<p>Thanks in advance for reading what is sure to be a long post.</p>

<p>Volume of a Solid</p>

<p>If the 3 visible sides of a rectangular shown above (too lazy to draw out, but basically front, top, and right side) have areas 10,36, and 10 respectively, what is the volume of the solid. The answer is 60, but alas, I have no idea why.</p>

<p>A Lot of Factors</p>

<p>X=(1/3 *3)(1/3^2 *3) (1/3^3 *3)...(1/3^50 *3)

The three dots (...) in the product above represent 46 missing factors of the form (1/3^n *3), where the integer n represents all of the consecutive integers from 4 to 49, inclusive. Which of the following is equal to X? The answer is 1/3^1225.</p>

<p>Deceptively Simple Work-Rate Problem</p>

<p>If a certain job can be performed by 20 clerks in 30 days, the number of clerks, working at the same rate, needed to perform the same job in 14 days is? The answer is 43, but I don't know how to get that.</p>

<p>Pendulum</p>

<p>The pendulum of a certain clock travels 30 degrees per swing. If the length of the pendulum is 3/pie meters and the pendulum swings back and forth once every second, what is the distance in meters covered by the lower end of the pendulum in one hour. The answer is 3600, but I got 1800. This is what I did. 30/360 times 6pie/6 and got .5 meters per second, then multiplied by 3600.</p>

<p>Searching for a Quicker Way</p>

<p>3, 2, 0, 6, 0, 8

If a and b represent any two unequal numbers from the list above, how many different values are possible for ab?</p>

<p>Obviously, anything times 0 is 0, and 3<em>2 is the same as 2</em>3, and there are few enough possibilities that I can make a chart, but is there a quicker way to do this?</p>