n2739178 wrote:

Hi,

MGMAT advocates using Venn diagrams for triple sets ... I have no idea how to do this with Venn diagrams... can someone please help me?

Thinking in Venn diagram terms here:

I thought there are actually 3 pairs of 2 overlapping rug areas in this question (r1 overlapping r2, r2 overlapping r3, r1 overlapping r3)

and not 2? So shouldnt it be 3*24 to count all double overlaps?

And, isn't there only 1 overlap of all 3 rugs!?

Sorry but I'm thoroughly confused here

Thanks

Venn Diagram:

I have given a letter to each region to clarify.

Attachment:

Ques1.jpg [ 16.36 KiB | Viewed 6540 times ]
Rug 1 + Rug 2 + Rug 3 = 200

(a + x + y + k) + (b + x + k + z) + (c + y + k + z) = 200

But area of floor covered is only 140 i.e. if each section is counted only once

a + b + c + x + y + z + k = 140

Subtracting second equation from first, x + y + z + 2k = 60

But x + y + z (Area with two layers of rug) = 24

So 2k = 36 or k = 18

This is how it can be done using a venn diagram.

Note: You obviously wouldn't need to make all these equations and can directly jump to x + y + z + 2k = 60 but I wrote them down for clarity. It is really hard to say 'Section of Rug 1 which is in single layer..section of rug 2 in two layers etc'

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