Math 129 - LAB 5

1. Let a, b, c, and d be integers. Prove that if a|b, b|c, and c|d, then a|d.

2. Give an example of a statement “If A, then B” that is false.

3. Ann gave Betty as many cents as Betty had. Betty then gave Ann as many cents as Ann
then had. At this point, each had 12 cents. How much did Ann have at the beginning?

4. Is there a four- digit number of the form aabb that is a perfect square (that is, aabb=N^2 for
some integer N)? If so, find all such numbers . If not, explain why this is the case.

5. Find three consecutive odd integers whose sum is 117. Can you find three even integers
whose sum is 117? Explain.

6. Find the angles of a triangle if one angle is half the second, and the third is twice the sum
of the first two .

7. If 12 + 22 +…+102 = 385 , then what is the sum 22 + 42 +…+ 202 ? Please do not use
your calculator on this one .

8. Jan, Amber, and Leslie play first base, second base, and third base on the school’s
softball team but not necessarily in that order . Jan and the person who plays third base
took Leslie to the movies yesterday. Jan does not get along with the person who plays
first base. Who’s on first? Can you determine which positions Jan, Amber, and Leslie

9. A certain rational number becomes 1 when 3 is added to its numerator and becomes ½
when 2 is added to its denominator . What is the rational number?

10. Brendan and Olivia go to a dinner party with four other couples. Each person shakes
hands with everyone he or she does not know. Later, Brendan does a survey and finds
that every one of the nine other partygoers shook hands with a different number of
people. How many people did Olivia meet for the first time?

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