[Math Center]


Quantity A Quantity B
[latex]{ 950 }^{ 2000 }[latex]  [latex]{ 10 }^{ 2000 }[latex]


2. Which of the following integers are multiples of both [latex]2[latex] and [latex]3[latex] ?
Indicate all such integers.

(A) [latex]8[latex]
(B) [latex]9[latex]
(C) [latex]12[latex]
(D) [latex]18[latex]
(E) [latex]21[latex]
(F) [latex]36[latex]


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

(A) [latex]1[latex]
(B) [latex]2[latex]
(C) [latex]4[latex]
(D) [latex]6[latex]
(E) [latex]11[latex]


4.  What is the least positive integer that is not a factor of and is not a [latex]25[latex]! prime number? 

(A) [latex]26[latex]
(B) [latex]28[latex]
(C) [latex]36[latex]
(D) [latex]56[latex]
(E) [latex]58[latex]


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

(A) [latex]3072[latex]
(B) [latex]3078[latex]
(C) [latex]3084[latex]  
(D) [latex]3088[latex]
(E) [latex]3094[latex]


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

(A) [latex]8[latex]
(B) [latex]12[latex]
(C) [latex]15[latex]
(D) [latex]18[latex]
(E) [latex]21[latex]



Quantity A Quantity B
The first number larger than [latex]300[latex] that is a multiple of both [latex]6[latex] and [latex]8[latex] [latex]324[latex]



Quantity A Quantity B
Least common multiple of the two positive integers [latex]m[latex] and [latex]n[latex] [latex]mn[latex]


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

(A) [latex]1[latex]
(B) [latex]2[latex]
(C) [latex]3[latex]
(D) [latex]5[latex]
(E) [latex]10[latex]


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

(A) [latex]3[latex]
(B) [latex]5[latex]
(C) [latex]11[latex]
(D) [latex]17[latex]
(E) [latex]19[latex]




1 B
2 C,D,F
3 B
4 E
5 A
6 B
7 B
8 D
9 A
10 D