Source: Official Guide for the GMAT 13th Ed. Problem Solving; #178 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #178

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Of the 300 subjects who participated in

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 subject experienced exactly two of these effects, how many subjects experienced only one of these effects?

3 Explanations

3

SONIKA VASANTH

From the question WKT 40% experienced wetting and 30% experienced vomiting
So it should be A+B. I dint understand why it is A +B+C
Total=A+B+C-(AnB+AnC+BnC)(or Exactly 2-group overlaps)- 2*(AnBnC)+Neither

Why do we subtract 2(AnBnCn)?

Dec 10, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Sonika,

As I mentioned before, we need to subtract 2(AnBnCn) in order to account for the over-counting of this group. Someone in this group experiences all of the symptoms and is therefore counted in the groups A, B, and C. However, a subject in the group (AnBnC) is really only one individual, so we should only be counting the subject once. To account for the over-counting, we subtract 2 of the 3 times the subject was counted as a part of the various groups. That way, we only count subjects in the group (AnBnC) once :)

I hope this clears up your doubts!

12

Cydney Seigerman, Magoosh Tutor

Hi Jonathan Wong!

Good question :) In the explanation above, Misagh used the formula for three overlapping sets:

Total = A + B + C - (AnB+AnC+BnC) - 2*(AnBnC) + Neither

where (AnB+AnC+BnC) is the sum of 2-group overlaps and (AnBnC) represents subjects with all three symptoms.

For the term 2*(AnBnC), we can think about why we need to subtract 2*(all three) in the following way: if a subject experiences all three symptoms, the subject will be counted 3 different times (once for A, once for B, and once for C.) However, we are still only talking about 1 subject. Since he is represented 3 times, we need to subtract the two extra times that he was counted.

Oct 10, 2015 • Comment

8

Misagh Tavajjoh

300*40/100= 120 sweaty palms
300*30/100=90 vomiting
300*75/100=225 dizziness
300*35/100=105 (35%subjects experienced exactly two of these effects)
Neither=0
At first we need to find overlapping between 3 groups(AnBnC):

Total=A+B+C-(AnB+AnC+BnC)(or Exactly 2-group overlaps)- 2*(AnBnC)+Neither

300=120+90+225-105-2(AnBnC)+0
300=435-105-2(AnBnC)
300=430-2(AnBnC)
(AnBnC) = 15

300-105(Exactly 2-group overlaps)-15(overlaps of three groups)=180
180= subjects experienced only one of these effects

May 21, 2015 • Comment

Jonathan , Magoosh Tutor

Great job! Note that you can also work out the problem in percents to get 60% and then just take 60% of 300 to get 180 at the end.

Robert Bailen

Shouldn't 300=430-2(AnBnC) actually be 300=330-2(AnBnC) ?

Jonathan , Magoosh Tutor

Yes, Robert, you're correct. Thanks for catching that typo! :)