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In a certain high school, 80 percent of the seniors are taki

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In a certain high school, 80 percent of the seniors are taki [#permalink] New post 26 Jun 2020, 09:39
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In a certain high school, 80 percent of the seniors are taking calculus, and 60 percent of the seniors who are taking calculus are also taking physics. If 10 percent of the seniors are taking neither calculus nor physics, what percent of the seniors are taking physics?

(A) 40%
(B) 42%
(C) 48%
(D) 58%
(E) 80%
[Reveal] Spoiler: OA

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Re: In a certain high school, 80 percent of the seniors are taki [#permalink] New post 26 Jun 2020, 09:40
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Re: In a certain high school, 80 percent of the seniors are taki [#permalink] New post 26 Jun 2020, 09:51
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Carcass wrote:
In a certain high school, 80 percent of the seniors are taking calculus, and 60 percent of the seniors who are taking calculus are also taking physics. If 10 percent of the seniors are taking neither calculus nor physics, what percent of the seniors are taking physics?

(A) 40%
(B) 42%
(C) 48%
(D) 58%
(E) 80%


One approach is to use the Double Matrix Method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of seniors, and the two characteristics are:
- taking calculus or not taking calculus
- taking physics or not taking physics

Since we are asked to find a certain PERCENT, let's say that there are 100 seniors in the school.

Our initial diagram looks like this:
Image


80 percent of the seniors are taking calculus
So 80 seniors are taking calculus, and the remaining 20 seniors are not taking calculus. We get:
Image


60 percent of the seniors who are taking calculus are also taking physics.
We know that 80 seniors are taking calculus
60 percent of 80 = 48
So, 48 seniors are taking calculus AND physics. We get:
Image


If 10 percent of the seniors are taking neither calculus nor physics, what percent of the seniors are taking physics?
10% of 100 = 10
So 10 seniors are taking NEITHER calculus NOT physics. We get:
Image


What percent of the seniors are taking physics?
When we complete the rest of the diagram we get:
Image


We can now see that 58 of the 100 seniors are taking physics.
In other words, 58% of the seniors are taking physics

Answer: D

Aside: We can also use Venn diagrams and formulae to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method works every time.

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Re: In a certain high school, 80 percent of the seniors are taki   [#permalink] 26 Jun 2020, 09:51
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