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Within a group of students, x students are taking English
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21 Jun 2018, 06:30
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Within a group of students, x students are taking English, y students are taking Math, and z students are taking both English and Math. Which of the following represents the number of students who are taking English or Math but not both?
A) x + y - z B) x + y + z C) 2x + 2y - z D) x + y - 2z E) x + y + 2z
Re: Within a group of students, x students are taking English
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24 Jun 2018, 06:15
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GMATPrepNow wrote:
Within a group of students, x students are taking English, y students are taking Math, and z students are taking both English and Math. Which of the following represents the number of students who are taking English or Math but not both?
A) x + y - z B) x + y + z C) 2x + 2y - z D) x + y - 2z E) x + y + 2z
We can solve this by using the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of students, and the two characteristics are: - taking English or not taking English - taking Math or not taking Math
We want to find: (number of students taking English but not Math) + (number of students taking Math but not English) So, we can set up our matrix as follows:
We need to find the number of students in the 2 boxes with stars in them.
GIVEN: x students are taking English, and y students are taking Math So, we can add this information to our diagram as follows:
GIVEN: z students are taking both English and Math So, we can add this information to our diagram as follows:
Let's first examine the top ROW. If a total of x students are taking English, and z of them are also taking Math, then x-z of them are NOT taking Math.
Now examine the left-hand COLUMN. If a total of y students are taking Math, and z of them are also taking English, then y-z of them are NOT taking English.
So, the number of students who are taking English or Math but not both = (x - z) + (y - z) = x + y - 2z
Answer: D
NOTE: 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:
Within a group of students, x students are taking English
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06 Jan 2020, 04:55
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Hey, all!
Could anyone plase explain why the standard formula doesn't work in this question, i.e. Total = Set1+Set2 + Neither - Both
I understand that according to the text neither in this case = 0, but other parts of the formula do not lead to the right asnwer. So, total = Set1(x) + Set2 (y) - Both (z) = x+y-z.
Thank you in advance!
UPD: the mystery is solved. When we substract z only once, we still acoount it but avoid doubling. And when we substract z twice we find pure set of x and set of y.
Re: Within a group of students, x students are taking English
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01 Feb 2021, 12:57
The key here is to recognize that x and y EACH include the number who are also taking English or math respectively. In other words, "Both English and Math" have been double-counted so if we want either English or Math, we have to remove z twice.
x + y - 2z
Answer is D. _________________
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