pifinity's problem set

Welcome to pifinity's problem set! This page contains problems created by pifinity. Please do not edit this page.

Finalized Problems

Problem I

Evaluate $\frac{48}{32} + \frac{24}{16}.$

Solution I

Simplify; no denominator conversion needed: $\frac{48}{32} + \frac{24}{16}=\frac{3}{2} + \frac{3}{2} = \boxed{3}.$

Unconfirmed Problems

Problem

What is the $``\,?\,"$ term? $(100-96)+100+(96-92)+94+(92-88)+88+\hdots+?+(4-0)$

Solution

We first wish to find the number of "telescoping" terms. The first one is $100$ minus something, so we can label it $\tfrac{100}4=25.$ The last term is $4$ minus something, so we can label it $\tfrac{4}4=1.$ Thus there are $25-(4-1)=22$ terms. Therefore, there are 21 gaps between the terms in parentheses. Since there is one less of the terms not in parentheses, then there are 20 gaps between these terms in total. And since $6$ is subtracted each time for the terms not in parentheses, then we have to subtract $6\times20=120$ from $100$ : $100-120=\boxed{-20}.$