Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 May 2017, 19:11

### 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
Your Progress

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 patients who suffered from at least one symptom

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

### Hide Tags

Senior Manager
Joined: 10 Dec 2004
Posts: 272
Followers: 2

Kudos [?]: 171 [0], given: 0

Of the 300 patients who suffered from at least one symptom [#permalink]

### Show Tags

17 May 2005, 08:20
12
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

50% (04:40) correct 50% (01:57) wrong based on 36 sessions

### HideShow timer Statistics

Of the 300 patients who suffered from at least one symptom of A, B, and C, 35 % suffered from A, 45% suffered from B, 40 % suffered from C, 10% suffered from exactly 2 of them. How many people suffered from exactly one symptom?

Pls explain answer choice..
Intern
Joined: 10 May 2005
Posts: 2
Followers: 0

Kudos [?]: 2 [2] , given: 0

### Show Tags

27 May 2005, 00:17
2
This post received
KUDOS
T=300
A=35%.300=105
B=135
C=120

(A intersect B) + (B intersect C) + (C intersect A) - (A intersect B intersect C) = 10%.300 = 30

T = A + B + C - (A inter B) - (B inter C) - (C inter A) + (A inter B inter C)
= A + B + C - 30 - 2 (A inter B inter C)
<--> 300 = 105 + 135 +120 - 30 - 2 (A inter B inter C)
--> (A inter B inter C) = 15

--> answer = 300 - 30 -15 = 225.
Senior Manager
Joined: 19 Feb 2005
Posts: 486
Location: Milan Italy
Followers: 1

Kudos [?]: 23 [0], given: 0

### Show Tags

17 May 2005, 09:28
Christoph,
are you assuming that nobody had all 3 symptoms?
VP
Joined: 30 Sep 2004
Posts: 1482
Location: Germany
Followers: 6

Kudos [?]: 347 [0], given: 0

### Show Tags

17 May 2005, 09:44
thearch wrote:
Christoph,
are you assuming that nobody had all 3 symptoms?

i assume that 30 have exactly two symptoms and 30 have all three symptomps. A+B+C=360. so 30 have i.e. AB and 30 have ABC. so its A-ABC-AB+(B-ABC-AB)+(C-ABC)=105-30-30+135-30-30+120-30=210. is it ?
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Senior Manager
Joined: 17 Apr 2005
Posts: 373
Location: India
Followers: 1

Kudos [?]: 27 [0], given: 0

### Show Tags

21 May 2005, 00:01
Dan wrote:
255

I too got 255.

Does anyone know the forumla based soln. I did it with V diagrams and no matter how many times I do such problems , I take eons.

HMTG
Manager
Joined: 28 Aug 2004
Posts: 205
Followers: 1

Kudos [?]: 2 [0], given: 0

### Show Tags

21 May 2005, 00:10
1
This post was
BOOKMARKED
I deferred solution till OA is out, but here it goes..

T = A + B + C - (2 of them) - 2 * (ABC) + neither

300 = 105 + 135 + 120 -30 -2*ABC

ABC = 15.

a + 2*b + 3*c = 105 + 135 + 120 = 360

a + 2*30 + 3*15 = 360

==> a = 255
Director
Joined: 18 Apr 2005
Posts: 547
Location: Canuckland
Followers: 1

Kudos [?]: 37 [0], given: 0

### Show Tags

21 May 2005, 02:38
1
This post was
BOOKMARKED
I got 255 as well.

Venn diagram is very helpful here

knowing that 30 people suffered from two symptoms

number of ppl suffereing exactly from 1 and 3 symptoms is (360 - 2*30 (since 2 sets intersect) - 3 (ABC) (since 3 sets intersect)) + ABC = 300 - 30 = 270

so ABC = 15

300 - 30 -15 = 255
Director
Joined: 20 Apr 2005
Posts: 584
Followers: 2

Kudos [?]: 227 [0], given: 0

Further question [#permalink]

### Show Tags

25 May 2005, 15:41
Is it possible to take this problem further and deduce the exact number of patients who suffers only from A, only from B and only from C ?
Director
Joined: 18 Feb 2005
Posts: 670
Followers: 1

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

### Show Tags

25 May 2005, 20:51
Please explain this problem ....I didnt get the solution.....
Director
Joined: 18 Apr 2005
Posts: 547
Location: Canuckland
Followers: 1

Kudos [?]: 37 [0], given: 0

### Show Tags

25 May 2005, 22:08
gmat2me2 wrote:
Please explain this problem ....I didnt get the solution.....

gmat, use Venn diagram, draw three intersecting circles representing A B C, there will be 3 areas where only to sets intersect, and 1 where all three intersect. Solution should be clear if you do that. Sorry I have no idea how to draw things on my comp, otherwise I would do it.
VP
Joined: 30 Sep 2004
Posts: 1482
Location: Germany
Followers: 6

Kudos [?]: 347 [0], given: 0

### Show Tags

26 May 2005, 05:13
can someone explain this to me,plz !

i calculated it the folowing way:

35%-x-10%-0+40%-x-0-10%+45%-0-0-x=100%

x=all 3 symptoms

where am i wrong ?
Attachments

venn2.JPG [ 9.36 KiB | Viewed 5580 times ]

_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Manager
Joined: 28 Aug 2004
Posts: 205
Followers: 1

Kudos [?]: 2 [0], given: 0

### Show Tags

26 May 2005, 05:23
christoph wrote:
can someone explain this to me,plz !

i calculated it the folowing way:

35%-x-10%-0+40%-x-0-10%+45%-0-0-x=100%

x=all 3 symptoms

where am i wrong ?

chris, you're subtracting x 3 times; A, B and C all include ABC, so you've to subtract x = ABC only twice to keep one ABC in the loop.

Also you're subtracting 10% twice; should be once otherwise double coutning.
VP
Joined: 30 Sep 2004
Posts: 1482
Location: Germany
Followers: 6

Kudos [?]: 347 [0], given: 0

### Show Tags

26 May 2005, 14:34
thx,dan.

A=35%=105 and B=40%=135 and C=45%=120

105-(AB+AC+ABC)+135-(AB+BC+ABC)+120-(BC+AC+ABC)+(AB+AC+BC+ABC)=300

=>

105-(30+0+ABC)+135-(30+0+ABC)+120-(0+0+ABC)+(30+0+0+ABC)=300

=>

105-30-ABC+135-30-ABC+120-ABC+30+ABC=300

=>

330-2ABC=300 => ABC=15 => 300-30-15=255
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Director
Joined: 18 Apr 2005
Posts: 547
Location: Canuckland
Followers: 1

Kudos [?]: 37 [0], given: 0

### Show Tags

26 May 2005, 15:43
Chris, see those areas where you have 10%, 0, and 0? Their sum has to be equal to 10%, not just one area as it is on your diagram.

Venn diagram is the most powerful way to sort out simple set and probability problems.
Manager
Joined: 11 Sep 2009
Posts: 101
Followers: 2

Kudos [?]: 28 [0], given: 0

Re: PS - Venn Diag [#permalink]

### Show Tags

24 Oct 2009, 23:47
pb_india wrote:
Of the 300 patients who suffered from at least one symptom of A, B, and C, 35 % suffered from A, 45% suffered from B, 40 % suffered from C, 10% suffered from exactly 2 of them. How many people suffered from exactly one symptom?

Pls explain answer choice..

255

Sol:
First find N3 : 100 = 35 + 45 + 40 - 10 - 2*N3
N3 = 5%

Second find N1: 100 = N1 + N2 + N3 = N1 + 10 + 5
N1 = 85% or 255

Cheers
Director
Joined: 25 Aug 2007
Posts: 943
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Followers: 77

Kudos [?]: 1329 [0], given: 40

Re: PS - Venn Diag [#permalink]

### Show Tags

11 May 2010, 10:17
I have a different way to solve this using venn diag.

Let take the variables as:
a = exactly one for A,
b = exactly one for B,
c = exactly one for C,

d = exactly two from A and B,
e = exactly two from B and C,
f = exactly two from C and A

g = all three from A, B and C

We are given d+e+f = 10%, so lets solve in % terms.

a+b+c+(d+e+f)+g = 100 >>>> a+b+c+g = 90 -------------(eq 1)

Now, we need g to find the required (a+b+c).

We know from Venn Diag that
(AUBUC) = A+B+C - (AB) - 2(ABC)
100 = 35+45+40 - 10 -2(g)

Therefore, g = 5%

Putting g = 5% in eq (1), we get a+b+c = 85% = (85/100)x300 = 255.

Hope this is useful.
_________________

Want to improve your CR: http://gmatclub.com/forum/cr-methods-an-approach-to-find-the-best-answers-93146.html
Tricky Quant problems: http://gmatclub.com/forum/50-tricky-questions-92834.html
Important Grammer Fundamentals: http://gmatclub.com/forum/key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html

Intern
Joined: 22 Jun 2010
Posts: 9
Followers: 0

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

Re: PS - Venn Diag [#permalink]

### Show Tags

22 Jun 2010, 16:58
300= 105 + 135 + 120 - (Both) + (all 3)

lets call (all 3) = x

exactly 2: 30 = Both - 3(x)
Both = 30 + 3x

300 = 360 -(both) + x
= 360 -(30-3x) + x
= 330 - 2x
x= 15

15 in all 3
75 in Both

exactly 1 = 360 - 2(both) + 3(x)
= 360 - 150 + 45
= 255

the trick here is to remember 4 main equations
union of three sets = (sum of 3) - (sum of 2) + (all 3)
exactly 2 = (sum of 2) - 3(all 3)
at least 2 = (sum of 2) - 2(all 3)
only 1 = (sum of 3) -2(sum of 2) + 3(all 3)

of course add neither to each one of these if not everyone is in a set...
Manager
Joined: 16 Jun 2010
Posts: 170
Followers: 3

Kudos [?]: 46 [0], given: 1

Re: PS - Venn Diag [#permalink]

### Show Tags

23 Jun 2010, 07:38
2
This post was
BOOKMARKED
255.

100 = 35 + 45 + 40 - 10 - 2x x all common

x = 15 percent

Required = 100 - ( 10 + 15 ) = 85 percent of 300 = 255
_________________

R E S P E C T

Finally KISSedGMAT 700 times 450 to 700 An exprience

Manager
Joined: 07 Jun 2010
Posts: 50
Location: United States
Followers: 1

Kudos [?]: 42 [0], given: 7

Re: PS - Venn Diag [#permalink]

### Show Tags

24 Jun 2010, 17:34
I thinks the Venn diagram should look like this , since no patients have all 3

so answer should be 200
Attachments

vennUntitled.png [ 12.05 KiB | Viewed 3189 times ]

Senior Manager
Joined: 23 May 2010
Posts: 430
Followers: 5

Kudos [?]: 117 [0], given: 112

Re: PS - Venn Diag [#permalink]

### Show Tags

20 Aug 2010, 03:51
pb_india wrote:
Of the 300 patients who suffered from at least one symptom of A, B, and C, 35 % suffered from A, 45% suffered from B, 40 % suffered from C, 10% suffered from exactly 2 of them. How many people suffered from exactly one symptom?

Pls explain answer choice..

deferred solution till OA is out, but here it goes..

T = A + B + C - (2 of them) - 2 * (ABC) + neither

300 = 105 + 135 + 120 -30 -2*ABC

ABC = 15.

a + 2*b + 3*c = 105 + 135 + 120 = 360 a + 2*30 + 3*15 = 360

==> a = 255
pls explain the step in the red color
Re: PS - Venn Diag   [#permalink] 20 Aug 2010, 03:51

Go to page    1   2    Next  [ 26 posts ]

Similar topics Replies Last post
Similar
Topics:
3 35% of all Huhulians own at least one TV. 24% of Huhulians who own at 7 19 May 2017, 06:18
16 Among 250 viewers interviewed who watch at least one of the three TV 7 22 Apr 2017, 14:15
286 Of the 300 subjects who participated in an experiment using 36 10 Oct 2016, 08:12
33 A medical researcher must choose one of 14 patients to 15 09 Feb 2017, 04:24
1 At least one solution-Postive and negatives 2 13 Sep 2011, 01:13
Display posts from previous: Sort by

# Of the 300 patients who suffered from at least one symptom

 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®.