You are here:Home > Olympiad Program > Contests > Samples > Problem of the Month > Awards > Enrollment > What They Wrote > MOEMS Board of Directors

 

Copyright © 2016 by MOEMS® (Mathematical Olympiads for
Elementary and Middle Schools). All rights reserved.

 

a

a
a
October's Problem
a

Vickie has 4 times as many pretzels as Angela. Vickie has 24 more pretzels than Angela. How many pretzels does Angela have?

a
A solution to this problem will appear along with next month’s problem.
a
a
a
a

 

 

a

a
a
September's Problem
a

Justin's new music player has more than 50 songs but less than 90 songs. The number of songs is 3 more than a multiple of 5. It is also 2 more than a multiple of 6. How many songs are on the player?

a

METHOD 1: Make a chart:
Make a table that compares sentence 2 against sentence 3 for the interval between 50 and 90.


There are 68 songs on the player.

METHOD 2: Use a simpler problem:
A multiple of 6 is one more than a multiple of 5 immediately following a common multiple. Following 0, 5 is one less than 6. Following 30, 35 is one less than 36. Following 60, 65 is one less than 66. This is between 60 and 90, so 3 more than the multiple is 68, the same as 2 more than the multiple of 6. The number of songs is 68.

METHOD 3: Find a pattern:
3 more than a multiple of 5 ends in 3 or 8. However, 2 more than a multiple of 6 is an even number, so the number of songs ends in 8: 58, 68, 78, or 88. Only 68 is 3 more than a multiple of 5 and also 2 more than a multiple of 6.
(Notice that the least common multiple of 5 and 6 is 30 and that all the numbers satisfying sentences 2 and 3 are 8, 38, 68, 98, 128, and so on.)

a
a
a
a

 

 

 

a

a
a
August's Problem
a

The members of a school club attend a movie. They pay a total of $100 for 15 movie tickets. Two members are adults and pay $11 each. The other members are all students. What is the price of a student ticket?

a

METHOD 1: Divide and conquer:
Two adult tickets cost $22, so the student tickets cost a total of $100 - $22 = $78. Divided among 13 students, each student ticket costs $6 .


METHOD 2: Use algebra:

Suppose each student ticket costs s dollars. Then 13s + 2(11) = 100 dollars. Solving, 13s = 78 and s = 6 dollars.

a
a
a
a

 

 

 

 

 

For many additional problems we highly recommend the following books:

Math Olympiad Contest Problems for Elementary and Middle Schools by Dr. G. Lenchner
and
Math Olympiad Contest Problems Volume 2 edited by Richard Kalman
and
MOEMS® Contest Problems Volume 3
edited by Richard Kalman & Nicholas J. Restivo.
are sources of many such problems.

Creative Problem Solving in School Mathematics 2nd Edition by Dr. George Lenchner
can help you to teach solving these types of problems