Category Archives: MATHCOUNTS

________ 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 →

________ 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 →

________ 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 →

________ In base $b$, $441_b$ is equal to $n^2$ in base 10, and $351_b$ is equal to $(n-2)^2$. What is the value of $b$, expressed in base 10? ________ The base-three representation of $0.\overline{12}$ is equivalent to what base-ten common … Continue reading →