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