Three rugs have a combined area of 200 square meters. By overlapping t

Agree with A..

This is a triple overlapping set.

Here is how I did it (thanks for Horacio Quiroga of MGMAT for teaching me this technique)

S is the sum of just the single carpets, D is sum of double overlaps, and T is sum of the triple overlaps

S + 2D + 3T = 200 (accounts for the total area of carpets and overlaps)
S + D + T = 140 (excludes double counting)

Subtracting the equations gets me:

D + 2T = 60

I know that the total "double overlap" is 24 so I substitute in

2T = 60 - 24
T = 18

So far this technique has gotten me through all triple overlapping sets

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

wow that is awesome! I didn't realise you could simply solve using equations like that. This has clarified this 100% for me! thanks!

actually - how would you jump directly to x + y + z + 2k = 60 without writing the equations?

It is again a matter of thinking vs solving. If I think more, I have to solve less.
Combined area of rugs is 200 sq m while area of floor they cover is only 140 sq m. So what does the extra 60 sq m do? It covers another rug!
Wherever there are two rugs overlapping, one rug is not covering the floor but just another rug.
Wherever there are three rugs overlapping, two rugs are not covering the floor but just the third rug at the bottom.
so can I say that x + y + z is the area where one rug is covering another rug and k is the area where two rugs are covering another rug?
or put another way, can I say x + y + z + 2k = 60?

This entire 'thinking process' takes ten seconds once you are comfortable with it and your answer would be out in 30 sec flat!

I am new here from Melbourne, Australia and trying to solve as many questions as I can for my test. I am looking or more rugs type questions.

Hi paul,

Please refer to the links below:

search.php?search_tags=all&selected_search_tags%5B%5D=65&selected_search_tags%5B%5D=216

search.php?search_tags=all&selected_search_tags%5B%5D=65&selected_search_tags%5B%5D=187

search.php?search_tags=all&selected_search_tags%5B%5D=65&selected_search_tags%5B%5D=217


For any specific catagory of Questions please be guided by the directory

gmat-ps-question-directory-by-topic-difficulty-127957.html
ds-question-directory-by-topic-difficulty-128728.html

I hope it helps!

Hope it helps.

Thanks, these are really helping1

Effective area covered = individual areas - overlap of two areas - 2 x overlap of 3 areas.

So,

140 = 200 - 24 - 2x where x is the overlap of 3 areas.
x= 36/2 = 18

A is my answer.

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