**Question 1 :**

Given that 0 < x < 1, and set A = {x, x^{2}, x^{3}, x^{4}}, what is the smallest value in set A ?

(A) x (B) x^{2} (C) x^{3} (D) x^{4 }

(E) cannot be determined

**Solution :**

Let x = 0.5

x^{2} = 0.25

x^{3} = 0.125

x^{4} = 0.0625

When the power is being increased, the answer get decreased. Hence the smallest value of the given set is x^{4}

**Question 2 :**

Sammy has a faulty clock. Every 15 degrees that one of the hands moves, 5 minutes passes. If a hand is initially 5 : 35 PM, in how long will be the hand be at that same position ?

(A) 65 minutes (B) 2 hours (C) 1 hour

(D) 45 minutes (E) 1 hour and 15 minutes

**Solution :**

There are 360 degree that the hands must move to complete a full revolution and to be at the same time of 5 :35, if every 15 degree, 5 minutes passes, then (24 ⋅5) minutes will have passed by the time it is 5 : 35 again. This is 2 hours.

**Question 3 :**

If (x - 2) (x + 2) = ax^{2} + bx + c, what is the sum of a, b and c ?

(A) -4 (B) -3 (C) 0 (D) 1 (E) 5

**Solution :**

ax^{2} + bx + c = (x - 2)(x + 2)

= x^{2} - 2x + 2x - 4

= x^{2} - 0x - 4

a = 1, b = 0 and c = -4

a + b + c = 1 + 0 + (-4)

a + b + c = -3

**Question 4 :**

Natalie walks in a special way. After every 2 steps she takes, she takes 1 step in the opposite direction. She starts at point A and walks forward. When she is 7 steps away from the point A, she has reached her destination point B. How many steps in total did she take to get from point A to B.

(A) 7 (B) 8 (C) 17 (D) 15 (E) 18

**Solution :**

When she takes two steps forward, she has to go 1 step back ward.

From the picture given above, she has taken 3 steps.

1st time |
landing in step 2 and going back to step 1 |
3 steps taken. | |

2nd time |
landing in step 3 and going back to step 2 |
6 steps taken. | |

3rd time |
landing in step 4 and going back to step 3 |
9 steps taken. | |

4th time |
landing in step 5 and going back to step 4 |
12 steps taken. | |

5th time |
landing in step 6 and going back to step 5 |
15 steps taken. | |

6th time |
landing in step 7, reached destination |
17 steps taken. |

**Question 5 :**

If Cmn = C(m + n), for what value of n is Cmn neither positive nor negative ?

(A) -C (B) -m (C) 2m (D) 0 (E) 1/m

**Solution :**

We must pick value of n that makes the expression O, since O neither positive nor negative. This occurs when n is the negative of m.

Hence the value of n is -m.

**Question 6 :**

Two sides of a triangle at 6 and 8. What is the length of the third side ?

(A) 2 (B) 4 (C) 5 (D) 10 (E) Cannot be determined

**Solution :**

The sum of length of 2 sides will be greater than the other side. But we could not say the exact length of third side.

Hence, we cannot determine.

**Question 7 :**

2 + (1/3) = 14/b, what is b ?

(A) 3 (B) 6 (C) 7 (D) 9 (E) 28

**Solution :**

2 + (1/3) = 14/b

(6 + 1)/3 = 14/b

7/3 = 14/b

b = 14 (3)/7

b = 6

**Question 8 :**

The radius of circle A is x and the radius of circle B is 2. If the circumference of circle A is two times the circumference of the circle B, find the value of x.

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

**Solution :**

2πx = 2[2π(2)]

2πx = 2(4π)

2πx = 8π

Divide each side by 2π.

x = 4

**Question 9 :**

In the formula V = r^{2}h, if h is doubled and r is tripled, then V is multiplied by ?

(A) 6 (B) 9 (C) 12 (D) 18 (E) 36

**Solution :**

h = 2h, r = 3r

V = r^{2}h

V = (3r)^{2}(2h)

V = 9r^{2}(2h)

V = 18r^{2}h

**Question 10 :**

Max A returns the largest value in the set A, min A returns the lowest value in the set A. For example, max {1, 2, 3} = 3 and min {0, 4, 5} = 0. What is max {min{x, 2x, 3x}, max{x/2, x/4,x/8}} ?

(A) x (B) 2x (C) x/2 (D) 3x

(E) cannot be determined.

**Solution :**

The answer cannot be uniquely determined, since we do not know if x is negative or positive.

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