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Question #1
Topic 1

Roy is now 4 years older than Erik and half of that amount older than Iris. If in 2 years, Roy will be twice as old as Erik, then in 2 years what would be Roy's age multiplied by Iris's age?

- A. 8
- B. 28
- C. 48
- D. 50
- E. 52 C

**Correct Answer:**
Explanation
🗳️

Translate piece by piece into numbers. R (Roy) = Erik E. + 4. The second equation: R = I (Iris) + 2.

The third equation: R +7 = 2(E + 7). We have three equations with three variables.

Roy is 6, Iris is 4 and Erik is 2. In four years Erik would be 6 and Iris 8, the answer is 48. The correct answer is C.

Question #2
Topic 1

An investment yields an interest payment of $228 each month. If the simple annual interest rate is 9%, what is the amount of the investment?

- A. $28,300
- B. $30,400
- C. $31,300
- D. $32,500
- E. $35,100

**Correct Answer:**
B
🗳️

Principal Ã— percent interest Ã— time = interest earned

Principle Ã— (0.09) Ã— 1/12 = $228.

Solve to find the principal (228 Ã— 12)/0.09= $30,400.

The correct answer is B.

Question #3
Topic 1

X, Y, Z, and W are integers. The expression X-Y-Z is even and the Expression Y-Z-W is odd. If X is even what must be true?

- A. Y-Z must be odd.
- B. W must be even.
- C. W must be odd.
- D. W must be even.
- E. Z must be odd

**Correct Answer:**
C
🗳️

The first expression is even and the second is odd, the only difference between the expressions is that the first expression has X and the second has W. So, if X is even W must be odd and the correct answer is C.

Question #4
Topic 1

Q is a prime number bigger than 10. What is the smallest positive number (except 1) that 3Q can be divided by equally?

- A. 3 Q.
- B. Q
- C. 3
- D. Q+3
- E. 2Q C

**Correct Answer:**
Explanation
🗳️

3Q is a prime number so it can be divide equally by 3Q, by 1 and by the components 3 and Q. The smallest number therefore is 3. The correct answer is C.

Question #5
Topic 1

In a box there are green balls, 3A + 6 red balls and 2 yellow ones.

If there are no other colors, what is the probability of taking out a green or a yellow ball?

- A. 1/5.
- B. 1/2.
- C. 1/3
- D. 1/4.
- E. 2/3.

**Correct Answer:**
D
🗳️

The number of green and yellow balls in the box is A+2. The total number of balls is 4A +8. The probability of taking out a green or a yellow ball is: A + 2 / 4 A + 8

= 1/4

Question #6
Topic 1

Kelly used to get a 30% discount on movie tickets. When the price of the movie ticket increased by 50%, the amount of discount in dollars remained the same.

What is Kelly's discount with the new Ticket price in percent terms?

- A. 10%
- B. 20%
- C. 25%
- D. 35%
- E. 38% B

**Correct Answer:**
Explanation
🗳️

The price of the ticket is unknown. It would be most convenient to plug in 100 as the price of the ticket.

A 30% discount of 100 is $30, that amount remained the same after the price of a ticket increased by 50%.

The new price of a ticket is $150, so 30/150 is 20%. The correct answer is B.

Question #7
Topic 1

In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey's grade at the end of the first year is 40, what will be his grade at the end of the third year?

- A. 44.
- B. 56.
- C. 62.
- D. 75.
- E. 80.

**Correct Answer:**
D
🗳️

From the grade 40 at the end of the first year we learn that his age is 20.

At the end of the second year, he will be 21 and his grade will be

(21 x 2 + 1/2 x 40 = 62).

At the end of the third year, he will be 22 and his grade will be (22 x 2 + 1/2 x 62 = 75). The correct answer is D.

Question #8
Topic 1

A is a prime number (A>2). If C = A3, by how many different integers can C be equally divided?

- A. 3.
- B. 4.
- C. 5.
- D. 6
- E. 7

**Correct Answer:**
B
🗳️

Factorize C: C = A x A x A: C can be equally divided into 1, A, A2, and A3 =C is 4 numbers total. The correct answer is B.

Question #9
Topic 1

If X is a positive integer and (405) 4 is a multiple of 3X, what is the largest possible value of X?

- A. 5.
- B. 12.
- C. 16.
- D. 20
- E. 26.

**Correct Answer:**
C
🗳️

Find the factors of (405) 4 and see what the largest value of X can be.

405 = 81 x 5 = 9 x 9 x 5 = 3 x 3 x 3 x 3 x 5 - (405) 4 = (3 x 3 x 3 x 3 x 5) 4 = 316 x 54.

The largest possible value of 3X that is still a factor of (405) 4 is the largest possible value of X and that is 316. X = 16. The correct answer is C.

Question #10
Topic 1

N is a prime number bigger than 5. Which of the following expressions must be even?

- A. (N+2)2.
- B. N2+2.
- C. N (N+2).
- D. (N+1) (N+2).
- E. (N "" 2)2.

**Correct Answer:**
D
🗳️

Answer D is a multiplication of two consecutive numbers, therefore one of them must be even, and an even number multiplied by a different number is an even number.

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