Would you guys mind giving me your thoughts regarding the following problems? If you prefer to read the actual questions, the pdf for this test is located at http://www.ets.org/Media/Tests/GRE/pdf/Math.pdf. Thanks a bunch.

23.

In the euclidean plane, point A is on a circle centered at point O, and O is on a circle centered at A. The circles intersect at points B and C. What is the measure of the angle BAC?

ans. 120 degrees

29.

Assume that p is a polynomial function on the set of real numbers. If p(0) = p(2) = 3 and p'(0) = p'(2) = -1, then integral(0 to 2) {xp''(x)dx =?

ans. -2

32.

When 20 children in a classroom line up for lunch, Pat insists on being somewhere ahead of Lynn. If Pat's demand is to be satisfied, in how many ways can the children line up?

ans. 20!/2

I know the answer is not 20!

36.

For each real number x, let mu(x) be the mean of the numbers 4, 5, 7, 9 and x; and let n(x) be the median of these five numbers. For how many values of x is mu(x) = to n(x)?

ans. 3

mu(x) = (25 + x)/5

50.

How many continuous real-valued functions f are there with domain [-1,1] such that (f(x))^2 = x^2 for each x in [-1,1]?

ans. four

63.

At how many points in the xy-plane do the graphs of y = x^12 and y = 2^x intersect?

ans. Three

I tried to solve this and get to the point, 12 log x = x log 2.