This post contains problems from the first relay round of the Duke Math Meet 2009. Try to solve these problems.

**1A. Find the lowest positive angle that satisfies the equation expressed in degrees.**

**Discussion:**

Now this gives

or

Thus the possible values of are or .

Since we require the smallest positive angle hence the answer is .

**1B Let n be two times the tens digit of TNYWR. Find the coefficient of the term in the expansion of **

**Discussion:**

TNYWR is 3. Hence n = 6 Thus we are required to find coefficient of term in the expansion of

This can be easily found from trinomial expansion. The required term is

**1C Let k be TNYWR, and let n = k/2. Find the smallest integer m greater than n such that 15divides m and 12 divides the number of positive integer factors of m.**

**Discussion:**

k = 198, hence n = 99.

So we have to look at multiples of 15 greater than 99. We want 12 to divide the number of positive divisors of m.

Suppose . The number positive divisors of k is

The first multiple of 15 greater than 99 is . By inspection we see that m = 150.

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