Understand the problem For how many positive integers (n) does 1+2+3+4+….+n evenly divide from 6n? (a)3. (b)5. (c)7. (d)9. (e)11 Source of the problem American Mathematical Contest 2005 10A Problem 21 Topic Number Theory Difficulty Level...

Understand the problem Let S be the set of the 2005 smallest positive multiples of 4, and let T be the set of the 2005 smallest positive multiples of 6. How many elements are common to S and T? (a) 166. (b)333. (c)500. (d)668. (e)1001 Source of...

Understand the problem How many 4 digit positive numbers have at least that is a 2 or a 3? (a)2439. (b)4096. (c)4903. (d)4904. (e)5416 Source of the problem American Mathematical Contest 2006 10 A Problem 21 Topic Combinatorics Difficulty Level 4/10...

Understand the problem A group of pirates agree to divide a treasure chest of gold coins among themselves as follows. The pirate to take a share takes of the coins that remain in the chest. The number of coins initially in the chest is the smallest number for which...

Understand the problem A sequence of natural numbers is constructed by listing the first , then skipping one, listing the next , skipping , listing , skipping , and, on the th iteration, listing and skipping . The sequence begins . What is the th number in the...

Understand the problem Suppose that the number (a) satisfies the equation (a)+(frac{1}{a})=(4) What is the value of (a^4)+(frac{1}{a^4})? (a) 164. (b)172. (c)192. (d)194. (e)212 Source of the problem American Mathematical Contest 2007...