Task 18, basic level.
Task 1.When physics teacher Nikolai Dmitrievich teaches a lesson, he always turns off his phone. Choose the statements that are true under the given condition.
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2. If Nikolai Dmitrievich’s phone is turned on, it means he is teaching a lesson.
Solution.The first statement is true, since if Nikolai Dmitrievich is teaching a lesson, then the phone is turned off. Therefore the second statement is false.
Answer 13.
Task 2.— —
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Solution.This problem can be solved using the inequalities.
K>N, N>B
K>SH
Answer 24.
Logical tasks (continued).
Task 1.When physics teacher Nikolai Dmitrievich teaches a lesson, he always turns off his phone. Choose the statements that are true under the given conditions.
- If Nikolai Dmitrievich’s phone is turned on, it means he is not teaching a lesson.
- If Nikolai Dmitrievich’s phone is turned on, it means he is teaching a lesson
- If Nikolai Dmitrievich conducts laboratory work in physics during class, it means that his phone is turned off.
- If Nikolai Dmitrievich is teaching a physics lesson, then his phone is on.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Solution.The first statement is true, since if Nikolai Dmitrievich is teaching a lesson, then the phone is turned off. Therefore the second statement is false.
The third statement is true, since the phone is turned off during any lesson.
The fourth statement is false, since the phone is turned off during any lesson.
Answer 13.
Task 2.At the Winter Olympics, the Canadian team won more medals than the Dutch team and the Belarusian team— less than the Netherlands team, and the Swiss team— less than Team Canada. Select the statements that are true under the given conditions.
1. Of the named teams, the Belarusian team took second place in the number of medals.
2. The Belarusian team won fewer medals than the Canadian team.
3. Among the named teams, there are three that won an equal number of medals.
4. Team Canada won more medals than each of the other three teams.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Solution.This problem can be solved using inequalities.
K>N, N>B
K>SH
It follows that statements 2 and 4 are true.
Answer 24.
Problems for independent solution.
Task 1.There are 20 people in the class, of which 13 people attend a history club, and 10— math club. Select the statements that are true under the given conditions.
1. Every student in this class attends both clubs.
3. If a student from this class goes to a history club, then he definitely goes to a math club.
4. There are not 11 people from this class who attend both clubs.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Task 2.When math teacher Ivan Petrovich teaches a lesson, he always turns off his phone. Choose the statements that are true
under the given condition.
1. If Ivan Petrovich's phone is on, it means he is not teaching a lesson.
2. If Ivan Petrovich's phone is on, it means he is teaching a lesson.
3. If Ivan Petrovich is taking a test in mathematics, it means his phone is turned off.
4. If Ivan Petrovich is teaching a math lesson, it means his phone is on.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Task 3.—
1. Each student from this class also attends a club English language, and circle by German language.
2. There are at least three people from this class who attend both clubs.
3. If a student from this class goes to an English language club, then he must attend a German language club.
4. There are 4 people from this class who attend both clubs.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Task 4.There are 25 people in the class, of which 16 people attend an English language club, and 13— German language club. Select the statements that are true under the given conditions.
1. Among these graduates there is a person who received 75 points for the Unified State Exam in social studies.
2. Among these graduates there are twenty-two people with equal scores for the Unified State Exam in social studies.
3. Among these graduates there is a person who received 20 points for the Unified State Exam in social studies.
4. Any of these twenty people’s Unified State Exam scores in social studies are no lower than 35.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Task 5.There are 30 people in the class, of which 20 people attend a biology club, and 16— geography club. Select the statements that are true under the given conditions.
1. There will be at least two from this class who attend both clubs.
2. If a student from this class goes to a biology club, then he definitely goes to a geography club.
3. Every student in this class attends both clubs.
4. There are not 17 people from this class who attend both clubs.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Task 6.Among those registered on VKontakte there are schoolchildren from Tver. Among the schoolchildren from Tver there are those who are registered in Odnoklassniki. Select the statements that are true under the given conditions.
1. All schoolchildren from Tver are not registered on VKontakte or Odnoklassniki.
2. There are no schoolchildren from Tver who are registered on VKontakte.
3. Among the schoolchildren from Tver there are those who are registered on VKontakte.
4. At least one of the Odnoklassniki users is a schoolboy from Tver.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Task 7.Among the residents of the house№ 23 There are those who work, and there are those who study. And there are also those who do not work and do not study. Some residents of the house№ 23 who study also work. Select the statements that are true under the given conditions.
1. At least one of the working residents of the house No. 23 is studying.
2. All residents of house No. 23 work.
3. Among the residents of the house№ 23 there are no those who do not work and do not study.
4. At least one of the residents of the house No. 23 is working.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Task 8.Players' heights were measured before the basketball tournament basketball team city N. It turned out that the height of each of the basketball players of this team is more than 180 cm and less than 195 cm. Choose the statements that are true under the specified conditions.
1. The basketball team in city N must have a player whose height is 200 cm.
2. There are no players in the city N basketball team with a height of 179 cm.
3. The height of any basketball player on this team is less than 195 cm.
4. The difference in height between any two players on the city N basketball team is more than 15 cm.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Task 9.If an athlete participating in Olympic Games, set a world record, then his result is Olympic record. Choose the statements that are true under the given conditions.
1. If the result of an athlete participating in the Olympic Games is not an Olympic record, then it is not a world record.
2. If the result of an athlete participating in the Olympic Games is not an Olympic record, then it is a world record.
3. If the result of an athlete participating in the Olympic Games is a world record, then it is not an Olympic record.
4. If an athlete participating in the Olympic Games sets a world record in the 100 m race, then his result is also an Olympic record.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Problem 10.At the Winter Olympics, the Russian team won more medals than the Canadian team, the Canadian team— more than the German team, and the Norwegian team— less than Team Canada. Select the statements that are true under the given conditions.
1. Of the named teams, the Canadian team took second place in the number of medals.
2. Among the named teams, there are three that won an equal number of medals.
3. The German team won more medals than the Russian team.
4. The Russian team won more medals than each of the other three teams.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Problem 11.Before football tournament measured the height of the players football team city N. It turned out that the height of each of the football players on this team is more than 170 cm and less than 190 cm. Choose the statements that are true under the specified conditions. 3. The height of any player on this team is less than 190 cm.
4. The difference in height between any two players on the city N football team is more than 20 cm.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Problem 12.Before volleyball tournament measured the height of the players of the volleyball team of the city N. It turned out that the height of each of the volleyball players of this team is more than 190 cm and less than 210 cm. Choose the statements that are true under the specified conditions.
4. The difference in height of any two players of the volleyball team of city N is more than 20 cm.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Problem 13.Kostya's house has more floors than Oleg's house, Tanya's house has fewer floors than Oleg's house, and Fedya's house has more floors than Tanya's house. Select the statements that are true under the given conditions.
4. Among these four houses, there are three houses with the same number of floors.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Problem 14.Masha's house has fewer floors than Stas's house, Ksyusha's house has more floors than Stas's house, and Nadya's house has more floors than Masha's house, but less than Ksyusha's house. Select the statements that are true under the given conditions.
4. Nadya's house has one floor.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
Problem 15.Mitya's house has more floors than Masha's house, Lena's house has fewer floors than Masha's house, and Tolya's house has more floors than Lenin's house. Select the statements that are true under the given conditions.
- Lena's house is the lowest among the four listed.
- Masha's house has fewer floors than Lena's house.
- Mitya's house has more floors than Lenin's.
- Among these four houses, there are three with the same number of floors.
In your answer, write down the numbers of the selected statements without spaces, commas or other additional characters.
The box contains mixed tea bags with black and green tea, identical in appearance, and there are 9 times more bags of black tea than bags of green tea. Find the probability that a bag randomly selected from this box will be a bag of green tea.
Answer: ___________________________.
There are identical-looking pies on the plate: 5 with meat, 8 with cabbage, and 3 with cherries. Petya chooses one pie at random. Find the probability that he will end up with cabbage.
Answer: ___________________________.
Some of the company's employees vacationed at the dacha in the summer of 2014, while others went to the sea. All employees of the company who did not vacation at sea vacationed at the dacha. Choose the statements that are true under the given conditions.
1) Every employee of this company vacationed in the summer of 2014 either at sea, or at the dacha, or both.
2) An employee of this company, who did not vacation at sea in the summer of 2014, did not vacation at the dacha either.
3) If Faina did not vacation in the summer of 2014 either at the dacha or at the seaside, then she is not an employee of this company.
4) If an employee of this company did not vacation at sea in the summer of 2014, then he vacationed at the dacha.
Answer: ___________________________.
Before the basketball tournament, the height of the players of the basketball team of the city N was measured. It turned out that the height of each of the basketball players of this team is more than 180 cm and less than 195 cm. Choose the statements that are true under the specified conditions.
1) In the basketball team of city N there are no players taller than 179 cm.
2) The basketball team in city N must have a player whose height is 200 cm.
3) The height of any basketball player on this team is less than 195 cm.
4) The difference in height of any two players on the basketball team in city N is more than 15 cm.
In your answer, write down the number of the selected statements without spaces, commas or other additional characters.
Answer: ___________________________.
Answers to tasks in section 2.3
Practice-oriented tasks
Job No. | |
7th grade preparation for the Moscow Center for Education
Option 1
Calculate: - 5 9 +8 .
Choose the correct statements.
If a number ends with 0, then it is divisible by 2 and 5.
If the numerator of a fraction is increased by 7 times and the denominator is increased by 7 times, then the fraction will not change.
The sum of two proper fractions cannot be a whole number.
If you divide a positive number by 0.01, the number will decrease by 100 times.
In your answer, indicate the numbers of the correct statements without spaces, commas and
Answer: ___________________________.
Solve Equation 6 ( X - 2 ) = 2 x + 4.
Answer: ___________________________.
On checkered paper with a square size of 1 cm x1 cm
a figure is depicted (see picture). Find the side
square having the same perimeter.
Give your answer in centimeters.
Answer: ___________________________.
In the boarding house, the number of adults to children is 8:7. How many children are there in this boarding house if there are 96 adults in it?
Answer: ___________________________.
a common fraction with a denominator of 20?
1)31,4 2)5 3) 2,45 4) 7
additional characters.
Answer: ___________________________.
7. A pound is approximately equal to 16.4 kg. Nine poods is closest to the value:
1) 400 kg 2) 16 t 3) 150 kg 4) 18 kg
Answer: ___________________________
Mitya approached the platform at the station at 10:45. At the beginning of the platform he saw two electronic boards with the commuter train schedule.
1 way 2 way
Direction
Departure time
Direction
Departure time
Shchelkovo
Pushkino
Fryazevo
Monino
Alexandrov
10:37
10:42
11:04
12:07
12:15
Shchelkovo
Monino
Fryazevo
Alexandrov
Pushkino
10:42
11:08
11:14
11:27
11:45
Any train to Monino or Fryazevo is suitable for Mitya. How many minutes
Before the basketball tournament, the height of each player on the basketball team in the city of N was measured. It turned out that the height of each of the basketball players on this team was more than 185 cm and less than 202 cm. Select the statements that follow from the given data.
The basketball team in city N must have a player whose height is
equal to 190 cm.
2) In the basketball team of city N there are no players with a height of 182 cm.
3) The height of any basketball player on this team is less than 200 cm.
4) The difference in height of any two players of the basketball team of city N
is no more than 17 cm.
other additional characters.
Answer: ___________________________.
Part 2
Give an example of two numbers whose sum is less than their difference, and the modulus of each number is greater than 50 but less than 90.
Answer:___________________
Solution:
Three pastry chefs working at the same speed can, in 2 hours,
make 48 gingerbread cookies. How many gingerbread cookies can 4 confectioners make in 1 hour?
Solution:
Answer:_______________________
A group consisting of three teachers and 35 schoolchildren decided to take an excursion trip to Suzdal. They need to buy train tickets. A ticket costs 1,800 rubles for an adult and 1,200 rubles for a student. For a group of 10 schoolchildren, you can purchase a group ticket for 8,000 rubles. What is the minimum amount in rubles that a group must pay when organizing a trip? Explain your answer.
Solution:
Answer:_______________________
Given a square. Draw 3 segments with ends on the sides of the square or at its vertices so that the square is divided into 6 parts: a pentagon, a quadrilateral and four triangles.
Draft: Answer
Answers
Option 1. Option 2.
-37 1. -42
12 2. 34
4 3. 16
4 4. 10
84 5. 72
13 6. 23
3 7. 2
19 8. 39
24 9. 124
80 and – 60 10. 45 and -50
29,4 11. -7,8
32 12. 54
35 400 13. 20800
14
7th grade preparation for the Moscow Center for Education
Option 2
Calculate:- 7 ∙ (71 - 65) .
Answer: ___________________________.
2 . Choose the correct statements.
If a number ends with 4, then it is divisible by 4.
If the numerator of a fraction is increased by 6 and the denominator is decreased by 6, the fraction will decrease.
The difference of two ordinary fractions can be an integer.
If a positive number is divided by 0.01, the number will increase by 100 times.
Answer: ___________________________.
Solve Equation 6∙ ( X - 9) = 3 X - 6 .
Answer: ___________________________.
On checkered paper with a square size of 1 cm x 1 cm
a figure is depicted (see picture). Rectangle, one
whose side is 2 cm has the same area. Find
the other side of the rectangle. Give your answer in centimeters.
Answer: ___________________________.
In the sanatorium, the number of adults to children is 12:8. How many adults are there in this sanatorium if there are 48 children?
Answer: ___________________________.
Which of the following fractions can be represented in the form
a common fraction with a denominator of 10?
1)3,55 2)1 3) 12,7 4)
In your answer, write down the numbers of the selected fractions without spaces, commas, etc.
additional characters.
Answer: ___________________________.
7. One inch is approximately equal to 2.54 cm. 22 inches is closest to the value:
1) 2 m 2) 60 cm 3) 20 mm 4) 8 cm
Answer: ___________________________.
8. Mitya approached the platform at the station at 11:06. At the beginning of the platform he saw two electronic boards with the commuter train schedule.
1 way 2 way
Direction
Departure time
Direction
Departure time
Shchelkovo
Pushkino
Fryazevo
Monino
Alexandrov
10:37
10:42
11:04
12:07
12:15
Shchelkovo
Monino
Fryazevo
Alexandrov
Pushkino
10:42
11:08
11:14
11:27
11:45
Any train to Pushkino or Shchelkovo suits Mitya. How many minutes
time left until the nearest suitable train for him? Answer: ___________________________.
9. Before the volleyball tournament, the height of each player of the volleyball team of the city N was measured. It turned out that the height of each of the volleyball players of this team is more than 177 cm and less than 195 cm. Select the statements that follow from the given data.
The volleyball team in city N has no players with a height of 196 cm.
The height of any volleyball player of this team is more than 177 cm.
In the volleyball team of city N there is always a player whose height is
equal to 190 cm.
Difference in height of any two players of a volleyball team in city N
is no more than 20 cm.
In your answer, indicate the numbers of the selected statements without spaces, commas and
other additional characters.
Answer: ___________________________.
Part 2
For tasks 10–14, write your answer in the space provided. For
tasks 11, 12 and 13 write down the complete solution.
10. Give an example of two numbers whose sum is less than their difference, and the modulus of each number is greater than 40 but less than 60.
Solution:
Answer:_______________________
13. A group of two teachers and 24 schoolchildren decided to go on a field trip. They need to buy train tickets. A ticket costs 1,700 rubles for an adult and 850 rubles for a student. For a group of 10 schoolchildren, you can purchase a group ticket for 7,000 rubles. Which
the minimum amount in rubles must be paid by the group when organizing
trips? Explain your answer.
Solution:
Answer:_______________________
14. Given a square. Draw 3 segments with ends on the sides of the square or at its vertices so that the square is divided into 7 parts: two quadrangles, one pentagon and four triangles.
One of the drawings can be used as a draft.
Draft: Answer
