Category Archives: Math Classes

AMC 8 Exercises 1 – 02/01/2024

Posted on February 1, 2022 by kevin

The sum of the first three prime number greater than 50 is $$ $$ $\textbf{(A) }169 \qquad\textbf{(B) }171 \qquad\textbf{(C) }173 \qquad\textbf{(D) }175 \qquad \textbf{(E) } 177$ $$ $$ In a regular hexagon, the ratio between the shortest diagonal and the … Continue reading →

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MATHCOUNTS 2022 Exercises – 4

Posted on January 14, 2022 by kevin

Given $n>1$, what is the smallest positive integer $n$ whose positive divisors have a product of $n^6$? What is the largest integer value of $n$ for which $8^n$ evenly divides $100!$? A positive number is called $n$-primable if it is … Continue reading →

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Math Olympiad for 3th Grade – 7

Posted on January 7, 2022 by kevin

I have $30$ coins consisting of nickels and quarters. The total value of the coins is $\$4.10$. How many of each kind do I have? If we count by $3s$ starting with $1$, the following sequence is obtained. $1, 4, … Continue reading →

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MATHCOUNTS 2022 Exercises – 3

Posted on December 17, 2021 by kevin

5 persons to be seated on 5 chairs arranged in a row. Two of these persons cannot sit next to each other. How many seating arrangements are possible? How many four-digit integers for which the thousands digit equals the sum of the other … Continue reading →

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MATHCOUNTS 2022 Exercises – 2

Posted on December 3, 2021 by kevin

An ant is traveling along the side of a regular dodecagon with side length as $1$. What is the expected value of minimum distance the ant travels between two different vertices randomly chosen? Express your answer as a common fraction … Continue reading →

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