Question

Два класса с одинаковым количеством учеников написали контрольную. проверив контрольные, строгий директор сказал, что он поставил двоек на 13 больше, чем остальных оценок. не ошибся ли директор?

Answer 1

Если в одном классе n учеников, то в двух классах их 2n, то есть чётное количество (т.к. 2 чётное число и его произведение с любым числом даст чётное).
13 - нечётное число.
Если количество двоек чётно, то количество остальных оценок НЕчётно, т.к. чётное-нечётное = нечётное. Тогда количество учеников нечётно (чётное+нечётное = нечётное), а такого быть не может.
Если количество если количество двоек НЕчётно, то количество остальных оценок чётно, т.к. чётное-нечётное = нечётное. Тогда количество учеников нечётно (нечётное+чётное = нечётное), а такого тоже быть не может.
Значит, директор ошибся =)

Answer 2

Problem Analysis

Two classes with the same number of students took a test. The strict principal said that he gave 13 more "2" grades than other grades. The question is whether the principal made a mistake.

Solution

To determine if the principal made a mistake, we need to compare the number of "2" grades with the number of other grades. Let's assume that the number of students in each class is "n".

According to the information provided, the principal gave 13 more "2" grades than other grades. This means that the number of "2" grades is equal to the number of other grades plus 13.

Let's calculate the number of "2" grades and other grades for each class.

Calculation

For each class: - Number of "2" grades = Number of other grades + 13

Since both classes have the same number of students, the number of "2" grades and other grades in each class will be the same.

Let's calculate the number of "2" grades and other grades for one class.

Number of "2" grades = Number of other grades + 13

Let's represent the number of other grades as "x".

Number of "2" grades = x + 13

Now, let's calculate the total number of grades for one class.

Total number of grades = Number of "2" grades + Number of other grades

Total number of grades = (x + 13) + x = 2x + 13

Since both classes have the same number of students, the total number of grades for both classes will be twice the total number of grades for one class.

Total number of grades for both classes = 2 * (2x + 13) = 4x + 26

Now, let's calculate the average grade for both classes.

Average grade = Total number of grades for both classes / Total number of students in both classes

Since both classes have the same number of students, the total number of students in both classes will be twice the number of students in one class.

Total number of students in both classes = 2 * n = 2n

Average grade = (4x + 26) / (2n)

To determine if the principal made a mistake, we need to compare the average grade with the number "2".

If the average grade is equal to "2", then the principal did not make a mistake.

If the average grade is not equal to "2", then the principal made a mistake.

Let's calculate the average grade and compare it with "2".

Calculation Continued

Average grade = (4x + 26) / (2n)

Since we don't have the specific values for "x" and "n", we cannot calculate the exact average grade. However, we can make a general observation.

If the average grade is greater than "2", then the principal made a mistake because the average grade is higher than the grade he claimed to have given more.

If the average grade is less than "2", then the principal made a mistake because the average grade is lower than the grade he claimed to have given more.

If the average grade is equal to "2", then the principal did not make a mistake because the average grade matches the grade he claimed to have given more.

Therefore, to determine if the principal made a mistake, we need more information about the specific values of "x" and "n" or the average grade.

Conclusion

Based on the information provided, we cannot determine if the principal made a mistake without additional information. We need either the specific values of "x" and "n" or the average grade to make a definitive conclusion.

Please note that the above analysis is based on the assumption that the number of "2" grades is equal to the number of other grades plus 13, as stated by the principal. If this assumption is incorrect, the conclusion may change.