In a certain high school, 80 percent of the seniors are taking calculus, and 60 percent

[BTGModeratorVI]

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%

Answer: D
Source: Official guide

[Brent@GMATPrepNow]

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%

Answer: D
Source: Official guide

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:



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:



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:



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:



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



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.
This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
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- https://www.beatthegmat.com/motel-t271938.html
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- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

[swerve]

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%

Answer: D
Source: Official guide

\(2\times 2\) Matrix
Consider total seniors as \(100S\)
\begin{array}{|c|c|c|c|}
\hline
& \text{Calculus} & \text{No Calculus} & \text{Total} \\ \hline
\text{Physics} & 48S & 10S & 58S \\ \hline
\text{No Physics} & 32S & 10S & 42S \\ \hline
\text{Total} & 80S & 20S & 100S \\ \hline
\end{array}

\(80\%\) takes calculus, so \(80S\) (Calculus) and \(20S\) (No Calculus)
\(60\%\) of those who take calculus also takes physics, so, \(60\%\) of \(80S= 48S\), takes both calculus and physics.

Therefore, \(32S\) takes only calculus and no physics.

\(10\%\) takes neither, so \(10S\) for no physics and no calculus.

Therefore, total physics \(= 58S\)
physics\(\%= \dfrac{58S}{100S} \Rightarrow 58\%\)

Hence, D

[Scott@TargetTestPrep]

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%

Answer: D
Source: Official guide

Solution:

We can create the equation:

Total = Calculus + Physics - Both + Neither

100 = 80 + P - 0.6(80) + 10

10 = P - 48

58 = P

Alternate Solution:

Let the number of seniors be 100. Since 80 are taking calculus and 10 are not taking either subject, 100 - (80 + 10) = 10 students take physics only. Further, 80 x 60/100 = 48 students take both calculus and physics. Thus, 48 + 10 = 58 students take physics, and this is 58% of all the seniors.

Answer: D