Math 396

The MTH 386 Problem Solving Exam will cover the following strategies:

From book: Chapters 1-7,11,12:

·  Draw a diagram

·  Make a systematic list

·  Eliminate possibilities

·  Use Matrix Logic

·  Look for a Pattern

·  Guess and Check

·  Identify Subproblems

·  Work Backwards

·  Venn Diagrams

From In-class work:

·  Visual Methods (i.e., percentage, ratio and puzzle problems)

·  Counting

·  Venn Diagrams

On the exam you may use any of these strategies you wish to solve the problem unless the problem specifies which strategy to use in which case you must use that strategy.

·  You may use a calculator on the exam

·  Cell phones must be off

·  You may NOT use notes


Sample Problems

1.  Solve using visual methods: The ratio of teachers to children at Great Start Preschool is now 2:9. If 5 more teachers were hired, the ratio would be 1:3. How many children attend Great Start Preschool?

2.  Solve using A GUESS AND CHECK TABLE (clearly label columns in the table): A group of friends decided to rent a house in Aspen, Colorado, for a week of skiing. They each had to chip in $70 for the week’s lodging. If they had been able to convince three more people to go, the cost per person would have been reduced by $14. What was the rent for the week?

3.  When I reset my clocks for daylight saving time, I took care to make sure that each one had exactly the same time on it. A week later however, I noticed that the clock on the VCR was 14 minutes slow. I didn’t have time to reset it, and as I drove to work, I noticed that my car clock was 7 minutes fast. I decided not to reset the slow clocks, but I finally got sick of it and changed them when the car clock was exactly one hour ahead of my VCR clock. I initially set the clocks to daylight saving time on a Sunday. Ho many days later, and on what day of the week, did I reset them?

4.  Four friends get together. One tells the truth all the time. One lies all the time. One tells the truth on odd-numbered days and lies on even numbered days. One tells the truth on even-numbered days and lies on odd-numbered days. One day in May, they made the following statements:

Abe: I lied yesterday.

Blanca: Today is the twelfth.

Carol: Yesterday’s date was even.

Doug: Carol’s statement is true.

Which of the four friends tells the truth on even-numbered days and lies on odd-numbered days?

5.  Solve using VENN DIAGRAMS (clearly label circles): A number of people in the Atlanta Braves organization got together recently for a party. Of those, 1/12 were all-stars; 2/3 of the all-stars were hitters. Of the people at the party, 1/2 were players, and 1/2 of the players were neither hitters nor all-stars. Of the hitters, 1/4 were all-stars. There were 6 hitters who were not all-stars. How many people were at the party?

6.  Solve by working backwards: Leona set up a fruit stand to sell some of the crop of oranges. The first person who came by bought 1/3 of her oranges. The second person bought 4. The third person then bought 1/4 of the remaining oranges. Leona took the last 15 oranges home and made orange juice. How many oranges did Leona have when she set up the fruit stand?

7.  Three couples are good friends. At a dinner party one night, they discovered that their anniversaries were in different months: May, June, and July. They also discovered that they had each been married a different number of years: 11, 12, and 13. From the clues below, match up each husband (one is Pierre) with each wife (one is Lorna), the month of their anniversary, and the number of years each couple has been married.

  1. Jorge and his wife have 3 children. Their anniversary is not in July. They have not been married as long as Tara and her husband have.
  2. Nylia and her husband have 4 children. Their anniversary is in June. They have been married longer than Ahmed and his wife.

8.  A bag contains 20 jelly beans. There are 10 black, 6 red, and 4 green.

  1. How many ways can you reach into the bag and grab a handful of 8 jelly beans?
  2. How many ways can you choose 8 jelly beans where 4 are black and 4 are green?
  3. Suppose you have 2 black, 1 red and 1 green jelly bean. How many different ways can you line them up where order matters, but you cannot tell the black jelly beans apart?