[Math Center]

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