1999 TRINITY MATH TRIATHLON

1. If a car is going 55 miles per hour, how far does it travel in three hours?

2.  A parking garage charges $1.50 for the first hour and $0.50 for each additional hour or part of an hour.  How much will it cost to park in the garage for 5 ½  hours?

3.  Round to the nearest integer: .

4. As shown in the figure below, a triangular corner with side lengths DB = EB = 1 is cut from equilateral triangle ABC of side length 3.  What is the perimeter of the remaining quadrilateral ADEC? 

5. What two positive integers whose product is 24 will have the smallest sum?

6.   Is the mathematical sentence Always, Sometimes, or Never true?

7.  Find G, if A = D, B = 4, E = 3, D = E, and G = A + 1.

8.  When looking at a tile floor, you notice that the pattern is made up of dots and lines, like the image at right.  How many dots would be necessary if the floor is a square region with 8 tiles on each side? 

9.  The average basketball score for a school basketball team is 70 points.  If the scores for four of five games are known to be 88, 72, 50, and 80, what is the missing score?

10.  One hundred students were asked if they liked Christian rock or classical music.  The results were that 5 students liked neither kind of music, 84 liked Christian rock, and 23 liked classical music.  How many students like both kinds of music?

11. Find the percent increase in the area of a circular pizza, if the radius is increased from ten inches to eleven inches.

12.   What is the area of the region that is formed by overlapping the two squares as shown?  The point D is in the center of the square ACEF, and the lengths of segments are
  AE = 6, CG = 2, and BF = 2.

13.  A man spent 1/3 of his money and lost 2/3 of the remainder.  He than had 12 pieces.  How many pieces did he have at first?

14.  Fifty umbrellas were sold on a rainy day.  Five times as many red as blue were sold, three times as many green as blue, nine more black than blue, and seven fewer purple than black.  Five umbrellas were purple and six were white.  How many of each color were sold?

15.  Three rectangles are lined up horizontally as shown.  The dimensions of rectangle A are 1 × 2, rectangle B are 2 × 4, and rectangle C are 4 × 8.  Find the area of the shaded region. 

16.  Evaluate: 

17.  A palindrome is a word that is the same forwards and backwards, like the word "mom."  How many three-digit numbers are number palindromes?

18.  Consider the integers from 1 to 100 (including 1 and 100).  What is the difference between the sum of all the even numbers and the sum of all the odd numbers?

19.  What is the units digit of  ?

20.  Maria buys candy bars at the price of 4 for $5 and sells them at a price of 3 for $5.  How many candy bars must she sell to make a profit of $100?