Of the 300 subjects who participated in an experiment using : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 23 Feb 2017, 14:06

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Of the 300 subjects who participated in an experiment using

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Affiliations: UWC
Joined: 09 May 2012
Posts: 399
GMAT 1: 620 Q42 V33
GMAT 2: 680 Q44 V38
GPA: 3.43
WE: Engineering (Entertainment and Sports)
Followers: 29

Kudos [?]: 1153 [14] , given: 100

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

### Show Tags

08 Jun 2012, 00:16
14
KUDOS
90
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

60% (04:19) correct 40% (03:21) wrong based on 1568 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA
Senior Manager
Joined: 13 Jan 2012
Posts: 309
Weight: 170lbs
GMAT 1: 740 Q48 V42
GMAT 2: 760 Q50 V42
WE: Analyst (Other)
Followers: 16

Kudos [?]: 150 [32] , given: 38

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

### Show Tags

08 Jun 2012, 00:43
32
KUDOS
15
This post was
BOOKMARKED
The best way to tackle this question is probably the formula for three overlapping sets:

Total = Group1 + Group 2 + Group 3 - (sum of 2-group 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 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer
= 120 + 90 + 225 - 105*2 - 15*3
= 435 - 210 - 45
= 180
Joined: 28 Mar 2012
Posts: 321
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 29

Kudos [?]: 406 [30] , given: 23

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

### Show Tags

08 Jun 2012, 00:57
30
KUDOS
14
This post was
BOOKMARKED
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

Regards,
Attachments

Venn.jpg [ 21.47 KiB | Viewed 47679 times ]

Intern
Joined: 08 May 2012
Posts: 6
Followers: 0

Kudos [?]: 4 [2] , given: 1

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

### Show Tags

11 Feb 2013, 02:27
2
KUDOS
The best way to tackle this question is probably the formula for three overlapping sets:

Total = Group1 + Group 2 + Group 3 - (sum of 2-group 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 - 2-group overlaps * 2 - 3-group 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?

Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96431 [8] , given: 10751

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

### Show Tags

11 Feb 2013, 04:43
8
KUDOS
Expert's post
4
This post was
BOOKMARKED
iwillbeatthegmat wrote:
The best way to tackle this question is probably the formula for three overlapping sets:

Total = Group1 + Group 2 + Group 3 - (sum of 2-group 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 - 2-group overlaps * 2 - 3-group 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?

Hope it helps.
_________________
Intern
Joined: 08 May 2012
Posts: 6
Followers: 0

Kudos [?]: 4 [1] , given: 1

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

### Show Tags

12 Feb 2013, 01:46
1
KUDOS
It helped a great deal! Thanks Bunuel! As always, your input is priceless!!
Intern
Joined: 28 Apr 2013
Posts: 2
Followers: 0

Kudos [?]: 7 [6] , given: 13

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

### Show Tags

25 May 2013, 06:40
6
KUDOS
1
This post was
BOOKMARKED
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
Manager
Joined: 24 Apr 2013
Posts: 54
Schools: Duke '16
Followers: 0

Kudos [?]: 11 [1] , given: 76

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

### Show Tags

28 May 2013, 15:09
1
KUDOS
The best way to tackle this question is probably the formula for three overlapping sets:

Total = Group1 + Group 2 + Group 3 - (sum of 2-group 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 - 2-group overlaps * 2 - 3-group 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
Intern
Joined: 02 May 2013
Posts: 26
Concentration: International Business, Technology
WE: Engineering (Aerospace and Defense)
Followers: 1

Kudos [?]: 40 [6] , given: 16

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

### Show Tags

28 May 2013, 21:44
6
KUDOS
3
This post was
BOOKMARKED
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
Attachments

Venn.JPG [ 13.05 KiB | Viewed 43389 times ]

Current Student
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 991
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)
Followers: 166

Kudos [?]: 1502 [22] , given: 227

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

### Show Tags

15 Aug 2013, 07:26
22
KUDOS
8
This post was
BOOKMARKED
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.
_________________

Piyush K
-----------------------
Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison
Don't forget to press--> Kudos
My Articles: 1. WOULD: when to use? | 2. All GMATPrep RCs (New)
Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

Manager
Joined: 15 Jan 2011
Posts: 103
Followers: 11

Kudos [?]: 160 [1] , given: 13

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

### Show Tags

15 Aug 2013, 10:18
1
KUDOS
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?
Senior Manager
Joined: 10 Jul 2013
Posts: 335
Followers: 3

Kudos [?]: 322 [3] , given: 102

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

### Show Tags

15 Aug 2013, 13:25
3
KUDOS
1
This post was
BOOKMARKED
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)
_________________

Asif vai.....

Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96431 [1] , given: 10751

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

### Show Tags

16 Aug 2013, 01:00
1
KUDOS
Expert's post
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?

Hope it helps.
_________________
Manager
Status: Persevering
Joined: 15 May 2013
Posts: 225
Location: India
GMAT Date: 08-02-2013
GPA: 3.7
WE: Consulting (Consulting)
Followers: 1

Kudos [?]: 87 [2] , given: 34

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

### Show Tags

18 Aug 2013, 04:53
2
KUDOS
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 exactly 2 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.

Intern
Joined: 09 Jul 2013
Posts: 2
Followers: 0

Kudos [?]: 6 [4] , given: 0

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

### Show Tags

19 Aug 2013, 11:55
4
KUDOS
2
This post was
BOOKMARKED
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
Intern
Joined: 02 Aug 2013
Posts: 16
Followers: 1

Kudos [?]: 7 [0], given: 1

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

### Show Tags

13 Sep 2013, 09:28
the venn diagram is so much easier than the formula
Manager
Status: Persevering
Joined: 15 May 2013
Posts: 225
Location: India
GMAT Date: 08-02-2013
GPA: 3.7
WE: Consulting (Consulting)
Followers: 1

Kudos [?]: 87 [0], given: 34

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

### Show Tags

13 Sep 2013, 09:32
legitpro wrote:
the venn diagram is so much easier than the formula

But that is how the formula is derived .
_________________

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

Manager
Joined: 09 Nov 2012
Posts: 66
Followers: 0

Kudos [?]: 120 [0], given: 40

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

### Show Tags

05 Oct 2013, 16:00
The best way to tackle this question is probably the formula for three overlapping sets:

Total = Group1 + Group 2 + Group 3 - (sum of 2-group 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 - 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.
Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96431 [0], given: 10751

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

### Show Tags

05 Oct 2013, 16:01
saintforlife wrote:
The best way to tackle this question is probably the formula for three overlapping sets:

Total = Group1 + Group 2 + Group 3 - (sum of 2-group 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 - 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.

Hope it helps.
_________________
Current Student
Joined: 12 Feb 2011
Posts: 104
Followers: 0

Kudos [?]: 35 [0], given: 3363

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

### Show Tags

01 Jul 2014, 09:10
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

Regards,

One correction: In 100= 40+30+75-(35-3x)+x, it should be (35+3x)
Re: Of the 300 subjects who participated in an experiment using   [#permalink] 01 Jul 2014, 09:10

Go to page    1   2    Next  [ 37 posts ]

Similar topics Replies Last post
Similar
Topics:
At Perry High School, the ratio of students who participate in either 1 22 Feb 2017, 01:44
1 In a recent tender, X people participated. 35% of the X people, who ma 1 30 Apr 2016, 10:52
For an agricultural experiment, 300 seeds were planted in one plot and 3 07 Oct 2014, 00:55
6 The s subjects in an experiment are divided into 4 groups 7 04 Mar 2012, 10:47
For an agricultural experiment, 300 seeds were planted in 1 07 Feb 2012, 03:25
Display posts from previous: Sort by

# Of the 300 subjects who participated in an experiment using

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.