If x^2 /4 is an integer greater than 50, and x is a positive integer, then what is the smallest possible value for x^2 ?

A. 121
B. 144
C. 169
D. 225
E. 256

If x, y, and z are positive integers and 3x = 4y = 7z, then the least possible value of x + y + z is

A. 33
B. 40
C. 49
D. 61
E. 84

An arithmetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 13th member of this sequence?

A. 37
B. 40
C. 26p + 13
D. 53
E. 129p + 13

If x is a positive integer and 4x–3=y, which of the following CANNOT be a value of y ?

A. 1
B. 7
C. 13
D. 61
E. 253

The ratio of the present ages of a father and a son is 8 : 1. Eight years from now, the ratio would be 10 : 3. What is the present age of the father?

A. 24
B. 32
C. 40
D. 48
E. 56

For how many integer values of x, is |3x−3|+|2x+8|<15 ?

A. 2
B. 3
C. 4
D. 5
E. 6

Three machines, individually, can do a certain job in 4, 5, and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?

(A) 11/30
(B) 9/20
(C) 3/5
(D) 11/15
(E) 5/6

The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

(A) 5
(B) 8
(C) 10
(D) 12
(E) 15

If -4 is one solution to the equation x^2 + bx + c = 0, where b and c are constants, and b + c = -21, what is the other solution?

A) -5

B) -1

C) 5

D) 7

E) 10

If |x + 3| = 12 and |y +2| = 9, the maximum value of xy =

A 63
B 84
C 99
D 132
E 165