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EXAM 3
Math 365_503
Oct. Dec. 3, 1999

Name SSN

Part I. Select the best answer for each question. You may write a statement in support of your answer if so desire. (3 points each)

  1. TrueFalse If tex2html_wrap_inline63 then GCD(a, b)=a.
  2. TrueFalse If tex2html_wrap_inline67 then either tex2html_wrap_inline63 or tex2html_wrap_inline71 .
  3. TrueFalse If a, b and c are whole numbers such that a=bc then c is a
    multiple of a.
  4. TrueFalse For any whole number n it is always the case that n divides 0.
  5. TrueFalse If a, b and c are whole numbers such that tex2html_wrap_inline91 , then both a
    and b divide c.
  6. TrueFalse If tex2html_wrap_inline99 and tex2html_wrap_inline101 then GCD(m,n)=ac.
  7. TrueFalse The number 456,323,456,786 is divisible by 4.

Part II. Answer each question. For full credit, show work necessary to arrive at your answer.

  1. Decide whether or not 441 is a prime number. If it is not prime, write a factor tree. (6 points)
  2. Consider the statement ``If tex2html_wrap_inline105 then either tex2html_wrap_inline63 or tex2html_wrap_inline71 .'' Either prove this statement or find a counter-example. (6 points)

  3. Find the prime power representation of 2250. (5 points)

  4. Find the GCD(36,40) and LCM(36,40). (6 points)

  5. Fill in the missing digit so that tex2html_wrap_inline115 . (4 points)
  6. Let tex2html_wrap_inline117 . Does 3 divide n? Why or why not? (4 points)

  7. Find the GCD(624, 1024). (Hint: Euclidean Algorithm) (6 points).

  8. Are the two rational numbers tex2html_wrap_inline123 and tex2html_wrap_inline125 equivalent? If so, show why, if not, find some

    rational number between these two numbers. (6 points)

Part III. Answer the following questions as completely as possible.

  1. for each of the following problems write an appropriate equation to solve the problem, draw an appropriate illustration (model) of the problem, and then solve the equation.
    1. Lynn and Kyle are working on a puzzle. Lynn worked first and completed one-third of the puzzle. Kyle has completed three-fourths of the rest of the puzzle. How much of the puzzle has been completed? (6 points)
    2. It takes two-thirds of a container of orange concentrate to make one batch of orange juice. Suppose you have four and one-half containers of orange concentrate. How many batches of orange juice can you make. (6 points)

  2. If tex2html_wrap_inline63 and tex2html_wrap_inline71 then tex2html_wrap_inline105 . Prove this statement. (10 points)

  3. Solve tex2html_wrap_inline133 . (8 points)
  4. Order, from smallest to largest, the following set of numbers. tex2html_wrap_inline135 (4 points)


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Next: About this document

Andrew Diener
Tue Dec 7 13:17:00 CST 1999