Category Archives: MATHCOUNTS

AMC 10 Exercise – 2

Posted on October 20, 2024 by kevin

What is the tens digit of $2019^{2020}-2021$? All the numbers $2$,$3$,$4$,$5$ are assigned to the four faces of a tetrahedron. For each of the four vertices of the tetrahedron, a product of three numbers are computed, where the three numbers … Continue reading →

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AMC 10 Exercise – 1

Posted on September 20, 2024 by kevin

Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be $2:1$? Two right circular cylinders … Continue reading →

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A MATHCOUNTS Problem with Multiple Answers 🙂

Posted on August 19, 2024 by kevin

The following is MATHCOUNTS 2012 National Competition Sprint Round Problem 22: In circle $O$, shown, $OP=2$ units, $PL=8$ units, $PK=9$ units and $NK=18$ units. Points $K$, $P$ and $M$ are collinear, as are points $L$, $P$, $O$ and $N$. What … Continue reading →

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AMC 8/MathLeague Mock Test – 1

Posted on January 26, 2024 by kevin

If the hands on a circular clock start at midnight, what number will the hour hand point to 1000 hours later? $(A)\ 2 \ \ \ \ \ \ \ \ \ (B)\ 4 \ \ \ \ \ \ … Continue reading →

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MathCounts Training – Number Theory – 6

Posted on September 22, 2023 by kevin

________ What is the sum of all positive two-digit integers with exactly 12 positive factors? $$ $$ ________ What is the sum of the three numbers less than 1000 that have exactly five positive integer divisors? $$ $$ ________ The … Continue reading →

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