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
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Of the students at a certain high school, 40% take physics. Of those students who don’t take physics, 20% do take
This topic has expert replies
-
orthodoxparadox
- Junior | Next Rank: 30 Posts
- Posts: 15
- Joined: Sat May 30, 2020 10:48 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
\(a\%\) - 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
