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Overlapping Sets

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Overlapping Sets

by mtripathy » Sun Sep 16, 2012 9:58 pm
Source: OG 13th Edition

Of the 300 subjects who participated in an experiment using virtual-reality therapy to reduce their fear of heights, 40 percent experienced sweaty palms, 30 percent experienced vomiting, and 75 percent experienced dizziness. If all of the subjects experienced at least one of these effects and 35 percent of the subjects experienced exactly two of these effects, how many of the subjects experienced only one of these effects?

(A) 105
(B) 125
(C) 130
(D) 180
(E) 195

OA: D

I have found the OG answer explanation too complicated. Can anyone (experts) please suggest a better explanation using the overlapping set tables, which is generally used for solving such problems?
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by everything's eventual » Sun Sep 16, 2012 10:19 pm
I do not know how to post images so I will try ans explain algebraically.

Assume the following :

No. of participants who experienced only sweaty palms : a
No. of participants who experienced only Vomiting : b
No. of participants who experienced only dizziness : c

No. of participants who experienced sweaty palms and Vomiting : d
No. of participants who experienced vomiting and dizziness : f
No. of participants who experienced sweaty palms and dizziness: e

No. of participants who experienced all three: g

Now total participants are 300

Therefore, a + b + c + d + e + f + g = 300

It is also given that 35% of subjects experienced exactly two of these effect.

Therefore d + e + f = 105 ( 35% of 300)

Therefore main equation becomes - a + b + c + g = 195......equation (1)

Now, it is also given in the question that:

a + d + g + e = 120 ( 40% of 300)
b + d + f + g = 90 ( 30% of 300)
c + e + f + g = 225 ( 75% of 300)

Add all above equations and you get - a+b+c+ 2d+2e+2f+3g = 435

Again substitute d+e+f = 105 and you get

a+b+c+3g = 225....equation (2)

Solve equation (1) and equation (2) and you get a + b + c = 180
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by GMATGuruNY » Mon Sep 17, 2012 1:48 am
I posted a solution here:

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by avada » Mon Sep 17, 2012 11:26 am
how would you solve with image?
i am sure its a venn but have trouble setting them up
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