**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.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**