MA 137 Exam Three Review Problems Note: This is NOT a practice exam. It is a collection of problems to help you review some of the material for the exam and to practice some kinds of problems. This collection is not necessarily exhaustive; you should expect some problems on the exam to look different from these problems.In addition to looking at old homework assignments and quiz problems, you might want to give these problems a try.Textbook Chapter 3 Test (p 210) #12Textbook Chapter 4 Test (p 252) #1-11, 13, 15Textbook Chapter 5 Test (p 336) #2, 31. Classify the following statements as True or False. Explain your answers.a. 8 | 4b. 0 | 4c. 4 | 0d. If a number is divisible by 4 and by 6, then it is divisible by 24.e. If a number is not divisible by 12, then it is not divisible by 3.2. Test the following number for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, and 11. Show how the divisibility tests justify your answers!a. 83,160b. 83,1933. Fill each blank with 1 digit to make the statement true (find all possible answers). Be able to explain your answers using divisibility tests.a. 6 | 87___4b. 9 | 4___856c. 11 | 998___54. Determine whether the following numbers are prime or composite:a. 143b. 2235. Construct a number that has exactly five factors. Explain your work. (Hint: the question asks for factors, not prime factors.)6. Use factor trees to find the prime factorizations of the following:a. 172b. 288c. 260d. 1117. Two bells ring at 8:00 A.M. For the remainder of the day, one bell rings every half-hour, and the other bell rings every 45 minutes. What is the next time that the bells will ring together? What does this question have to do with the material we’ve been studying?p. 18. The numbers 2 and 3 are consecutive primes, because they are consecutive numbers that are both prime. Are any two other numbers consecutive primes? Justify your answer.9. A chewing gum factory packages five sticks of gum into a small pack, and puts three small packs together to make a large pack. A total of 43,860 sticks of gum are produced in a unit of time. How can you use divisibility rules to decide whether a whole number offull large packs are produced in that time? Do it!10. A stamp collector has 280 stamps from North America and 264 stamps from South America. The collector wants to place the same number of stamps on each page of a large album, but he does not want to mix the stamps from different continents. What is the greatest number of stamps the collector can place on each page? How many pages would the book have? What does this question have to do with the material we’ve been studying?11. Solve the following:a. –6 – 2 =b. 8 – (–1) = c. –23 + 43 = d. –4 × –8 = e. 16 × –3 = f. 408 ÷ –3 = 12. A sports announcer kept track of the yardage gained and lost by the Boilermakers over a series plays in a football game. The announcer’s notepad showed the following : +8, –3, +34, +2, –14, 0, –1. What was the net yardage gained or lost of this series of plays?13. Give three equivalent fractions for each of the following:a. 67b. 0100c. 152514. If represents 35, draw and explain a picture to represent 1.15. If represents 35, draw and explain a picture to represent 910.16.If each of the grey bars in this diagram represent a unit, what is the length of a white bar? Explain.p. 217. A store had a new spool of ribbon that held 33 yards of ribbon. Sally bought 13 of the spool to decorate her teddy bears. Sam bought 12 of the remaining amount to use as part of his Halloween costume. Sarah needed 8 yards for a bunch of wedding decorations. Was there enough ribbon on the spool for Sarah? Was any ribbon left on the spool after her purchase, or did she need to go find another store with more ribbon?18. Lindsey made 24 cookies. Kyle ate 13 of the cookies. Matthew ate 14 of what remained. Jillian ate 13 of what remained. What fraction of the cookies was left when Lindsey returned? 19. Which is greater, 23 of 30 or 35 of 50? How do you know?20. Which is greater, 45 of 25 or 14 of 84? How do you know?21. Which is greater, 764 or 516? How do you know?22. Danny needed to drill a hole to mount a bathroom fixture on the wall. He found that a 38-inch drill bit was too big, and a 14-inch drill bit was too small. Which of the following sizes could possibly be right for the job: 18, 364, 316, 2364, 764, 1332? How do you know?23. Find two fractions that are larger than 78 but less than 1.24. Which fraction is larger: 67 or 56? How do you know?p.