# 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 1^{2} + 2^{2} +…+10^{2} = 385 , then what is the sum 2^{2} + 4^{2} +…+ 20^{2} ? 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

play?

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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