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

 

Copyright © 2017 by MOEMS® (Mathematical Olympiads for
Elementary and Middle Schools). All rights reserved.

 

a

a
a
October's Problem
a

As shown, three 3-digit numbers have a 4-digit sum. Different letters represent different digits. What is the greatest prime factor of the sum, ACCA?

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

 

 

 

a

a
a
September's Problem
a

An inexpensive toy normally sells for 20 cents each. At a special reduced price, a store sold all of its toys, one at a time, for a total of $3.91. How many of these toys were sold if the reduced price is a whole number of cents?

a
METHOD: Find the new price.
Divide 391 cents by the new price which is an odd whole number less than 20. The result must also be a whole number. Dividing by 19 leaves a remainder. 391 divided by 17 is 23. Thus 23 toys sold for 17 cents each.

a
a

 

 

 

a

a
a
August's Problem
a

David removes 30% of the water in a jar. He then removes 40% of what remains in the jar. What percent of the original amount of water is now in the jar?

a

METHOD 1: Use the percents remaining
When 30% of the water is removed, 70% remains. Then when 40% of that 70% is removed, 60% of the 70% remains. Thus, 0.6 × 70% = 42% of the original amount that remains in the jar.

METHOD 2: Use a convenient example
The answer will be the same no matter how much water the jar starts with, so assume the jar starts with 1000 mL of water. When 30% is removed (that is 300 mL) then 700 mL is left. Next, 40% of 700 mL = 280 mL is removed, leaving 420 mL in the jar. Thus 420 mL ÷ 1000 mL = 42% of the original amount remains in the jar.

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