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

Question

Three rugs have a combined area of 200 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 24 square meters. What is the area that is covered with three layers of rug ?

A. 18 square meters
B. 20 square meters
C. 24 square meters
D. 28 square meters
E. 30 square meters

A. 18 square meters
B. 20 square meters
C. 24 square meters
D. 28 square meters
E. 30 square meters

Bunuel · Accepted Answer

Total = Rug1 + Rug2 + Rug3 - {overlap of exactly 2 rugs} - 2*{overlap of exactly 3 rugs} 140 = 200 - 24 - 2*{overlap of exactly 2 rugs} --> {overlap of exactly 3 rugs} = 18. Answer: A. For more about the formula used and the way it's derived see my post here: formulae-for-3-overlapping-sets-69014.html?hilit=exactly%20groups Hope it helps.

KarishmaB · Answer

Venn Diagram: I have given a letter to each region to clarify. Ques1.jpg 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'

krazo · Answer

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

n2739178 · Answer

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

n2739178 · Answer

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

n2739178 · Answer

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

KarishmaB · Answer

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!

PaulShep · Answer

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.

GMATinsight · Answer

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!

Bunuel · Answer

Theory on Overlapping Sets:
advanced-overlapping-sets-problems-144260.html
how-to-draw-a-venn-diagram-for-problems-98036.html

All DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
All PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65

PaulShep · Answer

Thanks, these are really helping1

Aamirso · Answer

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.

bumpbot · Answer

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

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

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