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2014 CEMC Gauss (Grade 8) Problems/Problem 17

Revision as of 13:32, 24 April 2025 by Anabel.disher (talk | contribs) (Created page with "==Problem== On a science test, Janine got <math>80\%</math> of the <math>10</math> multiple choice questions correct and <math>70\%</math> of the <math>30</math> short answer...")
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Problem

On a science test, Janine got $80\%$ of the $10$ multiple choice questions correct and $70\%$ of the $30$ short answer questions correct. What percentage of the $40$ questions on the test did she answer correctly. $\text{ (A) }\ 74\% \qquad\text{ (B) }\ 72.5\% \qquad\text{ (C) }\ 76\% \qquad\text{ (D) }\ 73\% \qquad\text{ (E) }\ 73.5\%$

Solution

We can add the number of multiple choice questions that Janine did correctly added to the free-response/short answer questions that she got correct:

$80\% \times 10 + 70\% \times 30 = 8 + 21 = 29$

Next, we can now find the percentage that she got right out of the total 40 questions:

$\frac{29}{40} \times 100\%$ = $\boxed {\textbf {(B) } 72.5\%}$

~anabel.disher

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