Young Mathematician Olympiad, 2017-2018, Stage A

• Question from sources: Grades 3-4(1), Grades 5-6(1) - Signs

  A cyclist is riding on a straight road without turns and sees the following sign by the side of the road:

  

   

  He continues moving and sees another sign:

  

  Find the distance between cities B and C.

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  Topics:

  Arithmetic Algebra -> Word Problems
  Sources:
  • Young Mathematician Olympiad, 2017-2018, Stage A, Grades 3-4 Question 1
  • Young Mathematician Olympiad, 2017-2018, Stage A, Grades 5-6 Question 1

• Question from sources: Grades 3-4(2) - What is the Smiley?

  In the following exercise, one of the digits has been replaced by a smiley face. Find the digit.

  `1☺xx6-☺=70`

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  Topics:

  Arithmetic Algebra -> Equations
  Sources:
  • Young Mathematician Olympiad, 2017-2018, Stage A, Grades 3-4 Question 2

• Question from sources: Grades 3-4(3) - Triangles in a Hexagon

  How many triangles are in the picture? Count all the triangles formed by the lines.

  

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  Topics:

  Combinatorics Geometry -> Plane Geometry -> Triangles
  Sources:
  • Young Mathematician Olympiad, 2017-2018, Stage A, Grades 3-4 Question 3

• Question from sources: Grades 3-4(4) - Cats for Grandma

  Grandma Hannah has a number of cats. One day, her three grandchildren, Avi, Benny, and Gili, came to visit and tried to guess how many cats she has.

  Avi said: "Grandma has at least 7 cats",

  Benny said: "But less than 10, I think",

  Then Gili said: "Grandma Hannah has either 9, or 10, or 11 cats".

  "You are all correct!" replied the grandma

   So how many cats does she have?
   

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  Topics:

  Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2017-2018, Stage A, Grades 3-4 Question 4

• Question from sources: Grades 3-4(5) - Palindromic Number

  Find a four-digit palindromic number that is divisible by 25 and not divisible by 3.

  Note: A palindromic number is a number that does not change if its digits are read in reverse order. For example, the number 5775 is a palindromic number, and the number 5778 is not a palindromic number.

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  Topics:

  Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rules by 3 and 9 Number Theory -> Division -> Parity (Even/Odd) Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rules by 5 and 25 Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2017-2018, Stage A, Grades 3-4 Question 5

• Question from sources: Grades 3-4(6) - 5 but not 7

  How many numbers from 1 to 100 (inclusive) are divisible by 5 but not divisible by 7?
   

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  Topics:

  Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules Number Theory -> Division
  Sources:
  • Young Mathematician Olympiad, 2017-2018, Stage A, Grades 3-4 Question 6

• Question from sources: Grades 3-4(7) - Area of the Shape

  Given a grid paper where the area of each square is one unit area. Find the area of the shape (in unit areas)

   

  

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  Topics:

  Geometry -> Plane Geometry Geometry -> Area Calculation Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry
  Sources:
  • Young Mathematician Olympiad, 2017-2018, Stage A, Grades 3-4 Question 7

• Question from sources: Grades 3-4(8), Grades 5-6(8) - Differences in the Multiplication Table

  Color the `10xx10` multiplication table with a black and white chessboard coloring, such that the cell of `1xx1` is colored black.
  Find the difference between the sum of all the numbers in the black cells and the sum of all the numbers in the white cells.
   

  	1	2	3	4	5	6	7	8	9	10
  1	1	2	3	4	5	6	7	8	9	10
  2	2	4	6	8	10	12	14	16	18	20
  3	3	6	9	12	15	18	21	24	27	30
  4	4	8	12	16	20	24	28	32	36	40
  5	5	10	15	20	25	30	35	40	45	50
  6	6	12	18	24	30	36	42	48	54	60
  7	7	14	21	28	35	42	49	56	63	70
  8	8	16	24	32	40	48	56	64	72	80
  9	9	18	27	36	45	54	63	72	81	90
  10	10	20	30	40	50	60	70	80	90	100

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  Topics:

  Arithmetic Combinatorics -> Number Tables Combinatorics -> Colorings -> Chessboard Coloring
  Sources:
  • Young Mathematician Olympiad, 2017-2018, Stage A, Grades 3-4 Question 8
  • Young Mathematician Olympiad, 2017-2018, Stage A, Grades 5-6 Question 8

• Question from sources: Grades 3-4(1), Grades 5-6(1) - Signs

  A cyclist is riding on a straight road without turns and sees the following sign by the side of the road:

  

   

  He continues moving and sees another sign:

  

  Find the distance between cities B and C.

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  Topics:

  Arithmetic Algebra -> Word Problems
  Sources:
  • Young Mathematician Olympiad, 2017-2018, Stage A, Grades 3-4 Question 1
  • Young Mathematician Olympiad, 2017-2018, Stage A, Grades 5-6 Question 1

• Question from sources: Grades 5-6(2)

  By what factor is the sum of all numbers from 1 to 99 smaller than the sum of all numbers from 1 to 9999?

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  Topics:

  Algebra -> Sequences -> Arithmetic Progression / Arithmetic Sequence
  Sources:
  • Young Mathematician Olympiad, 2017-2018, Stage A, Grades 5-6 Question 2