Author 
Message 
VP
Joined: 22 Aug 2005
Posts: 1112
Location: CA

In a consumer survey, 85 percent of those surveyed liked at [#permalink]
Show Tags
24 Nov 2005, 18:24
Question Stats:
0% (00:00) correct
100% (02:05) wrong based on 0 sessions
HideShow timer Statistics
This topic is locked. If you want to discuss this question please repost it in the respective forum. In a consumer survey, 85 percent of those surveyed liked at least one of three products: 1, 2, and 3. 50 percent of those asked liked product 1, 30 percent liked product 2, and 20 percent liked product 3. If 5 percent of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
_________________
Whether you think you can or think you can't. You're right!  Henry Ford (1863  1947)



Director
Joined: 14 Sep 2005
Posts: 985
Location: South Korea

Let the three products be A, B, and C.
Let the number of people surveyed be 100.
85 people liked at least one of the three products.
A+B+C(A&B)(B&C)(C&A)3(A&B&C)
= 50 + 30 + 20  (A&B + B&C + C&A)  15
= 85  (A&B + B&C + C&A)
= 85
Therefore, (A&B + B&C + C&A) = 0
15/100 = 15%
_________________
Auge um Auge, Zahn um Zahn !



Manager
Joined: 04 Sep 2005
Posts: 141
Location: Fringes of the Boreal, Canada

I agree with 15%. Good variation of this type of question.
_________________
"To hell with circumstances; I create opportunities."  Bruce Lee



VP
Joined: 22 Aug 2005
Posts: 1112
Location: CA

gamjatang wrote: Let the three products be A, B, and C. Let the number of people surveyed be 100.
85 people liked at least one of the three products.
A+B+C(A&B)(B&C)(C&A)3(A&B&C) = 50 + 30 + 20  (A&B + B&C + C&A)  15 = 85  (A&B + B&C + C&A) = 85
Therefore, (A&B + B&C + C&A) = 0
15/100 = 15%
I doubt if bold portion of formula correct in this case.
A&B includes A&B&C
so it will ne deducted thrice already :
 (A&B + B&C + C&A)
am i missing something?
_________________
Whether you think you can or think you can't. You're right!  Henry Ford (1863  1947)



Director
Joined: 21 Aug 2005
Posts: 789

A+B+C[(A&B)+(B&C)+(C&A)]+(A&B&C) = 85
100[(A&B)+(B&C)+(C&A)]+5=85
(A&B)+(B&C)+(C&A) = 20 or 20%
Is this correct?



VP
Joined: 22 Aug 2005
Posts: 1112
Location: CA

gsr wrote: A+B+C[(A&B)+(B&C)+(C&A)]+(A&B&C) = 85 100[(A&B)+(B&C)+(C&A)]+5=85 (A&B)+(B&C)+(C&A) = 20 or 20%
Is this correct?
I solved the same way, but OA is not 20%
Looks like:
(A&B)+(B&C)+(C&A) above includes A&B&C thrice...?
_________________
Whether you think you can or think you can't. You're right!  Henry Ford (1863  1947)



Director
Joined: 21 Aug 2005
Posts: 789

duttsit wrote: Looks like: (A&B)+(B&C)+(C&A) above includes A&B&C thrice...?
True
(A&B)+(B&C)+(C&A)  2*(A&B&C) = 20  10 = 10% ?



SVP
Joined: 03 Jan 2005
Posts: 2233

Re: PS: Set [#permalink]
Show Tags
24 Nov 2005, 20:53
duttsit wrote: In a consumer survey, 85 percent of those surveyed liked at least one of three products: 1, 2, and 3. 50 percent of those asked liked product 1, 30 percent liked product 2, and 20 percent liked product 3. If 5 percent of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
A=0.5
B=0.3
C=0.2
AUBUC=.85
AandBandC=.05
AUBUC=A+B+C(people who liked at least two)  AandBandC
.85=1X.05
x=1.85.05=.1
10%
(I tried to summerize all related formulas into one post, please check to see if they are right.)
http://www.gmatclub.com/phpbb/viewtopic ... 938#139938
_________________
Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.



VP
Joined: 22 Aug 2005
Posts: 1112
Location: CA

Great explanation qsr, HongHu. thanks.
OA is 10%
_________________
Whether you think you can or think you can't. You're right!  Henry Ford (1863  1947)



Director
Joined: 24 Oct 2005
Posts: 659
Location: London

Re: PS: Set [#permalink]
Show Tags
25 Nov 2005, 04:28
HongHu wrote: duttsit wrote: In a consumer survey, 85 percent of those surveyed liked at least one of three products: 1, 2, and 3. 50 percent of those asked liked product 1, 30 percent liked product 2, and 20 percent liked product 3. If 5 percent of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? A=0.5 B=0.3 C=0.2 AUBUC=.85 AandBandC=.05 AUBUC=A+B+C(people who liked at least two)  AandBandC .85=1X.05 x=1.85.05=.1 10% (I tried to summerize all related formulas into one post, please check to see if they are right.) http://www.gmatclub.com/phpbb/viewtopic ... 938#139938
Please correct me if I am wrong, but as per what I have understood out of sets,
n(A U B U C) = n(A) + n(B) + n(C)  n(A U' B)  n(B U' C)  n(A U' C) + n(A U' B U' C)
ie. it should be
AUBUC=A+B+C(people who liked at least two) "+" AandBandC
So it has to be 20% isn't it.



SVP
Joined: 03 Jan 2005
Posts: 2233

You get different results when you count people together or when you count them seperately. For example, say there are three items A, B, and C. If 3 people like A and B, 3 people like B and C, and 3 people like A and C. The number of people who like at least two items are not necessarily 9. Perhaps there are only 7 people who like at least two items, because 1 person likes all the three of them. (2 A and B only, 2 B and C only, 2 A and C only, and 1 like all of them.) This is why the two formulas are different. When you count them seperately and add them up, you have twice overcounted the center when they intersept each other.
In other words, the original formula is this:
N(AUBUC) = N(A) + N(B) + N(C)  N(A n B)  N(A n C)  N(C n B) + N(A n B n C)
When you subsititute N(A n B) + N(A n C) + N(C n B) = N(at least two) + 2N(A n B n C)
You will get
N(AUBUC) = N(A) + N(B) + N(C)  N(at least two)  2N(A n B n C) + N(A n B n C)
Which means
N(AUBUC) = N(A) + N(B) + N(C)  N(at least two)  N(A n B n C)
_________________
Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.



Director
Joined: 24 Oct 2005
Posts: 659
Location: London

HongHu wrote: You get different results when you count people together or when you count them seperately. For example, say there are three items A, B, and C. If 3 people like A and B, 3 people like B and C, and 3 people like A and C. The number of people who like at least two items are not necessarily 9. Perhaps there are only 7 people who like at least two items, because 1 person likes all the three of them. (2 A and B only, 2 B and C only, 2 A and C only, and 1 like all of them.) This is why the two formulas are different. When you count them seperately and add them up, you have twice overcounted the center when they intersept each other.
In other words, the original formula is this: N(AUBUC) = N(A) + N(B) + N(C)  N(A n B)  N(A n C)  N(C n B) + N(A n B n C) When you subsititute N(A n B) + N(A n C) + N(C n B) = N(at least two) + 2N(A n B n C) You will get N(AUBUC) = N(A) + N(B) + N(C)  N(at least two)  2N(A n B n C) + N(A n B n C) Which means N(AUBUC) = N(A) + N(B) + N(C)  N(at least two)  N(A n B n C)
Wow.. I finally get this
Thanks HongHU



Manager
Joined: 30 Aug 2005
Posts: 186

Shouldn't do you be adding P1andP2andP3 to 10% giving an answer of 15%?



SVP
Joined: 05 Apr 2005
Posts: 1710

rianah100 wrote: Shouldn't do you be adding P1andP2andP3 to 10% giving an answer of 15%?
that 10% is resulted with the inclusion of that percentage figure for (P1 and P2 and P3).
the required % = % liked 2 products + % liked 3 or all products
= % of people liked products (1 & 2 +2 & 3+ 1 & 3) + % of people liked all 3 (P1 and P2 and P3)
= 5%+5%
= 10%
note: % of people liked products (1 & 2 +2 & 3+ 1 & 3) is calculated as under:
total % of people surveyed = % of people liked product 1 + % of people liked product 2 + % of people liked product 3  % of people liked products (1 & 2)  % of people liked products (2 & 3)  % of people liked products (1 & 3)  2 [% of people liked products (1, 2, & 3)]
85%= 50+30+20  p(1 & 2)  p(1 & 2)  p(2 & 3)  p(1 & 3)  2 (5%)
p(1 & 2) + p(1 & 2) + p(2 & 3) + p(1 & 3) = 1008510 = 5%



Senior Manager
Joined: 07 Jan 2008
Posts: 289

Re: PS: Set [#permalink]
Show Tags
20 May 2008, 13:53
AUBUC  N = A + B + C  X  2Y
N = Liked none/neither X = Liked excatly two Y = Liked all three.
100  15 = 50 + 30 + 20  X 2*5 85 = 100  10 X X = 5 So, 5% of the people like exactly two and 5% like exactly/all 3. So 10% like more than one. B.










