Integers - high school - practice problems - last page
Number of problems found: 58
- Three digits number
How many are three-digit integers such that they have no digit repeats? - Repairman
The repairman has vowed to do repair work at the plant for 25 days. However, work had to be shortened, so he took a helper worker. Together they made all the corrections for the whole day. How long would it take work to help workers? - Individual 82186
The average height of a member of a family of five is 1.5m, the mode of their height is 1.2m and the median is 1.6m. Find out the heights of individual members of this family if you know that they are integers in dm. - Task of the year
Find the number of integers from 1 to 106 with ending four digits 2015.
- Equations: 80499
In the field of real numbers, solve the system of equations: 2x + ⌊y⌋ = 2022, 3y + ⌊2x⌋ = 2023. (⌊a⌋ denotes the (lower) integer part of the real number a, i.e., the largest integer not greater than a., E.g., ⌊1.9⌋ = 1 and ⌊−1.1⌋ = −2.) - Three-digit integers
How many three-digit natural numbers exist that do not contain zero and are divisible by five? - Banknotes
$ 1390 was collected. How much was in $20 notes, and how many in $50 notes in that order? How many solutions exist? - AND-NOT-AND
If P is the set of multiples of 2, Q is the set of multiples of 3, and R is the set of multiples of 7, the following integers will be in P and Q but not in R: A=−54 B=−50 C=42 D=100 E=252 - Positive 7040
Find all positive integers x and y for which: 1 / x + 1 / y = 1/4
- AVG of INT
What is the average of the integers from 9 thought 52 inclusive? - Find x 2
Find x, y, and z such that x³+y³+z³=k for each k from 1 to 100. Write down the number of solutions. - The perimeter
The perimeter of the triangle is 24, and the sides are integers and form an arithmetic sequence. Specify the side sizes of this triangle. - Determine 5893
Determine the largest integer n for which the square table n×n can be filled with natural numbers from 1 to n² (n squared) so that at least one square power of the integer is written in each of its 3×3 square parts. - Points on circle
The Cartesian coordinate system with the origin O is a sketched circle k /center O; radius r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points on the circle I with center O and radius r=5 cm, whose
- Circumference 9811
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a circumference in millimeters equal to the number selected by Kristýna and whose sides have lengths in millimeters expressed by different integer - When will I be a millionaire?
Barry monthly send 280 euros to the bank, which he deposits bear interest of 2.1% p. A. Calculate how many months must Barry save to save 1000000 euros? Inflation, interest rate changes, or bank failures are ignored. - Dice
How many times must you throw the dice, and the probability of throwing at least one päťky was greater than 50%? - Shooter
The shooter fired at a target from a distance 49 m. The individual concentric circle of targets has radius increments of 1 cm (25 points) by 1 point. The shot was shifted by 16' (angle degree minutes). How many points should he win his shot?
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