Question

Три друга сделали по одному заявлению о целом числе x. Петя: число X больше 4 но меньше 8. Вася число Х больше 6 но меньше 9.Толя число Х больше 5 но меньше 8. найдите число Х если известно что двое из друзе сказали правду а трети солгал. нужно не только проверить что найденное число содится но и объяснить почему другие варианты ответы невозможно.

Answer 1

Петя сказал что х больше 4 и меньше 8 значит есть такие варианты х: (5,6,7). Вася сказал что х больше 6 и меньше 9 значит есть такие варианты х: (7,8). Толя сказал что х больше 5 и меньше 8 значит есть такие варианты х: ( 6,7). Число х должно быть в вариантах только у двоих людей так как третий соврал. 5 только у первого, 6 подходит так как есть у первого и у третьего, 7 у всех, 8 только у второго. Значит 6.

Answer 2

Problem Analysis

Three friends, Petya, Vasya, and Tolya, made statements about a whole number x. Petya said that x is greater than 4 but less than 8. Vasya said that x is greater than 6 but less than 9. Tolya said that x is greater than 5 but less than 8. Two of the friends told the truth, while one of them lied. We need to find the value of x and explain why other possible answers are not valid.

Solution

To solve this problem, we need to analyze the statements made by each friend and determine which statements are true and which one is false.

Let's consider the statements made by each friend:

1. Petya: x is greater than 4 but less than 8. 2. Vasya: x is greater than 6 but less than 9. 3. Tolya: x is greater than 5 but less than 8.

Since two friends told the truth and one lied, we can conclude that the statement made by Tolya is false. Therefore, we can eliminate the range specified by Tolya.

Now, let's analyze the remaining two ranges:

1. Petya: x is greater than 4 but less than 8. 2. Vasya: x is greater than 6 but less than 9.

The only overlapping range between these two statements is x is greater than 6 but less than 8. Therefore, the value of x must be 7.

Explanation

The value of x is 7 because it satisfies the statements made by Petya and Vasya. Petya said that x is greater than 4 but less than 8, and Vasya said that x is greater than 6 but less than 9. The only value that satisfies both statements is 7.

Other possible answers are not valid because they either do not satisfy the statements made by Petya and Vasya or they fall within the range specified by Tolya, who we determined to be lying.

For example, if x were 5, it would not satisfy the statement made by Vasya (x is greater than 6). Similarly, if x were 8, it would not satisfy the statement made by Petya (x is less than 8).

Therefore, the only valid value for x is 7.

Conclusion

The value of x is 7. This value satisfies the statements made by Petya and Vasya, while the statement made by Tolya is false. Other possible answers are not valid because they either do not satisfy the statements made by Petya and Vasya or they fall within the range specified by Tolya, who we determined to be lying.