# Task 2.

In a school test, there are 5 sections, each containing the same number of questions. Anton answered 20 questions correctly. The percentage of his correct answers was more than 60 but less than 70. How many questions were there in the test in total?
Answer: 30

Solution. According to the condition $\frac{60}{100}<\frac{20}{x}<\frac{70}{100}$, that is, $\frac{200}{7}<x<\frac{100}{3}$, so $29 \leqslant x \leqslant 33$. Since the number of questions must be divisible by 5, then $x=30$.

## B-2

In a school test, there are 4 sections, each containing the same number of questions. Anton answered 20 questions correctly. At the same time, the percentage of his correct answers was more than 60 but less than 70. How many questions were there in the test?

Answer: 32

## B-3

In a school test, there are 5 sections, each containing the same number of questions. Anton answered 20 questions correctly. At the same time, the percentage of his correct answers was more than 50 but less than 60. How many questions were there in the test?

Answer: 35

## B-4

In a school test, there are 4 sections, each containing the same number of questions. Anton answered 20 questions correctly. At the same time, the percentage of his correct answers was more than 50 but less than 60. How many questions were there in the test?

## Answer: 36

## Lomonosov School Olympiad in Mathematics

Preliminary stage $2020 / 21$ academic year for $7-8$ grades

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