Algebra

Algebra is a broad branch of mathematics that uses symbols (usually letters) to represent numbers and to state rules and relationships. It involves manipulating expressions, solving equations and inequalities, and studying functions and structures. Questions cover a wide range of these topics.

Algebraic Techniques Equations Inequalities Word Problems Sequences

• We went on a trip

  Grade 4, consisting of 32 students, went on a trip. The students had to bring hats, sunglasses, and water bottles.
  No child forgot all of these things, but:

  • Among the students who brought hats, 9 forgot sunglasses,
  • Among the students who brought sunglasses, 7 forgot water bottles,
  • And among the students who brought water bottles, 10 forgot sunglasses.

  How many students in the class brought everything needed for the trip?

  Topics:

  Arithmetic Algebra -> Word Problems Logic -> Reasoning / Logic Set Theory Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 5-6 Question 2

• Question

  In the following addition problem, different shapes replace different digits, and identical shapes replace identical digits:

  `triangle square triangle square triangle+ square triangle square triangle square = o+ triangle triangle triangle triangle o+`

  What is the result of the addition?

  Topics:

  Arithmetic Algebra -> Equations Logic -> Reasoning / Logic Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 3

• The Elevator

  Avi works in a multi-story building, on the top floor. His friends Benny and Gil also work in the same building. Every day, in the morning and evening, Avi goes to greet them.
  In the morning Avi enters the building,

  • goes up 21 floors in the elevator to Benny's office,
  • walks down to Gil's office,
  • goes up 17 floors in the elevator to his office.

  After work,

  • Avi goes down 9 floors in the elevator to Benny's office,
  • walks down to Gil's office,
  • goes down 13 floors in the elevator and exits the building.

  How many floors are in the building? (Reminder - the ground floor is also a floor)

  Topics:

  Arithmetic Algebra -> Word Problems
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 4

• Average of Averages

  Consider the following diagram:

  

  Each number in the diagram, connected to 4 other numbers, must be equal to their average:
  What is the number in the circle marked with a question mark?
  Note: The average of four numbers is their sum divided by 4.

  Topics:

  Algebra -> Equations Algebra -> Inequalities -> Averages / Means
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 5-6 Question 1

• The Truth-Teller and Liar Survey

  13 truth-tellers and 12 liars participated in a survey. In the survey, each participant was asked about every other participant (including themselves) whether they were a truth-teller. How many "yes" answers were received in the survey in total?

  Topics:

  Arithmetic Algebra -> Word Problems Logic -> Reasoning / Logic Logic -> Truth-tellers and Liars Problems
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 5-6 Question 2

• The Orange Path

  In the illustration, there is an orange path surrounding a blue square. The area of the path is 44% of the area of the square.
  What is the width of the orange path as a percentage relative to the side length of the blue square?

  

  Topics:

  Geometry -> Plane Geometry Geometry -> Area Calculation Algebra -> Word Problems Arithmetic -> Percentages
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 5-6 Question 3

• Average of Averages 2

  Consider the following diagram:

  

  Each number in the diagram, connected to 4 other numbers, must be equal to their average:
  What is the number in the circle marked with a question mark?

  Topics:

  Algebra -> Equations Algebra -> Inequalities -> Averages / Means
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 7-8 Question 1

• Length of the Segment

  On the side BC of triangle ABC, a point D is marked. The perimeter of triangle ABC is 15 centimeters, the perimeter of triangle ABD is 12 centimeters, and the perimeter of triangle ACD is 13 centimeters.
  What is the length of segment AD?

  Topics:

  Geometry -> Plane Geometry -> Triangles Algebra -> Equations
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 7-8 Question 2

• Clock Angle

  How many minutes after 7:00 will the angle between the hour and minute hands be exactly one degree for the first time?
  Note: The clock hands move continuously at a constant speed.

  Topics:

  Arithmetic Algebra -> Word Problems -> Motion Problems Geometry -> Plane Geometry -> Angle Calculation
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 7-8 Question 3
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grade 9 Question 3

• Consecutive Numbers and Deletion

  Yossi wrote 10 consecutive natural numbers on the board. Danny erased one of the numbers. The sum of the remaining numbers on the board is 2020.
  Which number was erased?

  Topics:

  Algebra -> Word Problems Algebra -> Sequences Arithmetic -> Division with Remainder
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 7-8 Question 5