Integers + prime numbers - practice problems
Number of problems found: 16
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, which of the following integers will be in P and Q but not in R? A=−54 B=−50 C=42 D=100 E=252
- Year 2018
The product of the three positive numbers is 2018. What are the numbers?
Less than 500 pupils attend school. When it is sorted into pairs, one pupil remains. Similarly, when sorted into 3, 4, 5 and 6 members team one remains. Sorted to seven members teams, no left behind. How many pupils are attending this school?
If 8 men, 10 women, 16 children collects ₹1024 in 4 days, how many days will be required for 6 men, 5 women and 4 boys to collect ₹768? (₹ is Indian Rupee)
- Endless lego set
The endless lego set contains only 6, 9, 20 kilograms 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. The
- 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 stamps? How many does the problem have solutions?
- MO Z6-6-1
Write integers greater than 1 to the blanks in the following figure so that each darker box was a product of the numbers in the neighboring lighter boxes. What number is in the middlebox?
- Ornamental shrubs
Children committed to planting 240 ornamental shrubs. Their commitment, however, exceeded by 48 shrubs. Write the ratio of actually planted shrubs and commitment by lowest possible integers a/b.
- Snowman 2
On the medal, which has the shape of a circle with a diameter 18 cm is sketched snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over snowman is the same as under it, 3. diameters of all circles express
In a circle with a diameter 50 cm are drawn 3 circles /as a snowman/ where: its diameters are integers, each larger circle diameter is 3 cm larger than the diameter of the previous circle. Determine snowman height if we wish highest snowman.
- Sugar - cuboid
Pejko received from his master cuboid composed of identical sugar cubes with count between 1000 and 2000. The Pejko eat sugar cubes in layers. The first day eat one layer from the front, second day one layer from right, the third day one layer above. Yet
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 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.
When Pythagoras asked how many students attend 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?
Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
- Diofant 2
Is equation 70x +52y = 34 solvable on the set of integers Z?
- 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)
Integers - practice problems. Prime numbers - practice problems.