Elementary Math Olympiad - MOEMS Exams

Mathematical Olympiads for Elementary and Middle Schools (MOEMS) is a worldwide math competition, organized by a not-for-profit foundation with the same name. Two dozen other nations also participate in the competition. There are two divisions, Elementary and Middle School. Elementary level problems are for grades 4-6 and Middle School level problems are for grades 7-8, though 4-6 graders may participate in Middle School problems.

Some sample of problem from this course with their details solution.

Problem: Evaluate: 51 – 33 + 42 – 33 + 24 – 33 + 15 – 33. ( Source: 2020 Contest 1 division E Q1)
Solution : Strategy: Find the difference between each pair of numbers and then find the sum.
Notice that each pair (51 – 33) + (42 – 33) + (24 – 33) + (15 – 33) = (+18) + (+9) + (– 9) + (–18).
The differences result in two pairs of additive inverses, (+28) + (–28) + (+9) + (–9), which sum to 0.

METHOD 2 Strategy: Use the Commutative and Associative Properties to find the sum of the positive numbers and the sum of the negative numbers and then combine them.
Looking at the problem, there are four groups of −33: 4 ✕ (−33) = −132. Also, there are two groups of +66 (15 + 51 and 24 + 42): 2 ✕ (+66) = +132. It follows that (−132) + (+132) = 0.
METHOD 3 Strategy: Do the arithmetic left to right.

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