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good one for practice of set theory

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by arora007 » Wed Jun 23, 2010 11:49 am
In a group of 30 students, 18 are enrolled in an english class and 16 are enrolled in an algebra class, how many students are enrolled in both an english and algebra class?

1) 20 are enrolled in exactly one of the these two classes
2) 3 are not enrolled in either of these classes.

OA is D

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Source: — Data Sufficiency |
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by jonathan123456 » Wed Jun 23, 2010 12:23 pm
Ans D
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by hemanthquartz1 » Wed Jun 23, 2010 12:32 pm
jonathan123456 - Please explain your answer.
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by jonathan123456 » Wed Jun 23, 2010 12:55 pm
Draw Chart for
A=16
E=18
NE (Not English)
NA= Not Algebra

1.

E & NA = x
A & NE = y

x + y = 20
NA & NE = 12-y
So x-y =2

So x=11 (E & NA)
and y=9

So you can find others

2. Put it into chart, this is simple to solve

Therefore D
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by hemanthquartz1 » Wed Jun 23, 2010 1:26 pm
Thanks Jonathan.
This is a good question.
Set problem is one of my weakest areas in math. Is there any guide which can help us with Set problem and venn diagrams?
I would really appreciate if you can share any good material on this subject if you have one.

Thanks
Hemanth
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by Haaress » Sun Jun 27, 2010 12:19 pm
I am not sure that I agree with the stretched meaning of stmt 1 as posited in Jonathan's explanation. Jonathan's calculation might be correct , however, the intended meaning is not potrayed in the statement.

1) 20 are enrolled in exactly one of the these two classes .

Here is my intepretation of the statement 1 - 20 students are enrolled in one of the two classes, but x + y would be the total number of students in 2 ( not 1)classes.

Please clarify. Thanks!
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by gmatrant » Sun Jun 27, 2010 5:54 pm
1) 20 are enrolled in exactly one of the these two classes .

NE E | Total
-------------------------------------
A | 16-X | X | 16
NA | | 18-X |
-------------------------------------
18

16-x + 18-x = 20
-2x = -14
x=7

1. Can you confirm if the above is the right calculation

2.
I don't understand the below?
E & NA = x
A & NE = y

x + y = 20
NA & NE = 12-y
So x-y =2

So x=11 (E & NA)
and y=9

Please explain
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by albatross86 » Mon Jun 28, 2010 8:31 am
Please refer to the attached image.

Here, E and A refer to "only english" and "only algebra" respectively. B - both. N - neither

Question stem:

E + A + B + N = 30 ....1
E + B = 18 ....2
A + B = 16 ....3

We have to find B.


Statement 1

E + A = 20 ...4

Some people were concerned about the word translation. Don't overthink - 20 people are enrolled in exactly one class. E represents those who only take english, and A are the ones who only take algebra. There is no other possibility in this world.

Add equations 2 and 3:

E + A + 2B = 34

Substituting the value of E + A:

20 + 2B = 34 .... SUFFICIENT


Statement 2

N = 3

Substituting in eqn 1:

E + A + B = 27

But we know E + A + 2B = 34

SUFFICIENT


Pick D
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~Abhay

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