2021 JMPSC Sprint Problems/Problem 10

Revision as of 12:27, 11 July 2021 by Mathdreams (talk | contribs) (Solution)

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

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