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

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Re: In a certain high school, 80 percent of the seniors are taking calculu [#permalink]
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gmatt1476 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%

PS21260.02

solved using 2x2 matrix

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

OPTION D
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In a certain high school, 80 percent of the seniors are taking calculu [#permalink]
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gmatt1476 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%

PS21260.02

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
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Re: In a certain high school, 80 percent of the seniors are taking calculu [#permalink]
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gmatt1476 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%

PS21260.02

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

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.

Then you can try answering the following practice question:
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Re: In a certain high school, 80 percent of the seniors are taking calculu [#permalink]
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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)
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Re: In a certain high school, 80 percent of the seniors are taking calculu [#permalink]
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gmatt1476 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%

PS21260.02

Video solution by GMATinsight

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Re: In a certain high school, 80 percent of the seniors are taking calculu [#permalink]
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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%.
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Re: In a certain high school, 80 percent of the seniors are taking calculu [#permalink]
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)
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In a certain high school, 80 percent of the seniors are taking calculu [#permalink]
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
In a certain high school, 80 percent of the seniors are taking calculu [#permalink]
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