Data for a certain biology experiment are given in the table above.  If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?

If x is an integer, which of the following must be an odd integer?

On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship.  If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?

The sum of three integers is 40.  The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer.  What is the product of the three integers?

If w, x, y, and z are integers such that 1 < w < x < y < z and wxyz = 462, then z =?

~$C_{\left ( m,n \right )}=\frac{m!}{\left ( m-n \right )!n!}$~ for nonnegative integers m and n, ~$m\geq n$~.  If C_(5,3) = C_(5,x) and ~$x\neq 3$~, what is the value of x?

There are 11 women and 9 men in a certain club.  If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?

The operation  ~$\bigotimes $~ is defined for all nonzero numbers a and b by ~$a\bigotimes b=\frac{a}{b}-\frac{b}{a}$~ .  If x and y are nonzero numbers, which of the following statements must be true?

I.  ~$x\bigotimes xy = x(1\bigotimes y)$~
II.  ~$x\bigotimes y = -(y\bigotimes x)$~
III.  ~$\frac{1}{x}\bigotimes \frac{1}{y} = y\bigotimes x$~

Square S is inscribed in circle T.  If the perimeter of S is 24, what is the circumference of T?

The figure above shows the dimensions of a semicircular cross section of a one-way tunnel.  The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel.  If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?