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Of the students at a certain high school, 40% take physics. Of those students who don’t take physics, 20% do take

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by M7MBA » Sat May 30, 2020 3:55 pm

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Of the students at a certain high school, 40% take physics. Of those students who don’t take physics, 20% do take calculus. What percentage of students take neither physics nor calculus?

A. 12%
B. 40%
C. 48%
D. 60%
E. 75%

[spoiler]OA=C[/spoiler]

Source: Manhattan GMAT
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Re: Of the students at a certain high school, 40% take physics. Of those students who don’t take physics, 20% do take

by orthodoxparadox » Sat May 30, 2020 11:56 pm
Let percentages be as follows

\(a\%\) - Physics
\(b\%\) - Calculus
\(c\%\) - Both
\(d\%\) - None

Clearly, $$a\ +\ b\ +\ c\ +\ d\ =\ 100$$ $$a\ +\ c\ =\ 40$$ $$\left(b\ +\ d\right)\ =\ 100\ -\ \left(a\ +\ c\right)\ =\ 60$$ $$20\%\ \cdot\ \left(b\ +\ d\right)\ =\ b\ \ =12\%$$ $$d\ =\ 100\ -\ a\ -\ b\ -\ c\ =\ 100\ -\ \left(a\ +\ c\right)\ -\ b\ =\ 100\ -\ 40\ -\ 12\ =\ 48\%$$ C
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