April 2002 TRINITY MATH TRIATHLON

1.  During a mathematics test, 18 students answered question 1 correctly, 23 students answered question 2 correctly, 8 of them got both problems correct and 11 students answered incorrectly on both questions.  How many students took the test?

2.  A room has two walls that measure 8 feet by 12 feet and two walls that measure 8 feet by 14 feet.  This room has two windows-one is 4 feet by 5 feet, and the other is 3 feet by 5 feet-and one door, which is 4 feet by 7 feet.

 a.  Paint for the ceiling will cover 300 square feet per gallon.  How many one-gallon cans of paint will be needed to paint the ceiling with two coats?

 b.  Wallpaper is sold in 40-square-feet rolls.  How many rolls of wallpaper must be purchased to cover the walls?

3.   The following facts are known:

 Fact #1: All birds fly.
 Fact #2: Some birds are cardinals.
 Fact #3: All robins sing.
 Fact #4: Some cardinals sing.
 Fact #5: All cardinals and robins are birds.

Assuming all of the above facts are true, decide whether the following statements are TRUE or FALSE:

a. All flying birds are robins.
b. All flying cardinals sing.
c. No flying cardinals sing.
d. Birds that do not sing are not robins
e. All cardinals do not fly.

4.  A car travels 40 km/h for 20 km, 36 km/h for 24 km, and 48 km/h for 16 km.  What is the car's average speed?  (Hint: the answer is NOT 41 km/hr.)

5.  There are five flavors of Original Fruit Skittles. However, by eating more than one flavor at a time, one can create hybrid flavors.

a.  If two Skittles are chosen to be eaten simultaneously, their flavors may match or be distinct.  How many flavors are possible when eating two at once? 

b.  If three Skittles are chosen to be eaten simultaneously, how many flavors are possible?