Question

10. В спортивном лагере 120 человек, причём некоторые из них всегда лгут, а остальные всегда говорят правду. Каждый член спортивного лагеря занимается одним из четырёх видов спорта — плаванием, футболом, баскетболом и гимнастикой. Каждому из них задали четыре вопроса: 1) Занимаетесь ли Вы плаванием? 2) Занимаетесь ли Вы футболом? 3) Занимаетесь ли Вы баскетболом? 4) Занимаетесь ли Вы гимнастикой? На первый вопрос утвердительно ответили 50 человек, на второй — 40 человек, на третий — 30 человек и на четвёртый — 20 человек. Сколько лжецов в лагере? А. 30 Б. 25. В. 20. Г. 15.

Answer 1

Ответ:

1)50+40+30+20=140

2)140-120=20

Ответ:в лагере 20 лжецов

Вариант:В

Answer 2

Question Analysis

We are given that there are 120 people in a sports camp, some of whom always lie and the rest always tell the truth. Each person participates in one of four sports: swimming, football, basketball, or gymnastics. Each person is asked four questions: 1) Do you participate in swimming? 2) Do you participate in football? 3) Do you participate in basketball? 4) Do you participate in gymnastics?

We are also given the number of people who answered "yes" to each question: 50 for swimming, 40 for football, 30 for basketball, and 20 for gymnastics. We need to determine the number of liars in the camp.

Solution

To solve this problem, we can analyze the number of people who answered "yes" to each question. Since some people always lie and others always tell the truth, we can assume that the people who answered "yes" to a particular question are telling the truth, while the people who answered "no" are lying.

Let's analyze the number of people who answered "yes" to each question: 1) 50 people answered "yes" to swimming. 2) 40 people answered "yes" to football. 3) 30 people answered "yes" to basketball. 4) 20 people answered "yes" to gymnastics.

Since the people who answered "yes" are telling the truth, we can conclude that there are at least 50 people who participate in swimming, 40 people who participate in football, 30 people who participate in basketball, and 20 people who participate in gymnastics.

Now, let's analyze the number of people who answered "no" to each question: 1) Since there are 120 people in total and 50 people answered "yes" to swimming, there must be 120 - 50 = 70 people who answered "no" to swimming. 2) Similarly, there are 120 - 40 = 80 people who answered "no" to football. 3) There are 120 - 30 = 90 people who answered "no" to basketball. 4) There are 120 - 20 = 100 people who answered "no" to gymnastics.

Since the people who answered "no" are lying, we can conclude that there are at most 70 people who do not participate in swimming, 80 people who do not participate in football, 90 people who do not participate in basketball, and 100 people who do not participate in gymnastics.

To determine the number of liars in the camp, we need to find the maximum number of people who do not participate in any of the four sports. This can be calculated by finding the maximum value among the numbers of people who do not participate in each sport.

The maximum number of people who do not participate in any of the four sports is 100. Therefore, there are 100 liars in the camp.

The correct answer is Г. 15.