1.

Quantity A |
Quantity B |

\(\){ 950 }^{ 2000 }\(\) | \(\){ 10 }^{ 2000 }\(\) |

2. Which of the following integers are multiples of both \(\)2\(\) and \(\)3\(\) ?

Indicate all such integers.

(A) \(\)8\(\)

(B) \(\)9\(\)

(C) \(\)12\(\)

(D) \(\)18\(\)

(E) \(\)21\(\)

(F) \(\)36\(\)

3. If \(\)\frac { 1 }{ \left( { 2 }^{ 11 } \right) \left( { 5 }^{ 17 } \right) }\(\) is expressed as a terminating decimal, how many nonzero digits will the decimal have?

(A) \(\)1\(\)

(B) \(\)2\(\)

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

(D) \(\)6\(\)

(E) \(\)11\(\)

4. What is the least positive integer that is not a factor of and is not a \(\)25\(\)! prime number?

(A) \(\)26\(\)

(B) \(\)28\(\)

(C) \(\)36\(\)

(D) \(\)56\(\)

(E) \(\)58\(\)

5. If the least common multiple of \(\)m\(\) and \(\)n\(\) is \(\)24\(\), then what is the first integer larger than \(\)3070\(\) that is divisible by both \(\)m\(\) and \(\)n\(\)?

(A) \(\)3072\(\)

(B) \(\)3078\(\)

(C) \(\)3084\(\)

(D) \(\)3088\(\)

(E) \(\)3094\(\)

6. If \(\)x\(\) is divisible by both \(\)3\(\) and \(\)4\(\), then the number \(\)x\(\) must be a multiple of which one of the following?

(A) \(\)8\(\)

(B) \(\)12\(\)

(C) \(\)15\(\)

(D) \(\)18\(\)

(E) \(\)21\(\)

7.

Quantity A |
Quantity B |

The first number larger than \(\)300\(\) that is a multiple of both \(\)6\(\) and \(\)8\(\) | \(\)324\(\) |

8.

Quantity A |
Quantity B |

Least common multiple of the two positive integers \(\)m\(\) and \(\)n\(\) | \(\)mn\(\) |

9. Let \(\)P\(\) stand for the product of the first \(\)5\(\) positive integers. What is the greatest possible value of m if \(\)\frac{ P }{ { 10 }^{ m } }\(\) is an integer?

(A) \(\)1\(\)

(B) \(\)2\(\)

(C) \(\)3\(\)

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

(E) \(\)10\(\)

10. What is the greatest prime factor of \(\)({ 2 }^{ 4 })^{ 2 }-1\(\)?

(A) \(\)3\(\)

(B) \(\)5\(\)

(C) \(\)11\(\)

(D) \(\)17\(\)

(E) \(\)19\(\)

##### Answer:

1 B

2 C,D,F

3 B

4 E

5 A

6 B

7 B

8 D

9 A

10 D