Summary: Problems Of The Week
Due January 22nd
Make sure to review the guidelines before you start!
1. Let ABCD be a rectangle such that AB= 32 cm and BC= 10 cm . Let M be a point on AB such
that AM=11 cm , N be a point on BC such that BN=4 cm , P be a point on CD such that CP=11
cm , and Q be a point on DA such that DQ=4 cm . What is the number of the square centimeters
in the area of the quadrilateral MNPQ ?
2. Alia's digital clock read 5:16 a.m. when she left for school. When she returned home 6 hours
and 11 minutes later, the clock read 3:37 a.m. because the power had gone off during the day. If
her clock automatically reset to 12:00 a.m. when the power was restored, at what time that
morning did the power return?
3. A sum is formed by alternatively adding and subtracting consecutive odd integers starting with
1 and ending with 1413 as indicated. What is the sum 1 - 3 + 5 - 7 + 9 -11 + ... + 1409 - 1411
+1413? (Do not add all these numbers... please!)
4. Angel wants to sell 90 identical pencils in groups of 5 or 2. In how many ways can the pencils
be grouped? (Do not just give me a number, explain why that is the correct number.)
5. Exactly one ordered pair of positive integers (x,y) satisfies the equation 19 x + 17 y = 108 .
What is the sum of x+y ? How did you find (x,y)?
Problems are from MAA American Mathematics Competitions and Laura's head!