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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