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655-705 (Hard)|   Overlapping Sets|   Word Problems|                                 
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gabrielta
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Of the 300 subjects who participated in an experiment using virtual-re 16 Aug 2025, 02:37
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[ltr]A∩B+B∩C+C∩A=A∩B+B∩C+C∩A = Exactly two - 3x (assuming A∩B∩C=xA∩B∩C=x)

You wrote as above, but there is 1 mistake. It must be: A∩B+B∩C+C∩A=A∩B+B∩C+C∩A = Exactly two + 3x (assuming A∩B∩C=xA∩B∩C=x), not -3x[/ltr]

Just for a more perfect response.

Cheers.
cyberjadugar
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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
Hi,

We know, \(A\cup B\cup C = A+B+C-A\cap B-B\cap C-C\cap A +A\cap B\cap C\)
where
\(A = 40%\)
\(B = 30%\)
\(C = 75%\)
As per the attached Venn diagram,
\(A\cup B\cup C=100%\)

\(A\cap B+B\cap C+C\cap A=\)Exactly two - 3x (assuming \(A\cap B\cap C=x\))
\(=35-3x\)
Thus,
\(100= 40+30+75-(35-3x)+x\)
or \(x = 5%\)

Thus, subjects expriencing only one effect = 100% - (subjects expriencing only two effects) - (subjects expriencing all effects)
or subjects expriencing only one effect = 100 - 35 - 5 = 60%

60% of 300 = 180

Answer is (D)

Regards,
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dhruvie
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Of the 300 subjects who participated in an experiment using virtual-re 26 Sep 2025, 06:14
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Can solve via Venn.


macjas
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
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DanTheGMATMan
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Of the 300 subjects who participated in an experiment using virtual-re 21 Oct 2025, 07:34
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No charts or venn diagrams:
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