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?
Overlapping Sets
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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
[/img]
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
[/img]
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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