How many positive three-digit integers are not divisible by 3 ?

A. 599
B. 600
C. 601
D. 602
E. 603

The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

(A) 7
(B) 4
(C) 2
(D) 1
(E) -2

The average weight of 36 students in a class is 62 kgs. If the weight of the teacher is also included the average becomes 62.5 kgs. Find the weight of the teacher.

A. 80
B. 80.25
C. 80.5
D. 80.75
E. 81

If b is a positive integer and b^4 is divisible by 81, which of the following could be the remainder when b is divided by 9?

A. 1

B. 2

C. 4

D. 6

E. 8

Solution X is 15% salt and solution Y is 50% salt. If the two solutions are combined to form 7 gallons of a 30% solution, how many gallons of solution X must be used?

(A) 2

(B) 2.5

(C) 3

(D) 4

(E) 4.2

If x^2 + 12x + 20 < 0, how many integer values can x be?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

What is the range of x such that x^7−x^5<0

A. x <−1

B. −1< x <1

C. x <−1 ,0 < x < 1

D. −1 < x < 0,1 < x

E. 0 < x < 1

The average of four integers is 8. If the greatest of the four integers is 16, what is the minimum possible value of the least of the four integers

A. -32
B. -16
C. -13
D. 0
E. 1

How many number between 300 and 500 are divisible by 13 ?

A. 13
B. 14
C. 15
D. 16
E. 17

If x, y, and z are positive integers such that x < y < z and x + y + z = 6, then what is the value of z ?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5