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

Question

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%

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

PS21260.02

ScottTargetTestPrep · Accepted Answer

We can create the equation:

Total = Calculus + Physics - Both + Neither

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

10 = P - 48

58 = P

Answer: D

nick1816 · Answer

Percentage of the seniors that are taking calculus or physics = 100-10 = 90%

Percentage of the seniors that are taking calculus = 80%

Percentage of the seniors that are taking both calculus and physics = 80*0.6 = 48%

percent of the seniors that are taking physics = (90-80)+48= 58%

Archit3110 · Answer

solved using 2x2 matrix

------Calculus------no calculus-----total
Physics--48---------10------------- 58 
no physics--32------10--------------42
total-------80-------20-------------100

OPTION D

rahulbhusan · Answer

2X2 Matrix Consider total seniors as 100S -----------------Calculus -----------No Calculus ----Total Physics----------48S-------------------10S-------------58S No Physics------32S-------------------10S-------------42S Total-------------80S------------------- 20S ------------100S 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 = 58 S physics%= 58S/100S => 58% ( Option D) Edited the alignments

BrentGMATPrepNow · Answer

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: 
 https://i.imgur.com/g7hBLmP.png

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: 
 https://i.imgur.com/gUnTuNl.png

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: 
 https://i.imgur.com/HGg7QBv.png

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: 
 https://i.imgur.com/7L0ndgD.png

What percent of the seniors are taking physics?  
When we complete the rest of the diagram we get:
 https://i.imgur.com/QsKUi8K.png

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.youtube.com/watch?v=jK-tiBrrf04

Then you can try answering the following practice question:
 https://www.youtube.com/watch?v=DsbPUSH_Wu4

CrackverbalGMAT · Answer

SOLUTION :
A NEW OG 2021 QUESTION

Its a question testing on your application skills in Overlapping sets(Concept-Set Theory).

Seniors taking Calculus (C)= 80% = 80 students

Seniors taking BOTH Calculus and Physics( C AND P) = 60% of 80 =48 students

=>Thus, seniors taking ONLY Calculus = 80 -48 =32

Seniors taking neither calculus nor physics= 10% = 10 students

We know Total = Only C + (C & P) + Only P +Neither

=> 100 = 32 + 48+ Only P + 10

=> 100 = 32+ 48 + Only P + 10
=> Only P = 100-90 = 10

The total number of seniors taking Physics
= Only P + (C & P)
=10 + 48 =58 (OPTION D)

Hope this helps

Devmitra Sen(Math)

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=cKzXw8iVdQQ

ArnauG · Answer

Let's calculate the percentage of seniors taking physics using the given information:

Let's assume there are 100 seniors in total.

80 percent of the seniors are taking calculus, which means 80 seniors are taking calculus.
Among the seniors taking calculus, 60 percent are also taking physics. So, 60 percent of 80 seniors (48 seniors) are taking both calculus and physics.
The percentage of seniors taking neither calculus nor physics is 10 percent, which means 10 seniors are not taking either subject.
To find the percentage of seniors taking physics, we need to calculate the number of seniors taking physics and divide it by the total number of seniors:

Number of seniors taking physics = Number of seniors taking both calculus and physics = 48

Percentage of seniors taking physics = (Number of seniors taking physics / Total number of seniors) * 100 = (48 / 100) * 100 = 48 percent

Therefore, the answer is (C) 48%.

Nikhil_Rai · Answer

I think you made an error as you will also have to account for the remaining seniors here.

Who took calculus= 80
Who took neither= 10
Who took only Physics= 100-(80+10)=10
(We did not take seniors with Physics and Calculus in this calculation as this is a subset of seniors who took calculus hence is already included in this number)

Hence, Percentage of seniors who took Physics= (Seniors who took Physics +Seniors who took both calculus and Physics)/100= (48+10)/100)= 58-- Option(D)

demawtf · Answer

double matrix method:

C                   No C                    TOT
P            60%*80%= 48                                 (100-48)=58 <---------

No P           (80-48)= 32          10 (given)                42

TOT            80 (given)             (100-80)=20           100

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards