is  with a remainder of  . Which of the following could be the value of  ?

(A) 
(B) 
(C) 
(D) 
(E) 

13.  divided by  yields remainder  , and  divided by  yields remainder  . What is  ?

 Quantity A Quantity B  

14.  If  is divisible by  and  is divisible by  ,  must have at least how many factors greater than  ?

(A) 
(B) 
(C) 
(D) 
(E) 

15. New cars leave a car factory in a repeating pattern of red, blue, black, and gray cars. If the first car to exit the factory was red, what color is the  rd car to exit the factory?

(A) red
(B) blue
(C) black
(D) gray
(E) It cannot be determined from the information given.

1 11
2 D
3 C
4 B,D,H,J
5 C
6 A,C
7 D
8 D
9 B
10 A
11 E
12 D
13 12
14 D
15 C