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Of the 300 subjects who participated in an experiment using [#permalink]
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08 Jun 2012, 01:16
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Of the 300 subjects who participated in an experiment using virtualreality 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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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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08 Jun 2012, 01:43
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The best way to tackle this question is probably the formula for three overlapping sets:
Total = Group1 + Group 2 + Group 3  (sum of 2group overlaps)  2*(all three) + Neither
Total = 300(.4) + 300(.3) + 300(.75)  300(.35)  2*(all three) + 0 300*.1 = 30 300 = 120 + 90 + 225  105  2*(all three) 2*(all three) = 30 :. 15 experienced all three effects
So Group 1 + Group 2 + Group 3  2group overlaps * 2  3group overlaps * 3 is our answer = 120 + 90 + 225  105*2  15*3 = 435  210  45 = 180



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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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08 Jun 2012, 01:57
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Quote: Of the 300 subjects who participated in an experiment using virtualreality 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, \(A\cup B\cup C = A+B+CA\cap BB\cap CC\cap A +A\cap B\cap C\) 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 \(A\cap B\cap C=x\)) \(=353x\) Thus, \(100= 40+30+75(353x)+x\) 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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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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11 Feb 2013, 03:27
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vandygrad11 wrote: The best way to tackle this question is probably the formula for three overlapping sets:
Total = Group1 + Group 2 + Group 3  (sum of 2group overlaps)  2*(all three) + Neither
Total = 300(.4) + 300(.3) + 300(.75)  300(.35)  2*(all three) + 0 300*.1 = 30 300 = 120 + 90 + 225  105  2*(all three) 2*(all three) = 30 :. 15 experienced all three effects
So Group 1 + Group 2 + Group 3  2group overlaps * 2  3group overlaps * 3 is our answer = 120 + 90 + 225  105*2  15*3 = 435  210  45 = 180 I'm having trouble understanding this formula. Why is the sum of all three overlaps multiplied by two? Thanks in advance.



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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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It helped a great deal! Thanks Bunuel! As always, your input is priceless!!



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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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25 May 2013, 07:40
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people who experienced
1 symptom only  a
2 symptom only b =35% (given)
3 symptom only c
no symptoms 0 a+b+c=100%
a+35%+c = 100% > (1)
also
Group 1= 40%
Group 2= 30%
Group 3= 75%
Total = Group1 + Group 2 + Group 3  (people with 2 symptoms only)  2*(people with 3 symptpoms only) + Neither
Total = Group1 + Group 2 + Group 3  (b)  2*(c) + 0
Total = 40% +30%+75%35%  2*(c) + 0= 100%
110%2c=100%
c=5% > (2)
from (1) and (2)
a + 35% + 5% = 100%
a= 60%= 60%(300)= 180. Answer D



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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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28 May 2013, 16:09
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vandygrad11 wrote: The best way to tackle this question is probably the formula for three overlapping sets:
Total = Group1 + Group 2 + Group 3  (sum of 2group overlaps)  2*(all three) + Neither
Total = 300(.4) + 300(.3) + 300(.75)  300(.35)  2*(all three) + 0 300*.1 = 30 300 = 120 + 90 + 225  105  2*(all three) 2*(all three) = 30 :. 15 experienced all three effects
So Group 1 + Group 2 + Group 3  2group overlaps * 2  3group overlaps * 3 is our answer = 120 + 90 + 225  105*2  15*3 = 435  210  45 = 180 got 195 i didnt add all and take that as the total but instead left 300 as the total



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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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28 May 2013, 22:44
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x+y+z+p+q+r+w = 300  (a) x+p+w+q = 120 (40% of 300) (1) p+q+w+r = 90 (30 % of 300)(2) similarly q+w+r+z = 225(3) Need to find x+y+z=? 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, 08:26
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100 = 40 + 30 + 75  35  2 x ALL (standard formula) ALL = 5% Exactly 3 = 5% Of 300 = 15 Exactly 2 = 35% of 300 = 105 Total = Exactly 1 + Exactly 2 + Exactly 3 300 = Exactly 1+ 15 + 105 Exactly 1= 180 Ans.
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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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Quote: So Group 1 + Group 2 + Group 3  2group overlaps * 2  3group 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?



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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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macjas wrote: Of the 300 subjects who participated in an experiment using virtualreality 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+C2(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)
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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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Galiya wrote: Quote: So Group 1 + Group 2 + Group 3  2group overlaps * 2  3group 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 exactly 2 common elements twice once with A and once with B ; so considering other combinations we subtract 2gr overlaps twice and not thrice.
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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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macjas wrote: Of the 300 subjects who participated in an experiment using virtualreality 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



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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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13 Sep 2013, 10:28
the venn diagram is so much easier than the formula



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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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13 Sep 2013, 10:32
legitpro wrote: the venn diagram is so much easier than the formula But that is how the formula is derived .
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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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05 Oct 2013, 17:00
vandygrad11 wrote: The best way to tackle this question is probably the formula for three overlapping sets:
Total = Group1 + Group 2 + Group 3  (sum of 2group overlaps)  2*(all three) + Neither
Total = 300(.4) + 300(.3) + 300(.75)  300(.35)  2*(all three) + 0 300*.1 = 30 300 = 120 + 90 + 225  105  2*(all three) 2*(all three) = 30 :. 15 experienced all three effects
So Group 1 + Group 2 + Group 3  2group overlaps * 2  3group 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 2group overlaps and 3group overlaps by 2 and 3 respectively? I didn't get that part. Thanks.



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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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05 Oct 2013, 17:01
saintforlife wrote: vandygrad11 wrote: The best way to tackle this question is probably the formula for three overlapping sets:
Total = Group1 + Group 2 + Group 3  (sum of 2group overlaps)  2*(all three) + Neither
Total = 300(.4) + 300(.3) + 300(.75)  300(.35)  2*(all three) + 0 300*.1 = 30 300 = 120 + 90 + 225  105  2*(all three) 2*(all three) = 30 :. 15 experienced all three effects
So Group 1 + Group 2 + Group 3  2group overlaps * 2  3group 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 2group overlaps and 3group overlaps by 2 and 3 respectively? I didn't get that part. Thanks. Explained here: advancedoverlappingsetsproblems144260.htmlHope it helps.
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Re: Of the 300 subjects who participated in an experiment using [#permalink]
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01 Jul 2014, 10:10
cyberjadugar wrote: Quote: Of the 300 subjects who participated in an experiment using virtualreality 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, \(A\cup B\cup C = A+B+CA\cap BB\cap CC\cap A +A\cap B\cap C\) 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 \(A\cap B\cap C=x\)) \(=353x\) Thus, \(100= 40+30+75(353x)+x\) 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( 353x)+x, it should be ( 35+3x)




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