Young Mathematician Olympiad, 2018-2019, Stage B

Grades 3-4 Grades 5-6

• Question from sources: Grades 5-6(4) - Divisible by 2 or 5 but not 3

  How many five-digit numbers are divisible by 2 or 5, but not divisible by 3?

  Topics:

  Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rules by 3 and 9 Combinatorics -> Product Rule / Rule of Product
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage B, Grades 5-6 Question 4

• Question from sources: Grades 3-4(5), Grades 5-6(5) - Hexagon and Triangle

  A regular hexagon and an equilateral triangle have the same perimeter. The area of the triangle is known to be 60. Find the area of the hexagon.

  

  Topics:

  Geometry -> Area Calculation Geometry -> Plane Geometry -> Triangles
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage B, Grades 3-4 Question 7
  • Young Mathematician Olympiad, 2018-2019, Stage B, Grades 5-6 Question 5

• Question from sources: Grades 5-6(6) - Horse, Camel, and Donkey in a Circle

  On a circular track of length 92, there is a horse, a donkey, and a camel that start from the same point and begin walking along the circle.
  The horse and the camel walk counterclockwise, and the donkey walks clockwise. The camel's speed is 1 meter per second, the donkey's is 3, and the horse's is 5.

  In how many seconds will all three meet again?

  Note: The meeting does not necessarily have to be at the starting point

  Topics:

  Algebra -> Word Problems -> Motion Problems
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage B, Grades 5-6 Question 6

• Question from sources: Grades 5-6(7) - Minimal Table

  Given a table of size `3 times 3`. Hilla wants to write digits from 1 to 9 in the table's cells, such that all the sums in the rows and columns of the table are different, and the total sum of the table is as small as possible.
  It is allowed to repeat the same digit multiple times. What is the smallest sum that Hilla can obtain?

  Topics:

  Arithmetic Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Combinatorics -> Number Tables
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage B, Grades 5-6 Question 7