2. Vasya claims that the number of his friends who are good at mathematics is not less than $96.8\%$ and not more than $97.6\%$. It is known that the number of Vasya's friends does not exceed 150. Determine the largest number within the specified range that cannot be the number of Vasya's friends.
# Solution

Let $\mathrm{N}$ be the number of Vasya's friends. The number $x$ of Vasya's friends who are not good at math is in the range $0.024 N < x < 0.032 N$, then for $x=1, 31 \frac{1}{4} < N < 41 \frac{2}{3}$; for $x=2, 62 \frac{1}{3} < N < 83 \frac{1}{3}$; for $x=3, 93 \frac{3}{4} < N < 125$; for $x=4, 125 < N < 166 \frac{2}{3}$. Thus, the largest sought number is 125.

## Grading Criteria

Correct answer with justification - 7 points.

In case of an arithmetic error - no more than 4 points.

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