2021 JMPSC Sprint Problems/Problem 10

Problem

Serena gets a grade of $75\%$ for her chapter test. She doesn't remember how many problems there were, but she remembers that there were at most $18$ problems, each problem solved correctly was worth an equal amount of points, and she did not receive any points for an incorrect or skipped question. Find the sum of all the possible numbers of problems that the test could have had.

Solution

Because $75\% = \frac{3}{4}$, $\frac{3}{4} n = s$ where $s$ is an integer. This implies that $n$ is a multiple of $4$. The multiples of $4$ less than $18$ are $4$, $8$, $12$, and $16$, so the answer is $4 + 8 + 12 + 16 = 40$.

~Mathdreams


See also

  1. Other 2021 JMPSC Sprint Problems
  2. 2021 JMPSC Sprint Answer Key
  3. All JMPSC Problems and Solutions

The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition. JMPSC.png

Invalid username
Login to AoPS