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

• Question

  Avi lives in apartment number `45`. On which floor is the apartment located if there are `2` apartments on the first floor of his building, and `4` apartments on every other floor? (Note: The building does not have a floor `0`)

  Topics:

  Algebra -> Word Problems Arithmetic -> Division with Remainder
  Sources:
  • problems.ru web site

• Question

  A vendor has two rolls of fabric, each `36` meters long. He sells the fabric in pieces of `3` meters. How many times will the vendor need to cut the fabric?

  Topics:

  Arithmetic Algebra -> Word Problems Logic -> Reasoning / Logic Number Theory -> Division
  Sources:
  • problems.ru web site

• Complete the sequence

  Complete the missing number:

  `2, 3, 5, 9, ?, 33`

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  Topics:

  Arithmetic Algebra -> Sequences -> Complete/Continue the Sequence

• Question

  Given two squares, each with a side length of `3` centimeters, and joined together to form a rectangle, what is the perimeter of the resulting rectangle?

  Topics:

  Arithmetic Geometry -> Plane Geometry Geometry -> Area Calculation Algebra -> Word Problems

• Question

  Samuel wants to tile a room measuring `3` by `4` meters using square tiles with a side length of `25` centimeters. How many tiles does Samuel need?

  Topics:

  Arithmetic Geometry -> Area Calculation Algebra -> Word Problems Units of Measurement

• Question

  Insert arithmetic operation symbols and parentheses so that the equality becomes correct:

  5    5    5  = 0

  Topics:

  Arithmetic Algebra -> Equations Puzzles and Rebuses

• Hanukkah Money

  Two brothers, Yosef and Danny, received Hanukkah money. Afterward, Danny said to Yosef: "If you give me `8` shekels, then I will have twice as much money as you." Yosef replies: "I think that's not very fair. I think it's better if you give me `8` shekels, and then we will have the same amount of money." How much Hanukkah money did each brother receive?

  Topics:

  Algebra -> Equations Algebra -> Word Problems

• Question

  Danny and Rachel are brother and sister. The number of Danny's brothers equals the number of his sisters. The number of Rachel's brothers is twice as large as the number of her sisters. How many boys and how many girls are there in this family?

  Topics:

  Algebra -> Equations Algebra -> Word Problems

• Question

  Samuel has three sons, and each son has one sister. How many children are there in this family?

  Topics:

  Algebra -> Word Problems Logic -> Reasoning / Logic

• Question

  Two workers pave two kilometers of road within two days. How many workers are needed to pave `20` kilometers of road within `20` days?

  Topics:

  Arithmetic Algebra -> Equations Algebra -> Word Problems Logic -> Reasoning / Logic Number Theory -> Division