Integers + divisibility - practice problems
Number of problems found: 30
- School
Less than 500 pupils attend school. When it is sorted into pairs, one pupil remains. Similarly, one remains when sorted into 3, 4, 5, and 6 members teams. Sorted to seven members teams, no left behind. How many pupils are attending this school? - Sometimes 2814
Adam was at some of his favorite football team's home games last season. Sometimes, he bought a seat ticket for €9, sometimes a standing ticket for €5. He spent a total of €76. How many times did Adam buy a seat ticket, and how many times did he buy a sta - Class
When Pythagoras asked how many students attended the school, he said: "Half of the students studying mathematics, 1/4 music, seventh silent, and there are three girls at school." How many students had Pythagoras at school? - Dozen
What is the product of 26 and 5? Write the answer in an Arabic numeral. Add up the digits. How many of this is in a dozen? Divide ; 114 by this
- What is 16
What is the sum of three consecutive even integers such that six more than twice the second is 2/3 of the first increased by 3/2 of the third? - Integers 6915
Which even integers are greater than -1 1/4 and less than 7 1/4? The mark is on the number axis. - One hundred stamps
A hundred letter stamps cost a hundred crowns. Its costs are four levels - twenty tenths, one crown, two-crown and five-crown. How many are each type of stamp? How many does the problem have solutions? - Divisibility
Write all the integers x divisible by seven and eight simultaneously, for which the following applies: 100 < x < 200. - Digit sum
Determine how many integers greater than 900 and less than 1,001 have the digit sum digit of the number 1.
- Remembered 2766
Aunt bought 6 identical mugs and one coffee pot. She paid €60 in total. A teapot was more expensive than one mug but cheaper than two mugs. Auntie remembered that all the prices were in whole euros. How much € was one mug, and how much was a kettle? - Package
The package has no more than 66 m of cloth. If we just cut it all on the blouses or all on dresses, no cloth left to remain. On the one blouse consumes 1.3 m of cloth and on one dress 5 m. Determine the amount of the cloth in the package. - Candy and boxes
We have some candy and empty boxes. When we put ten sweets in boxes, there will be two candies and eight empty boxes left. When of eight, there will be six candies and three boxes left. How many candy and empty boxes are gone when we put nine sweets into - Diofant equation
In the set of integers (Z), solve the equation: 212x +316y =0 Write result with integer parameter t in Z (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions) - Modulo
Find x in the modulo equation: 47x = 4 (mod 9) Hint - read as what number 47x divided by 9 (modulo 9) give remainder 4.
- Diofant 2
Is equation 70x +52y = 34 solvable on the set of integers Z? - The sum 2
The sum of five consecutive even integers is 150. Find the largest of the five integers. A.28 B.30 C.34 D.54 Show your solution and explain your answer. - Sum of odd numbers
Find the sum of all odd integers from 13 to 781. - Divisibility
Is the number 186317 exactly divisible by 7? (the result is the integer, and/or remainder is zero) - Snowman 2
On the medal, which has the shape of a circle with a diameter 18 cm, is sketched a snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over the snowman is the same as under it, 3. diameters of all circles
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