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1. A train traveling 60 miles per hour for 1 hour covers the same distance as a train traveling 30 miles per hour for how many hours?

　　A. 3

　　B. 2

　　C. 1

　　D. 1/2

　　E. 1/3

Answer: B

When the speed of a train in miles per hour is multiplied by the travel time in hours, the distance traveled by the train is obtained. The distance that the first train travels is 60 miles per hour times 1 hour, which is 60 miles. Using the variable x for the travel time, in hours, of the second train, the distance that the second train travels is 30 miles per hour times x hours, which is 30x miles. Since the two trains travel the same distance, 60 = 30x, which gives x = 2 hours, the travel time of the second train.

2. If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the greatest value?

　　A. f(-1)

　　B. f(0)

　　C. f(1)

　　D. f(3)

　　E. f(4)

3. Correct Answer: D

Explanation:

You can solve this by back solving – substitute the answer choices in the expression and see which gives the greatest value

　　A (-1 + 2) / (-1-2) = -2 / 2 = -1;

　　B (0 + 2) / (0-2) = 2/ -2 = -1;

　　C (1 + 2) / (1-2) = 3/-1 = -3;

　　D (3 + 2) / (3-2) = 5/1 = 5;

　　E (4+ 2) / (4-2) = 6/2 = 3

If you had just chosen the largest value for x you would have been wrong. So although it looks a long method, it is actually quick and accurate since the numbers are really simple and you can do the math in your head.

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