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In a certain high school, 80 percent of the seniors are taking calculu
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Author:  gmatt1476 [ 20 Apr 2020, 10:55 ]
Post subject:  In a certain high school, 80 percent of the seniors are taking calculu

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

Author:  ScottTargetTestPrep [ 13 May 2020, 06:21 ]
Post subject:  Re: In a certain high school, 80 percent of the seniors are taking calculu

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%



We can create the equation:

Total = Calculus + Physics - Both + Neither

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

10 = P - 48

58 = P

Answer: D

Author:  nick1816 [ 20 Apr 2020, 11:12 ]
Post subject:  Re: In a certain high school, 80 percent of the seniors are taking calculu

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%



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


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Author:  Archit3110 [ 21 Apr 2020, 09:02 ]
Post subject:  Re: In a certain high school, 80 percent of the seniors are taking calculu

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

Author:  rahulbhusan [ 22 Apr 2020, 06:09 ]
Post subject:  In a certain high school, 80 percent of the seniors are taking calculu

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 :)

Author:  BrentGMATPrepNow [ 28 Apr 2020, 09:08 ]
Post subject:  Re: In a certain high school, 80 percent of the seniors are taking calculu

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:
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.

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:


Then you can try answering the following practice question:

Author:  CrackverbalGMAT [ 11 Feb 2021, 23:36 ]
Post subject:  Re: In a certain high school, 80 percent of the seniors are taking calculu

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 :thumbsup:
Devmitra Sen(Math)

Author:  GMATinsight [ 17 Apr 2021, 00:41 ]
Post subject:  Re: In a certain high school, 80 percent of the seniors are taking calculu

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


Answer: Option D

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
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Post subject:  Re: In a certain high school, 80 percent of the seniors are taking calculu

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