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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Within a group of students, x students are taking English, y
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21 Jun 2018, 06:29
21 Jun 2018, 06:29
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59% (01:11) correct
40% (00:45) wrong based on 55 sessions
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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
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, y
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22 Jun 2018, 08:00
22 Jun 2018, 08:00
1
GreenlightTestPrep 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?
Here
E = number of students taking English
Y= number of students taking Math
Z= number of students taking both English and Math
Therefore number of students taking only english = X-Z
and number of student taking only math = Y-Z
Hence
number of students who are taking English or Math but not both = (X-Z)+(Y-Z) = X+Y-2Z
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Within a group of students, x students are taking English, y
[#permalink]
24 Jun 2018, 06:16
24 Jun 2018, 06:16
1
GreenlightTestPrep 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
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
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