Category Archives: Math Classes

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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MathCounts Training – Number Theory – 5

Posted on September 15, 2023 by kevin

________ Let $(a\times b\times c)\div(a+b+c)=341$ to be an equation where $a$, $b$ and $c$ are consecutive positive integers. What is the least possible value of $a$? $$ $$ ________ The letters $A$, $B$, $C$, $D$, $E$ and $F$ represent digits … Continue reading →

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MathCounts Training – Number Theory – 4

Posted on September 8, 2023 by kevin

________ What is the greatest positive integer that must divide the sum of the first ten terms of any arithmetic sequence whose terms are positive integers?$$ $$ ________ A digit can be placed in each of the boxes for hundreds … Continue reading →

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MathCounts Training – Number Theory – 3

Posted on September 1, 2023 by kevin

________ What is the sum of all integer values of $n$ such that $\dfrac{20}{2n-1}$ is an integer? ________ What is the units digit of the sum of the sum of all the integers from 100 to 202 inclusive? ________ How … Continue reading →

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MATHCOUNTS Exercises

Posted on August 27, 2023 by kevin

Two dices are thrown simultaneously. The probability that the sum of the two numbers on the top faces of the dices is a prime number is __________. Suppose $ABCD$ is a regular triangular pyramid, with each face as a unit … Continue reading →

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