2000 TRINITY MATH TRIATHLON

1. 

2.  Which of the following is NOT an integer?

A. 0
B. 2
C. -2
D. ½ 

3. A salesperson wants to rent a car for one day.  Rental Agency A charges $35 per day plus 10 cents per mile drive.  Rental Agency B charges $30 per day plus 20 cents per mile driven.  If she plans to drive 100 miles, which agency will give the better rate?

4. An island has no money; it instead has the following exchange rate:

50 bananas = 20 coconuts
30 coconuts = 25 fish
100 fish = 1 hammock

How many bananas equal 1 hammock?

5. Which of the following is closest to 500? 

A. 33% of 1200 
B. 75% of 800 
C. 400% of 120
D. 90% of 800

6. A man takes one hour to dig a hole 2 meters long, 2 meters wide, and 2 meters deep.  How long would it take the same man to dig a second hole 4 meters long, 4 meters wide, and 4 meters deep, if he digs at the same rate of speed as he did for the first hole?

7. A solid pyramid-like stack is made from a number of identical blocks.  A side and top view of the stack follow.  How many blocks were used for the stack?

8. A perfect number equals the sum of its factors excluding itself.  For example, 6 is a perfect number because it has factors other than itself of 1, 2, and 3 and 1 + 2 + 3 = 6.  Which of these numbers is also a perfect number?

A. 8 
B. 18 
C. 28
D. 38

9.  Four congruent circles are packed into a square of side 12" as shown in the figure.  What is the area of the part of the square NOT covered by the circles?  (Leave  in your answer.) 

10. Jessica, Amy, Marybeth, and Tracie all eat breakfast together every morning.  Each morning they like to line up differently.  How many days can they go without repeating the same order?

11. By drawing two straight lines, divide the face of a clock into three regions such that the numbers in the regions have the same total. 

12.   The odometer of the family car read 15951 miles when the driver noticed that the number read the same backwards and forwards (a palindrome).  "Curious," said the driver to herself.  "It will be a long time before that happens again."  But exactly two hours later, the odometer showed another number that read the same backwards and forwards!  If the car stayed at the same speed, how fast was the car traveling in those two hours?
 
 
 

13.  Harry has 3 sisters and 5 brothers.  His sister Harriet has S sisters and B brothers.  What is the product of S and B?

14.  Six students each try to guess the number of candies in a jar.  The six guesses are 42, 49, 52, 59, 62, and 65.  One guess is 12 away from the correct number, and the other guesses are 1, 4, 6, 9, and 11 away from it.  How many candies are in the jar?

15.  Adam, William, and Laurie are shopping in a store that is having a sale in which all merchandise is 20 percent off.  The state charges a 10 percent sales tax.  Adam says, "I'm going to pay less if I have them calculate the discount first and then the tax."  William says, "I think you're wrong.  Calculate the tax first, then the discount and you'll pay less."  Laurie says, "You guys are all messed up.  Either way it's the same."  Who is right?

16.  The figure shows three face diagonals of a cube.  What is the measure of angle ABC?

17.  Two different numbers are drawn from the set {2, 3, 4, 5, 6} without replacement.  What is the probability that the product of the numbers selected is a multiple of 3?

18.  For a counting number n, .  So, for example, . 
Solve for n: 

19.  Find the eighth term of a sequence where the first term is 1, the second term is 2, and each term after this is the sum of the previous term and one, divided by the term before that.

20.  What is the value of x if