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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?
Re: In a certain high school, 80 percent of the seniors are taking calculu
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20 Apr 2020, 11:12
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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?
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Re: In a certain high school, 80 percent of the seniors are taking calculu
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21 Apr 2020, 09:02
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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
In a certain high school, 80 percent of the seniors are taking calculu
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22 Apr 2020, 06:09
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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%
Re: In a certain high school, 80 percent of the seniors are taking calculu
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28 Apr 2020, 09:08
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Expert Reply
Top Contributor
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
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:
Re: In a certain high school, 80 percent of the seniors are taking calculu
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13 May 2020, 06:21
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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?
Re: In a certain high school, 80 percent of the seniors are taking calculu
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17 Apr 2021, 00:41
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Expert Reply
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
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