Two positive integers are in the ratio 7:9. If their highest common factor is 3, then what is the value of their least common multiple?

(A) 126
(B) 189
(C) 252
(D) 315
(E) 378

A perfect cake should have 25% cream and 75% bread. Oman bought material for a 5kg cake with 35% cream and 65% bread. How many more kg of bread should he buy if he wants to make a perfect cake?

A. 2kg
B. 2.5kg
C. 3kg
D. 4kg
E. 5kg

How many integer values of n satisfy the inequality |3 − n| ≤ 4?

A. 4
B. 5
C. 8
D. 9
E. 10

If a and b are both factors of 50, which of the following must be true?

(A) ab≥ 2
(B) a + b≤ 50
(C) ab is a factor of 100.
(D) ab is a factor of 2500.
(E) ab is even.

What is the range of the solutions to the equation |x^2 – 1| = 0 ?

A. 0
B. 1
C. 2
D. 3
E. 5

If a and b are real numbers such that the following expression is true.
a^2+5b^2+4ab+3=6b−6

Find the value of a+b?

A. -6
B. -3
C. 0
D. 3
E. 6

The number of ordered pairs of positive integers (x, y) satisfying the equation 7x + 3y = 123 is:

A. 3
B. 5
C. 12
D. 13
E. Infinite

If x = -3, what is the value of -3x^2 ?

(A) -27
(B) -18
(C) 18
(D) 27
(E) 81

The 180 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows EXCEPT

(A) 4
(B) 20
(C) 30
(D) 40
(E) 90

If x < 8, and y < 7, which of the following must be true?

I. 2x + 3y ≤ 32

II. x - y > -1

III. x + 2y < 22

A. I. only

B. III. only

C. II. and III.

D. I. and III.

E. I., II., and III.