[Math Center]

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.

 

 

Answer:

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

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