Last visit was: 18 May 2026, 16:54 It is currently 18 May 2026, 16:54
Home
Messages
Tests
Schools
Events
Close
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
pb_india
User avatar
Joined: 10 Dec 2004
Last visit: 27 May 2005
Posts: 173
Own Kudos:
1,386
 [27]
Posts: 173
Kudos: 1,386
 [27]
Of the 300 patients who suffered from at least one symptom of A, B, an 17 May 2005, 08:20
2
Kudos
Add Kudos
25
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

56% (02:43) correct 44% (02:35) wrong based on 178 sessions

History

Date
Time
Result
Not Attempted Yet
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?

A. 235
B. 240
C. 245
D. 250
E. 255
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 May 2026
Posts: 110,678
Own Kudos:
815,602
 [5]
Given Kudos: 106,295
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,678
Kudos: 815,602
 [5]
Of the 300 patients who suffered from at least one symptom of A, B, an 20 Aug 2010, 08:43
1
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
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?

Total=A+B+C - {People who suffered from exactly 2 symptoms} - 2*{People who suffered from exactly 3 symptoms} + {People who suffered from neither of symptoms};

100=35+45+40-10-2*{People who suffered from exactly 3 symptoms}+0 --> {People who suffered from exactly 3 symptoms}=5%;

So as {People who suffered from exactly 2 symptoms}=10% and {People who suffered from exactly 3 symptoms}=5% then {People who suffered from exactly one symptom} is 100-10-5=85% --> in numbers 300*85%=255.

Answer: 255.

Check for more on this formula at: formulae-for-3-overlapping-sets-69014.html#p729340

Hope it helps.
General Discussion
User avatar
Dan
User avatar
Joined: 28 Aug 2004
Last visit: 23 Feb 2006
Posts: 129
Own Kudos:
9
 [1]
Posts: 129
Kudos: 9
 [1]
Of the 300 patients who suffered from at least one symptom of A, B, an 21 May 2005, 00:10
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
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
User avatar
sparky
User avatar
Joined: 18 Apr 2005
Last visit: 30 Jul 2005
Posts: 321
Own Kudos:
106
 [2]
Location: Canuckland
Posts: 321
Kudos: 106
 [2]
Of the 300 patients who suffered from at least one symptom of A, B, an 21 May 2005, 02:38
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
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
User avatar
Dianadungtran
User avatar
Joined: 10 May 2005
Last visit: 17 Sep 2018
Posts: 2
Own Kudos:
2
 [2]
Posts: 2
Kudos: 2
 [2]
Of the 300 patients who suffered from at least one symptom of A, B, an 27 May 2005, 00:17
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
ykaiim
User avatar
Joined: 25 Aug 2007
Last visit: 21 Aug 2012
Posts: 516
Own Kudos:
6,004
 [1]
Given Kudos: 40
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Posts: 516
Kudos: 6,004
 [1]
Of the 300 patients who suffered from at least one symptom of A, B, an 11 May 2010, 10:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
KissGMAT
User avatar
Joined: 16 Jun 2010
Last visit: 02 Jun 2023
Posts: 68
Own Kudos:
113
 [2]
Given Kudos: 1
Posts: 68
Kudos: 113
 [2]
Of the 300 patients who suffered from at least one symptom of A, B, an 23 Jun 2010, 07:38
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
255.

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

x = 15 percent

Required = 100 - ( 10 + 15 ) = 85 percent of 300 = 255
User avatar
virupaksh2010
User avatar
Joined: 07 Jun 2010
Last visit: 29 Dec 2011
Posts: 39
Own Kudos:
155
Given Kudos: 7
Location: United States
Posts: 39
Kudos: 155
Of the 300 patients who suffered from at least one symptom of A, B, an 24 Jun 2010, 17:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I thinks the Venn diagram should look like this , since no patients have all 3

so answer should be 200
Attachments

vennUntitled.png
vennUntitled.png [ 12.05 KiB | Viewed 8428 times ]

User avatar
gauravnagpal
User avatar
Joined: 23 May 2010
Last visit: 23 Feb 2011
Posts: 160
Own Kudos:
384
 [1]
Given Kudos: 112
Posts: 160
Kudos: 384
 [1]
Of the 300 patients who suffered from at least one symptom of A, B, an 20 Aug 2010, 03:51
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
pb_india
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..
Show more
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
avatar
PareshGmat
avatar
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,531
Own Kudos:
8,306
Given Kudos: 193
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,531
Kudos: 8,306
Of the 300 patients who suffered from at least one symptom of A, B, an 25 Sep 2014, 03:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Refer diagram below:
Attachment:
lap.png
lap.png [ 10.19 KiB | Viewed 5546 times ]
We require to find the total of pink shaded region

Total = 300

White Region = 30

Remaining = 270 = Total Pink Region + Green Region

Total Pink Region = 270 - Green Region

Setting up the equation:

105 + 120-(q+r+x)+r+135-(p+r+x) = 300

x = 15

Total Pink region = 270-15 = 255
User avatar
AweG
User avatar
Joined: 05 Dec 2016
Last visit: 27 Jun 2018
Posts: 89
Own Kudos:
114
Given Kudos: 184
Posts: 89
Kudos: 114
Of the 300 patients who suffered from at least one symptom of A, B, an 19 Mar 2018, 15:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HowManyToGo
Dan
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
Show more
yes it is \(Total = Sum of Exactly1+ Sum of Exactly2+ Exactly3\) In this kind of problems you find the Exactly 3 from the formula \(Total= A+B+C-Sum of exactly2+2Exactly3+N\) and then you use the first formula to find Sum of Exactly1

Exactly3=AnBnC

Hope it helps !
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,097
Own Kudos:
1,125
Posts: 39,097
Kudos: 1,125
Of the 300 patients who suffered from at least one symptom of A, B, an 04 Mar 2026, 00:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
110678 posts
Krunaal
Tuck School Moderator
852 posts