**ANSWERS**

1. D

2. B

3. E

4. A

5. 198

**EXPLANATIONS**

1. It is best to simplify each stem first before making the calculation. We want to get both stems to have LCD, so the LCD of the firs is 9.

The first stem reduces to (9/9 - 5/9) = 4/9 The second stem reduces to 6/3 - 1/3 = 7/3. Multiplying them together yields 4/9* 7/3 which equals 28/27, so the answer is D.

2. With variables in the question stem and answer choices, let’s use Picking Numbers to test each choice.

*(A)* If *b* = 3, *b* = 3 + 3 = 6. This is not odd, so eliminate.

*(B)* If *b* = 3, *b* = 6 + 3 = 9. This is odd.

*(C)* If *b* = 2, *b* = 2 + 2 = 4. This is not odd, so eliminate.

The correct answer is Choice *(B)*.

3. In 1990, the profits of Company A were approximately 12,000,000 dollars and the profits of Company B were approximately 20,000,000. The sum of the profits of both companies in 1990 was approximately 20,000,000 + 12,000,000 = 32,000,000 dollars. In 1991, the profits of Company A were approximately 28,000,000 dollars and the profits of Company B were approximately 16,000,000. The sum of the profits of both companies in 1991 was approximately 28,000,000 + 16,000,000 = 44,000,000 dollars. In 1992, the profits of Company A were approximately 41,000,000 dollars and the profits of Company B were approximately 34,000,000. The sum of the profits of both companies in 1992 was approximately 41,000,000 + 34,000,000 = 75,000,000 dollars. In 1993, the profits of Company A were approximately 51,000,000 dollars and the profits of Company B were approximately 30,000,000. The sum of the profits of both companies in 1993 was approximately 51,000,000 + 30,000,000 = 81,000,000 dollars. In 1994, the profits of Company A were approximately 32,000,000 dollars and the profits of Company B were approximately 56,000,000 dollars. The sum of the profits of both companies in 1994 was approximately 32,000,000 + 56,000,000 = 88,000,000 dollars. In 1995, the profits of Company A were approximately 61,000,000 dollars and the profits of Company B were approximately 50,000,000 dollars. The sum of the profits of both companies in 1995 was approximately 50,000,000 + 61,000,000 = 111,000,000 dollars.

Thus, the approximate sums of the profits in the years, 1990, 1991, 1992, 1993, 1994, and 1995, in millions, were, respectively, 32, 44, 75, 81, 88, and 111. In each of the 5 years 1991 through 1995 inclusive, the sum of the profits increased over the previous year. Choice (E) is correct.

4. The equation for the volume of a right cylinder is: area of base x height = π*r^2 x **h *If Cylinder *B* has radius *r* and height *h*, then Cylinder *A *has radius 2*r* and height 1/2*h. *

* *The volume of Cylinder B is V(B) = π*r^2* x *h*

The volume of Cylinder A is V(A) = π(2r)^2 x (1/2)h = π(4*r^2*)(1/2*h*) = 2π*r^2* x *h*

Cylinder B’s volume is π*r^2**h *Cylinder A’s volume is 2π*r^2 **h. *Cylinder A has twice the volume of Cylinder B and is therefore greater.

5. In order to find the answer to this question, we could manually list and count all of the possibilities, but it may be quicker to use the combination formula. In this case, order does not matter, so we use a combination rather than a permutation. This gives us:

which simplifies to:

(12 x 11)/2 = 66

Since each team plays every other team three times, we must multiply this result by 3. We then get 198.