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How to draw a Venn Diagram for problems

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Re: How to draw a Venn Diagram for problems  [#permalink]

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New post 30 Jul 2013, 20:53
I really loved the way how you solved this problem and it has helped me immensely. However I spot a mistake at the end of your post.


whiplash2411 wrote:

\(x+y+z+171 - 2(x+y+z)= 144\)

Upon rearranging this you get:

[m]x+y+z = 171-144 = 37[/m]which is option A the right answer.

Hope this helps some of you! :) Please post a reply if there's anything else you want to know about my explanation or anything else.


171 - 144 = 27, but 27 is not one of the answers. :shock:

Edit: My bad, didn't see that other people have pointed this out! Sorry~
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Re: How to draw a Venn Diagram for problems  [#permalink]

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New post 02 Sep 2015, 11:05
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Thanks for the post whiplash2411. However, there is an easier and faster way to do this.

Math = 53
Chemistry = 88
English = 58
Total = 199

This total counts x, y, z twice (students taking 2 classes) and 6 thrice (students taking 3 classes). We need to count these only once to arrive at the number of students taking exactly 2 classes.

First get rid of the double counting by subtracting the actual number of students from the total above. Deal with the triple counting in the next step.

Total = 199
No. of students =(150)
Remaining = 49

Since 6 has been counted thrice, subtract 6 twice (6*2 = 12) from the remainder to count it exactly once.

Remaining = 49
Subtract 12 =(12)
Final = 37

Thus, the number of students taking exactly 2 classes is 37.

Hope this helps :)
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Re: How to draw a Venn Diagram for problems  [#permalink]

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New post 19 Nov 2015, 11:28
Great explanation!

Its amazing how complex word problems can come down to simple solutions (after you learn the step by step process, of course!)

1 - (88+53+58)-3(6) = 181

2 - (150-6) = 144

(1)-(2) =37.
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Re: How to draw a Venn Diagram for problems  [#permalink]

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New post 19 Nov 2015, 22:45
manhattan187 wrote:
Great explanation!

Its amazing how complex word problems can come down to simple solutions (after you learn the step by step process, of course!)

1 - (88+53+58)-3(6) = 181

2 - (150-6) = 144

(1)-(2) =37.


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Re: How to draw a Venn Diagram for problems  [#permalink]

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New post 11 Jun 2016, 19:32
Solution should be 27, not 37...but the explanation is great, and it's easy to follow!
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Re: How to draw a Venn Diagram for problems  [#permalink]

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New post 12 Sep 2017, 04:46
Love your work. Can you post for examples of venn diagram since I've found it very often in real test :)
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Re: How to draw a Venn Diagram for problems  [#permalink]

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New post 12 Sep 2017, 04:49
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Re: How to draw a Venn Diagram for problems  [#permalink]

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New post 26 Sep 2017, 02:02
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Loved the explanation. See the attachment: this is how I approached this question.
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Re: How to draw a Venn Diagram for problems  [#permalink]

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Re: How to draw a Venn Diagram for problems   [#permalink] 02 Oct 2018, 05:13

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