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# In a consumer survey 85% of respondents liked at least one

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Senior Manager
Joined: 01 May 2004
Posts: 336
Location: USA
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In a consumer survey 85% of respondents liked at least one [#permalink]  14 Jul 2004, 09:04
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0% (00:00) correct 0% (00:00) wrong based on 1 sessions
In a consumer survey 85% of respondents liked at least one of the three products 1, 2 and 3. 50% of respondents liked product 1, 30% of respondents liked pr.2, 20% of respondents liked pr.3. If 5 % of the people in the survey liked all three products, what percent of the respondents liked more than one of these products?
5, 10, 15, 20, 25
Director
Joined: 01 Feb 2003
Posts: 854
Followers: 1

Kudos [?]: 18 [0], given: 0

n(AUBUC) = n(A)+n(B)+n(C)-n(A&B)-n(A&C)-n(B&C)+n(A&B&C)

therefore plugging in the values above
85 = 105-n(A&B)-n(A&C)-n(B&C)
=> n(A&B)+n(A&C)+n(B&C) = 20 (ans)
Senior Manager
Joined: 01 May 2004
Posts: 336
Location: USA
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Kudos [?]: 4 [0], given: 0

The OA is different
Manager
Joined: 16 Jan 2004
Posts: 65
Location: NJ
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Kudos [?]: 0 [0], given: 0

50+30+20-Both+10 (2*5) =100
110-B = 100
B=10%

10%i should be the answer. what is the OA
Manager
Joined: 19 Jun 2003
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Kudos [?]: 4 [0], given: 0

pakoo wrote:
50+30+20-Both+10 (2*5) =100
110-B = 100
B=10%

10%i should be the answer. what is the OA

Pakoo, What is 10(2*5) ? Please elaborate your solution a bit, if you could.

GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4318
Followers: 22

Kudos [?]: 161 [0], given: 0

X=people liking at least 2 products
50+30+20-X-5 = 85
X=10
But you have to add 5 because those 5 like more than 2 products.
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Best Regards,

Paul

GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4318
Followers: 22

Kudos [?]: 161 [0], given: 0

pakoo wrote:
50+30+20-Both+10 (2*5) =100
110-B = 100
B=10%

10%i should be the answer. what is the OA

Pakoo, you failed to take into account the 15% of people who do not like any products
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Best Regards,

Paul

Director
Joined: 13 Nov 2003
Posts: 971
Location: Florida
Followers: 1

Kudos [?]: 18 [0], given: 0

Paul wrote:
X=people liking at least 2 products
50+30+20-X-5 = 85
X=10
But you have to add 5 because those 5 like more than 2 products.

Paul, the equation should be like:

50+30+20- 2X-5 = 85
2X = 10
X=5

now, we will add 5% (all 3) = 5+5 = 10
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4318
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Kudos [?]: 161 [0], given: 0

hmmm, I'm missing something here. What does the 2 in "2X" stand for?
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Best Regards,

Paul

Senior Manager
Joined: 21 Mar 2004
Posts: 445
Location: Cary,NC
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Kudos [?]: 6 [0], given: 0

I used venn diagrams for this and got 10%. Took me a few minutes but was foolproof.

x+y+z+a+b+c+5= 85 eq 1

x+a+c+5 = 50
y+b+c+5 = 30
z+a+b+5 = 20
_________________________
x+y+z+2(a+b+c) + 15 = 100 eq 2
_________________________

eq2 - eq1 gives

a+b+c = 5

final answer is a+b+c+5 = 10%
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_________________

ash
________________________
I'm crossing the bridge.........

Joined: 31 Dec 1969
Location: United States
Concentration: Marketing, Other
GMAT 1: 710 Q49 V38
GMAT 2: 660 Q V
GPA: 3.64
WE: Accounting (Accounting)
Followers: 0

Kudos [?]: 65 [0], given: 76890

Ok this is quite simple....
like probability assume all possibilities and simply add

100= 50+30+20+5+x-15

thus x=10
Manager
Joined: 21 Jun 2004
Posts: 52
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ashkg

Even though it takes doign the Venn diagram, it makes more sense, when you write that Venn diagram, Brings back school days!!!
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