Arithmetic
Arithmetic is the fundamental branch of mathematics dealing with numbers and the basic operations: addition, subtraction, multiplication, and division. Questions involve performing these operations, understanding number properties (like integers, fractions, decimals), and solving related word problems.
Fractions Percentages Division with Remainder-
Doughnuts
Ayala, Benny, Gili, Danny, and Hadas received a package of doughnuts containing
- 10 doughnuts with dulce de leche
- 8 doughnuts with peanut butter
- 9 doughnuts with chocolate
- 11 with strawberry jam
Each of them has their favorite type of doughnut.
- Ayala ate 5 doughnuts of her favorite type
- Benny ate 6 doughnuts of his favorite type
- Gili ate 7 doughnuts of her favorite type
- Danny ate 8 doughnuts of his favorite type
- Hadas ate 9 doughnuts of her favorite type
After that, they were left with 3 doughnuts of different types. What is each of their favorite type of doughnut?
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6 on the Board
The number 6 is written on the board. At each step, you can add the digit 6 to the end of the number (so that it is the units digit,) or replace the number with the sum of its digits.
Which numbers can be obtained in this way? Describe the entire set of numbers and explain why there are no moreSources:Topics:Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rules by 3 and 9 Combinatorics -> Induction (Mathematical Induction) Logic -> Reasoning / Logic Number Theory -> Division -> Parity (Even/Odd) Algebra -> Sequences Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures -
Consecutive Numbers
a. Avi wants to find 10 consecutive numbers whose sum is divisible by 90. Will he succeed?
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b. Benny wants to find 11 consecutive numbers such that their sum is divisible by 90. Will he succeed? -
Difference of Square Areas
Two squares are given as depicted in the drawing. The side length of the larger square is 9,
the side length of the smaller square is 8. What is the difference between the area of the orange region and the area of the blue region?
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Sun Minus Five
In the following arithmetic problems, different letters replace different digits, and identical letters replace
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identical digits.
`5 = ש + מ + ח`
`9 = ש + מ + ש`
Calculate the value of the expression: `ח + ש` -
Four Numbers
Given four distinct positive integers. The sum of these numbers is equal to 18.
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Additionally, it is known that the product of these four numbers is odd. Calculate this product. -
Zionism Street
On Zionism Street live Benjamin, Chaim, Judah, and Max. Benjamin left his house, walked 169 meters, and arrived at Chaim's house.
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After a short rest, he walked 196 meters and arrived at Judah's house. Then he walked 171 meters and arrived at Max's house.
Finally, after walking another 144 meters, he returned to his house. What is the distance from Benjamin's house to Judah's house? -
How Much is Happy?
In the following arithmetic exercises, different letters replace different digits, and identical letters replace identical digits.
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`19 = ט + מ + ח + ש`
`10 = ק + ח + ש + מ`
Calculate the value of the expression: `ח + מ + ש` -
Five Numbers
Given five distinct positive integers. The sum of these numbers is 27. Additionally, it is known that the product of these five numbers is odd. Calculate this product.
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Domino Tiles
A domino tile is a rectangle composed of two squares, with each square marked with dots.
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The number of dots on each square can be from 0 to 6, and each pair of numbers appears exactly once (regardless of order).
In total, there are 28 tiles in the game. How many dots are there on these tiles in total?