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In a consumer survey, 85% of those surveyed liked at least

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In a consumer survey, 85% of those surveyed liked at least [#permalink]

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New post 30 Nov 2006, 07:47
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In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% 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) 5

B) 10

C) 15

D) 20

E) 25
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New post 30 Nov 2006, 08:21
I get C - 15.

Assuming that the total number of people surveyed equals 100, we know that 85 people liked one or more of the products. 15 didn't like any.

50 people liked product 1
30 people liked product 2
20 people liked product 3
5 people liked all three products

If you add up all the people who liked the various products, you get a total of 100 people. However, the question tells us that only 85 people liked at least one of the three products.

Therefore, 15 people had to like at least 2 products.

(total people who like more than 1 product)/(total people surveyed) = 15/100.

Therefore, 15% of the people surveyed liked more than one product.

What's the OA?
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New post 30 Nov 2006, 08:25
not C

when do we use these formulas?

n(1U2U3) = n(1) + n(2) + n(3) - n(1n2) - n(2n3) - n(1n3) + n (1n2n3)

n(1U2U3) = n(1) + n(2) + n(3) - n(1n2) - n(2n3) - n(1n3) + 2(1n2n3)
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New post 30 Nov 2006, 08:39
In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% 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) 5 B) 10 C) 15 D) 20 E) 25

My answer is B IF RIGHT I CAN EXPLAIN
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New post 30 Nov 2006, 09:15
I'm getting B too.

if , Product 1 & 2 = a
Product 1 & 3 = b
Product 2 & 3 = c

then, we have to find (a + b + c +5)

From stem,

85 = 50 + 30 + 20 - a - b -c - 2*5 ( subtract the 5% twice, since it occurs 3 times in a Venn Diagram)

or, a + b +c = 5.

Hence, answer = 10.

What did I do wrong ?
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New post 30 Nov 2006, 23:19
It is E....

Using venn diagram you come up with the answer 10%

But then you look at the question and you see that you picked that from 85% of the people in the survey who liked at least one product.... therefore another 15% liked at least 2 products...

10+15=25%....
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New post 01 Dec 2006, 00:24
SimaQ wrote:
It is E....

Using venn diagram you come up with the answer 10%

But then you look at the question and you see that you picked that from 85% of the people in the survey who liked at least one product.... therefore another 15% liked at least 2 products...

10+15=25%....


I have a doubt here does'nt liking at least one cover all conditions.

My answer choice is also E and the working is

100 = people liking1 -people liking both +people liking all 3 + None
100 = 50+30+20 -both+5+15
both =20
People liking at least 2 or more = people liking both + people liking 3
= 20 +5=25

But if venn digrams are used one ends with choice B
Can any one please expaling the correct answer
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New post 01 Dec 2006, 04:21
sujayb wrote:
I'm getting B too.

if , Product 1 & 2 = a
Product 1 & 3 = b
Product 2 & 3 = c

then, we have to find (a + b + c +5)

From stem,

85 = 50 + 30 + 20 - a - b -c - 2*5 ( subtract the 5% twice, since it occurs 3 times in a Venn Diagram)

or, a + b +c = 5.

Hence, answer = 10.

What did I do wrong ?


It is correct...I too got the same :)
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New post 02 Dec 2006, 15:08
yogeshsheth wrote:

I have a doubt here does'nt liking at least one cover all conditions.

My answer choice is also E and the working is

100 = people liking1 -people liking both +people liking all 3 + None
100 = 50+30+20 -both+5+15
both =20
People liking at least 2 or more = people liking both + people liking 3
= 20 +5=25

But if venn digrams are used one ends with choice B
Can any one please expaling the correct answer


Should it not be - 2*(5) because you've counted the people who like all three 3 times in the 50 + 30 + 20?
  [#permalink] 02 Dec 2006, 15:08
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