2021 JMPSC Sprint Problems/Problem 10

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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.


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 $4 + 8 + 12 + 16 = 40$.


See also

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

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