1. If [latex]1+x+{ x }^{ 2 }+{ x }^{ 3 }=60[latex] then the average (arithmetic mean) of [latex]x,{ x }^{ 2 },{ x }^{ 3 },{ x }^{ 4 }[latex] is equal to which of the following?
A [latex]12x[latex]
B [latex]15x[latex]
C [latex]20x[latex]
D [latex]30x[latex]
E [latex]60x[latex]
2. [latex]0 < x < 2[latex]
| Quantity A | Quantity B |
| [latex]{ x }^{ 2 }[latex] | [latex]\sqrt { x }[latex] |
3. [latex]x > y > 0[latex]
| Quantity A | Quantity B |
| [latex]x-y[latex] | [latex]\frac{ x }{ 3 }+\frac{ y }{ 3 }[latex] |
4. If [latex]a, b[latex], and [latex]c[latex] are not equal to [latex]0[latex] or [latex][latex]1 and if [latex]{ a }^{ x }= b, { b }^{ y }= c[latex], and [latex]{ c }^{ z }= a[latex], then [latex]xyz =[latex]
(A) [latex]0[latex]
(B) [latex]1[latex]
(C) [latex]2[latex]
(D) [latex]a[latex]
(E) [latex]abc[latex]
5. If [latex]x = { 10 }^{ 1.4 }, y = { 10 }^{ 0.7 }[latex], and [latex]{ x }^{ z } = { y }^{ 3 }[latex], then what is the value of [latex]z[latex] ?
(A) [latex]0.5[latex]
(B) [latex]0.66[latex]
(C) [latex]1.5[latex]
(D) [latex]2[latex]
(E)[latex] 3[latex]
6. A perfect square is a positive integer which when square rooted results in an integer. If [latex]N={ 3 }^{ 4 } *{ 5 }^{ 3 }*7[latex], then what is the biggest perfect square that is a factor of [latex]N[latex] ?
(A) [latex]{ 3 }^{ 2 }[latex]
(B) [latex]{ 5 }^{ 2 }[latex]
(C) [latex]{ 9 }^{ 2 }[latex]
(D) [latex]{ (9*5) }^{ 2 }[latex]
(E) [latex]{ (3*5*7) }^{ 2 }[latex]
7. In which one of the following choices must [latex]p[latex] be greater than [latex]q[latex]?
(A) [latex]{ 0.9 }^{ p } = { 0.9 }^{ q }[latex]
(B) [latex]{ 0.9 }^{ p } = { 0.9 }^{ 2q }[latex]
(C) [latex]{ 0.9 }^{ p }>{ 0.9 }^{ q }[latex]
(D) [latex]{ 9 }^{ p } < { 9 }^{ q }[latex]
(E) [latex]{ 9 }^{ p } > { 9 }^{ q }[latex]
8.
| Quantity A | Quantity B |
| [latex]{ x({ x }^{ 2 }) }^{ 4 }[latex] | [latex]{ ({ x }^{ 3 }) }^{ 3 }[latex] |
Answers:
1 B
2 D
3 D
4 B
5 C
6 D
7 E
8 C
