Monthly Archives: September 2023

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 →

Posted in Algebra, Math Classes, MATHCOUNTS | Comments Off on MathCounts Training – Number Theory – 6

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 →

Posted in Math Classes, MATHCOUNTS, Number Theory | Comments Off on MathCounts Training – Number Theory – 5

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 →

Posted in Math Classes, MATHCOUNTS, Number Theory | Comments Off on MathCounts Training – Number Theory – 4

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 →

Posted in Math Classes, MATHCOUNTS, Number Theory | Comments Off on MathCounts Training – Number Theory – 3