Prime numbers - high school - practice problems
Number of problems found: 47
- What is 20
What is the least number that should be added to 2497 so that the sum of the digits is divisible by 5, 6, and 10? - 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 - Lcm to eliminate y
Identify the least common multiple that would eliminate the y-variable. 6x - 5y = -4 4x + 2y = 28 - How many
How many different rectangles with integer side lengths have an area S = 60 cm²?
- Wedding guests
Fifteen wedding guests could not agree on who would stand in the wedding photo. The groom suggested that all possible sets of wedding guests be made in the photographs. - Probability 17013
What is the probability that a randomly written two-digit number from number 20 to number 99 will be divisible by 11, the power of number 3, or a prime number? - Average monthly salary
A total of 10 teachers work at one small school in Moravia. The monthly salary of each is 21,500 CZK or 21,800 CZK or 22,500 CZK, according to their education and age. The average monthly salary for this school's teacher is 21 850 CZK. How many teachers o - 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 - Determine 8611
Determine all natural numbers A and B pairs for which the sum of twice the least common multiple and three times the greatest common divisor of natural numbers A and B is equal to their product.
- Two gears
The gearbox will use a large gear to turn a smaller gear. The large gear will make 75 revolutions per minute, while the smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM - There
There are two numbers on the screen - one in the blue and the other in the red box. In the beginning, both numbers are the same. With each beep, both numbers increase - by 1 in the blue field and by 3 in the red field. At one point, the number 49 appears - The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numerals sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in - Inverted nine
In the hotel Inverted Nine, each hotel room number is divisible by 6. How many rooms can we count with the three-digit number registered by digits 1,8,7,4,9? - PIN code
The PIN on Michael's credit card is a four-digit number. Michael told his friend: • It is a prime number - a number greater than 1, which is only divisible by number one and by itself. • The first digit is larger than the second. • The second digit is gre
- Diofant equation
250x + 120y = 5640 - Sum of two primes
Christian Goldbach, a mathematician, found out that every even number greater than two can be expressed as a sum of two prime numbers. Write or express 2018 as a sum of two prime numbers. - Children's 6140
The store received a total of 666 pairs of children's, men's and women's shoes. Men were 2.5 times less than children, while children were 1.4 times more than women. Express in whole numbers the ratio of the number of pairs of children's, men's, and women - Endless lego set
The endless lego set contains only 6, 9, and 20-kilogram blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And, of course, they wrote down how much the building weighed. - Cuboid walls
Calculate the cuboid volume if its different walls have an area of 195cm², 135cm², and 117cm².
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