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Of the 300 subjects who participated in an experiment using [#permalink]

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08 Jun 2012, 00:16

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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?

Re: Of the 300 subjects who participated in an experiment using [#permalink]

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08 Jun 2012, 00:57

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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%

Adding equations (1), (2) and (3) we get x+y+z+2(p+q+r+w)+w=435 subtract equation (a) from above equation we get p+q+r+2w = 135 given p+q+r = 105 (35% of 300)

so w =15 and p+q+r+w = 120

substitute value of above equation in (a) gets x+y+z = 180

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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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15 Aug 2013, 10:18

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So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer

i dont understand why Vandygrad multiplies 2 gr overlaps by 2 and 3 gr overlaps by 3? dont we need to minus 3 times "exactly 2 gr" overlaps and once "3 gr" overlaps?

Re: Of the 300 subjects who participated in an experiment using [#permalink]

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15 Aug 2013, 13:25

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macjas wrote:

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

exactly two = A+B+C-2(A n B n C)-(A u B u C) OR, 35 = 40+30+75 - 2(A n B n C) - 100 OR, (A n B n C) = 5% = 5% OF 300 = 15

Exactly 3 = 15 Exactly 2 = 35% of 300 = 105 So exactly one = 300 -(15+105) = 180 (Answer)
_________________

So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer

i dont understand why Vandygrad multiplies 2 gr overlaps by 2 and 3 gr overlaps by 3? dont we need to minus 3 times "exactly 2 gr" overlaps and once "3 gr" overlaps?

Re: Of the 300 subjects who participated in an experiment using [#permalink]

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18 Aug 2013, 04:53

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Galiya wrote:

Quote:

So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer

i dont understand why Vandygrad multiplies 2 gr overlaps by 2 and 3 gr overlaps by 3? dont we need to minus 3 times "exactly 2 gr" overlaps and once "3 gr" overlaps?

The reason is simple; you do not want to include any of the common elements. In this case there are three elements;

So when you add A and B you are counting the exactly2 common elements twice once with A and once with B ; so considering other combinations we subtract 2gr overlaps twice and not thrice.
_________________

--It's one thing to get defeated, but another to accept it.

Re: Of the 300 subjects who participated in an experiment using [#permalink]

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19 Aug 2013, 11:55

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macjas wrote:

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

100%=40%+30%+75%-35%-2*x or, 2x=10% or, x=5% Experienced only one of these effects=100%-35%-5%=60% By the way, 100%=300 or, 1%=300/100 or, 60%=300*60/100=180 So, the best answer is (D). posted By mannan mian

So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer = 120 + 90 + 225 - 105*2 - 15*3 = 435 - 210 - 45 = 180

Can someone explain how we get the formula highlighted in red above? Why do we multiply the 2-group overlaps and 3-group overlaps by 2 and 3 respectively? I didn't get that part. Thanks.

So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer = 120 + 90 + 225 - 105*2 - 15*3 = 435 - 210 - 45 = 180

Can someone explain how we get the formula highlighted in red above? Why do we multiply the 2-group overlaps and 3-group overlaps by 2 and 3 respectively? I didn't get that part. Thanks.

Re: Of the 300 subjects who participated in an experiment using [#permalink]

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01 Jul 2014, 09:10

cyberjadugar wrote:

Quote:

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,

One correction: In 100= 40+30+75-(35-3x)+x, it should be (35+3x)