# Sample Questions for Math Relay

1. The measure of an angle is 3 times the measure of its complement. Find the measure of the angle in degrees.

2. If Q (-3, 2), R (4, 2), and S (4, -2) are three vertices of rectangle QRST, what is the coordinates of T?

3. A 9-liter pail is filled with water at the rate of ˝ liter per minute. How many minutes will it take to fill 2/3 of this pail?

4. Given that a, b, and c are all positive, and that ab = 21, ac = 18, and bc = 42, find a + b + c.

5. According to the pattern suggested by the four examples below, how many consecutive odd integers are required to give a sum of 144?

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

1 + 3 + 5 + 7 + 9 = 25

6. 3 calculus books weigh as much as two geometry books. 7 geometry books weigh as much as nine algebra books. 6 trigonometry books weigh as much as 8 calculus books. How many algebra books weigh as much as 21 trigonometry books?

7. What two-digit integer is six times the sum of its digits?

8. On a map, 1 3/4 inch represents 10 miles. If two towns are 28 inches apart on the map, how far are they actually apart?

9. Detective Jones thought of two numbers. Their sum was 20 and the sum of their squares was 300. What was their product?

10. When 110 x 210 x 510 is multiplied out, how many digits are in the resulting number?

11. A triangle is drawn on a coordinate system. Its vertices are (0,4), (0,7), and (6,4). A larger triangle is drawn by multiplying each x- and y-coordinate by 2. How many times larger than the area of the larger triangle is the area of the smaller triangle?

12. Two numbers are said to be “relatively prime” if their greatest common factor is 1. How many integers greater than 10 and less than 30 are relatively prime with 28?