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In a survey on three products – A, B, and C – 50% of those surveyed

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In a survey on three products – A, B, and C – 50% of those surveyed  [#permalink]

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New post 03 May 2017, 03:42
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A
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C
D
E

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  85% (hard)

Question Stats:

47% (02:07) correct 53% (02:29) wrong based on 113 sessions

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In a survey on three products – A, B, and C – 50% of those surveyed liked product A, 30% liked product B, 20% liked product C, and 85% liked at least one of the three products. If 5% of those surveyed like all three products, then what percentage of those surveyed liked more than one of the products?

A. 5
B. 10
C. 15
D. 20
E. 25

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Re: In a survey on three products – A, B, and C – 50% of those surveyed  [#permalink]

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New post 03 May 2017, 05:21
5
Formula used
P(Total) = P(A) + P(B) + P(C) - P(exactly 2) - 2*P(all 3)


Substituting values
85 = 50 + 30 + 20 - P(exactly 2) - 2*5
P(exactly 2) = 90 - 85 = 5

Percentage or people who liked more than one product = p(exactly 2) + p(all 3) = 5+5 = 10(Option B)
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Re: In a survey on three products – A, B, and C – 50% of those surveyed  [#permalink]

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New post 03 May 2017, 05:35
pushpitkc wrote:
Formula used
P(Total) = P(A) + P(B) + P(C) - P(exactly 2) - 2*P(all 3)


Substituting values
85 = 50 + 30 + 20 - P(exactly 2) - 2*5
P(exactly 2) = 90 - 85 = 5

Percentage or people who liked more than one product = p(exactly 2) + p(all 3) = 5+5 = 10(Option B)

Sorry but I am a bit confused here!

In the formula that you used, isn't that supposed to ADD and not subtract the number for All Three?
You subtracted twice that number instead of adding it once. Can you please explain how did you come up with that formula?

Thanks

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Re: In a survey on three products – A, B, and C – 50% of those surveyed  [#permalink]

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New post 06 May 2017, 17:47
Bunuel wrote:
In a survey on three products – A, B, and C – 50% of those surveyed liked product A, 30% liked product B, 20% liked product C, and 85% liked at least one of the three products. If 5% of those surveyed like all three products, then what percentage of those surveyed liked more than one of the products?

A. 5
B. 10
C. 15
D. 20
E. 25


The problem really asks for the percentage of people who liked 2 or 3 products.

We can create the following equation:

Total percentage of people = percentage who like product A + percentage who like product B + percentage who like product C - (percentage who like 2 products) - 2(percentage who like 3 products) + percentage who like neither product

Let’s represent the percentage who like 2 products as D and percentage who like neither product as N. Then:

100 = 50 + 30 + 20 - D - 2(5) + N

100 = 90 - D + N

We are also given that 85% of the people surveyed liked at least one of the three products. Thus, 100 - 85 = 15 percent of the people liked none of the three products. So we have:

100 = 90 - D + 15

D = 5

Thus, 5 + 5 = 10 percent of the people like more than one product.

Answer: B
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In a survey on three products – A, B, and C – 50% of those surveyed  [#permalink]

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New post 02 Jul 2017, 03:08
khushbumodi wrote:
pushpitkc wrote:
Formula used
P(Total) = P(A) + P(B) + P(C) - P(exactly 2) - 2*P(all 3)


Substituting values
85 = 50 + 30 + 20 - P(exactly 2) - 2*5
P(exactly 2) = 90 - 85 = 5

Percentage or people who liked more than one product = p(exactly 2) + p(all 3) = 5+5 = 10(Option B)

Sorry but I am a bit confused here!

In the formula that you used, isn't that supposed to ADD and not subtract the number for All Three?
You subtracted twice that number instead of adding it once. Can you please explain how did you come up with that formula?

Thanks

Sent from my SM-N9200 using GMAT Club Forum mobile app

P(Total) = P(A) + P(B) + P(C) - P(exactly 2) - 2*P(all 3) is the formula whose clarification you had asked for

The clarification is as follows :
P(A) = P(Only A) + P(A U B) + P(A U C) + P(A U B U C)
P(B) = P(Only B) + P(B U C) + P(B U A) + P(A U B U C)
P(C) = P(Only C) + P(C U A) + P(C U B) + P(A U B U C)

P(exactly 2) = P(A U B) + P(A U C) + P(B U C)

P(all 3) = P(A U B U C)

Substituting these values in the formula,
P(Total) = P(A) + P(B) + P(C) - P(exactly 2) - 2*P(all 3)

P(Total) = P(Only A) + P(A U B) + P(A U C) + P(A U B U C) + P(Only B) + P(B U C) + P(B U A) + P(A U B U C) + P(Only C) + P(C U A) + P(C U B) + P(A U B U C) - P(A U B) - P(A U C) - P(B U C) - 2* P(A U B U C)

P(Total) = P(Only A) + P(Only B) + P(Only C) + P(B U A) + P(C U A) + P(C U B) + P(A U B U C)
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In a survey on three products – A, B, and C – 50% of those surveyed   [#permalink] 02 Jul 2017, 03:08
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