1.
| Quantity A | Quantity B |
| [latex]\frac {{ 2 }^{ 30 }-{ 2 }^{ 29 }}{ 2 }[latex] | [latex]{ 2 }^{ 28 }[latex] |
2.
| Quantity A | Quantity B |
| [latex]{ 3 }^{ x+1 }[latex] | [latex]{ 4 }^{ x }[latex] |
3. [latex]x[latex] and [latex]m[latex] are positive numbers, and [latex]m[latex] is a multiple of [latex]3[latex].
| Quantity A | Quantity B |
| [latex]\frac {{ x }^{ m }}{{ x }^{ 3 }}[latex] | [latex]{ x }^{ m/3 }[latex] |
4. If [latex]n={ 2 }^{ 3 }[latex] then [latex]{ n }^{ n }=[latex]
(A) [latex]{ 2 }^{ 6 }[latex]
(B) [latex]{ 2 }^{ 11 }[latex]
(C) [latex]{ 2 }^{ 18 }[latex]
(D) [latex]{ 2 }^{ 24 }[latex]
(E) [latex]{ 2 }^{ 27 }[latex]
5. [latex]s[latex] and [latex]t[latex] are positive integers, and [latex]{ 32 }^{ s }={ 2 }^{ t }[latex]
| Quantity A | Quantity B |
| [latex]\frac{ s }{ t }[latex] | [latex]\frac{ 1 }{ 5 }[latex] |
6. Given the system [latex]{ x }^{ 2 }=4, { y }^{ 3 }=-8[latex], which of the following is NOT necessarily true?
(A) [latex]y < 0[latex]
(B) [latex]x < 5[latex]
(C) [latex]y[latex] is an integer
(D) [latex]x > y[latex]
(E) [latex]xy[latex] is an integer
7.
| Quantity A | Quantity B |
| [latex]x{ ({ x }^{ 2 }) }^{ 4 }[latex] | [latex]{ ({ x }^{ 3 }) }^{ 3 }[latex] |
8. If [latex]x < 0[latex] and [latex]y[latex] is [latex]5[latex] more than the square of [latex]x[latex], which one of the following expresses [latex]x[latex] in terms of [latex]y[latex]?
(A) [latex]x =\sqrt{ y-5 }[latex]
(B) [latex]x =-\sqrt{ y-5 }[latex]
(C) [latex]x =\sqrt{ y+5 }[latex]
(D) [latex]x =\sqrt{ { y }^{ 2 }-5 }[latex]
(E) [latex]x =-\sqrt{ { y }^{ 2 }-5 }[latex]
9. 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]
10. If [latex]p ={ 216 }^{ -1/3 }+{243 }^{ -2/5 }+{256 }^{ -1/4 }[latex], then which one of the following is an integer?
(A) [latex]p/19[latex]
(B) [latex]p/36[latex]
(C) [latex]p[latex]
(D) [latex]19/p[latex]
(E) [latex]36/p[latex]
11. 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]
12. If [latex]{ 3 }^{ 2 }{ 9 }^{ 2 }={ 3 }^{ x }[latex], what is [latex]x[latex]?
(A) [latex]2[latex]
(B) [latex]3[latex]
(C) [latex]4[latex]
(D) [latex]5[latex]
(E) [latex]6[latex]
13. [latex]80[latex] is divisible by [latex]{ 2 }^{ x }[latex]
| Quantity A | Quantity B |
| [latex]x[latex] | [latex]3[latex] |
14. For what positive integer is the square of the integer divided by the cube root of the integer equal to nine times the integer?
(A) [latex]4[latex]
(B) [latex]8[latex]
(C) [latex]16[latex]
(D) [latex]27[latex]
(E) [latex]125[latex]
Answer:
1 C
2 D
3 D
4 D
5 C
6 D
7 C
8 B
9 D
10 D
11 E
12 E
13 D
14 D
