1.

Quantity A |
Quantity B |

\(\)\frac {{ 2 }^{ 30 }-{ 2 }^{ 29 }}{ 2 }\(\) | \(\){ 2 }^{ 28 }\(\) |

2.

Quantity A |
Quantity B |

\(\){ 3 }^{ x+1 }\(\) | \(\){ 4 }^{ x }\(\) |

3. \(\)x\(\) and \(\)m\(\) are positive numbers, and \(\)m\(\) is a multiple of \(\)3\(\).

Quantity A |
Quantity B |

\(\)\frac {{ x }^{ m }}{{ x }^{ 3 }}\(\) | \(\){ x }^{ m/3 }\(\) |

4. If \(\)n={ 2 }^{ 3 }\(\) then \(\){ n }^{ n }=\(\)

(A) \(\){ 2 }^{ 6 }\(\)

(B) \(\){ 2 }^{ 11 }\(\)

(C) \(\){ 2 }^{ 18 }\(\)

(D) \(\){ 2 }^{ 24 }\(\)

(E) \(\){ 2 }^{ 27 }\(\)

5. \(\)s\(\) and \(\)t\(\) are positive integers, and \(\){ 32 }^{ s }={ 2 }^{ t }\(\)

Quantity A |
Quantity B |

\(\)\frac{ s }{ t }\(\) | \(\)\frac{ 1 }{ 5 }\(\) |

6. Given the system \(\){ x }^{ 2 }=4, { y }^{ 3 }=-8\(\), which of the following is NOT necessarily true?

(A) \(\)y < 0\(\)

(B) \(\)x < 5\(\)

(C) \(\)y\(\) is an integer

(D) \(\)x > y\(\)

(E) \(\)xy\(\) is an integer

7.

Quantity A |
Quantity B |

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

8. If \(\)x < 0\(\) and \(\)y\(\) is \(\)5\(\) more than the square of \(\)x\(\), which one of the following expresses \(\)x\(\) in terms of \(\)y\(\)?

(A) \(\)x =\sqrt{ y-5 }\(\)

(B) \(\)x =-\sqrt{ y-5 }\(\)

(C) \(\)x =\sqrt{ y+5 }\(\)

(D) \(\)x =\sqrt{ { y }^{ 2 }-5 }\(\)

(E) \(\)x =-\sqrt{ { y }^{ 2 }-5 }\(\)

9. 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 }\(\)

10. If \(\)p ={ 216 }^{ -1/3 }+{243 }^{ -2/5 }+{256 }^{ -1/4 }\(\), then which one of the following is an integer?

(A) \(\)p/19\(\)

(B) \(\)p/36\(\)

(C) \(\)p\(\)

(D) \(\)19/p\(\)

(E) \(\)36/p\(\)

11. 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 }\(\)

12. If \(\){ 3 }^{ 2 }{ 9 }^{ 2 }={ 3 }^{ x }\(\), what is \(\)x\(\)?

(A) \(\)2\(\)

(B) \(\)3\(\)

(C) \(\)4\(\)

(D) \(\)5\(\)

(E) \(\)6\(\)

13. \(\)80\(\) is divisible by \(\){ 2 }^{ x }\(\)

Quantity A |
Quantity B |

\(\)x\(\) | \(\)3\(\) |

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) \(\)4\(\)

(B) \(\)8\(\)

(C) \(\)16\(\)

(D) \(\)27\(\)

(E) \(\)125\(\)

##### 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