1. If \(\)1+x+{ x }^{ 2 }+{ x }^{ 3 }=60\(\) then the average (arithmetic mean) of \(\)x,{ x }^{ 2 },{ x }^{ 3 },{ x }^{ 4 }\(\) is equal to which of the following?

A \(\)12x\(\)

B \(\)15x\(\)

C \(\)20x\(\)

D \(\)30x\(\)

E \(\)60x\(\)

2. \(\)0 < x < 2\(\)

Quantity A |
Quantity B |

\(\){ x }^{ 2 }\(\) | \(\)\sqrt { x }\(\) |

3. \(\)x > y > 0\(\)

Quantity A |
Quantity B |

\(\)x-y\(\) | \(\)\frac{ x }{ 3 }+\frac{ y }{ 3 }\(\) |

4. If \(\)a, b\(\), and \(\)c\(\) are not equal to \(\)0\(\) or \(\)\(\)1 and if \(\){ a }^{ x }= b, { b }^{ y }= c\(\), and \(\){ c }^{ z }= a\(\), then \(\)xyz =\(\)

(A) \(\)0\(\)

(B) \(\)1\(\)

(C) \(\)2\(\)

(D) \(\)a\(\)

(E) \(\)abc\(\)

5. If \(\)x = { 10 }^{ 1.4 }, y = { 10 }^{ 0.7 }\(\), and \(\){ x }^{ z } = { y }^{ 3 }\(\), then what is the value of \(\)z\(\) ?

(A) \(\)0.5\(\)

(B) \(\)0.66\(\)

(C) \(\)1.5\(\)

(D) \(\)2\(\)

(E)\(\) 3\(\)

6. A perfect square is a positive integer which when square rooted results in an integer. If \(\)N={ 3 }^{ 4 } *{ 5 }^{ 3 }*7\(\), then what is the biggest perfect square that is a factor of \(\)N\(\) ?

(A) \(\){ 3 }^{ 2 }\(\)

(B) \(\){ 5 }^{ 2 }\(\)

(C) \(\){ 9 }^{ 2 }\(\)

(D) \(\){ (9*5) }^{ 2 }\(\)

(E) \(\){ (3*5*7) }^{ 2 }\(\)

7. In which one of the following choices must \(\)p\(\) be greater than \(\)q\(\)?

(A) \(\){ 0.9 }^{ p } = { 0.9 }^{ q }\(\)

(B) \(\){ 0.9 }^{ p } = { 0.9 }^{ 2q }\(\)

(C) \(\){ 0.9 }^{ p }>{ 0.9 }^{ q }\(\)

(D) \(\){ 9 }^{ p } < { 9 }^{ q }\(\)

(E) \(\){ 9 }^{ p } > { 9 }^{ q }\(\)

8.

Quantity A |
Quantity B |

\(\){ x({ x }^{ 2 }) }^{ 4 }\(\) | \(\){ ({ x }^{ 3 }) }^{ 3 }\(\) |

##### Answers:

1 B

2 D

3 D

4 B

5 C

6 D

7 E

8 C