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

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26 Jul 2010, 03:53

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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?

Can someone help me how to solve this question...thanks in advance...

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

As 85% of those surveyed liked at least one of three products then 15% liked none of three products.

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} - 2*{liked exactly three product} + {liked none of three products}

\(100=50+30+20-x-2*5+15\) --> \(x=5\), so 5 people liked exactly two products. More than one product liked those who liked exactly two products, (5%) plusthose who liked exactly three products (5%), so 5+5=10% liked more than one product.

Re: Set theory-Need help in solving this [#permalink]

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09 Aug 2013, 08:28

2

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Bunuel wrote:

mitmat wrote:

Can someone help me how to solve this question...thanks in advance...

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

As 85% of those surveyed liked at least one of three products then 15% liked none of three products.

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} - 2*{liked exactly three product} + {liked none of three products}

\(100=50+30+20-x-2*5+15\) --> \(x=5\), so 5 people liked exactly two products. More than one product liked those who liked exactly two products, (5%) plusthose who liked exactly three products (5%), so 5+5=10% liked more than one product.

Hi Bunuel, Can you please clarify if we're to use first formula how the solution would look like?

If we consider '\(x=5\)' to be the overlaps of 3 sets A,B,C and overlaps of A&B, B&C, C&A; then eqn. should be\(100=50+30+20-x+5+15\) , So, x=20, now subtracting 2*5 (as 5 is taken thrice within x and qs demands 'at least one' so it should be considered once) So,x=20-10=10...

Re: Set theory-Need help in solving this [#permalink]

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27 Jul 2010, 11:34

1

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Bunuel wrote:

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} - 2*{liked exactly three product} + {liked none of three products}

100=50+30+20-x-2*5+15 --> x=5, so 5 people liked exactly two products. More than one product liked those who liked exactly two products, (5%)plusthose who liked exactly three products (5%), so 5+5=10% liked more than one product.

Answer: B.

Bunuel, you are close but have a small error as highlighted in red above and fixed in green below.

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} + {liked exactly three product} + {liked none of three products}

100=50+30+20-x+5+15 --> x=15, so 15 people liked exactly two products. "More than one product liked" equals those who liked exactly two products, (15%)plusthose who liked exactly three products (5%), so 15+5=20% liked more than one product

Answer: D
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Re: Set theory-Need help in solving this [#permalink]

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27 Jul 2010, 11:50

1

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Bunuel wrote:

dauntingmcgee wrote:

Bunuel wrote:

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} - 2*{liked exactly three product} + {liked none of three products}

100=50+30+20-x-2*5+15 --> x=5, so 5 people liked exactly two products. More than one product liked is equivalent to those who liked exactly two products, (5%)plusthose who liked exactly three products (5%), so 5+5=10% liked more than one product.

Answer: B.

Bunuel, you are close but have a small error as highlighted in red above and fixed in green below.

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} + {liked exactly three product} + {liked none of three products}

100=50+30+20-x+5+15 --> x=15, so 15 people liked exactly two products. More than one product liked those who liked exactly two products, (15%)plusthose who liked exactly three products (5%), so 15+5=20% liked more than one product

In my post in the end of the first page I explain the difference in two formulas: the one I used (right one for THIS question) and the one you propose (wrong for THIS question).

Hope it helps.

My apologies, you are quite correct. I should not have doubted the awesome power of Bunuel
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Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} - 2*{liked exactly three product} + {liked none of three products}

100=50+30+20-x-2*5+15 --> x=5, so 5 people liked exactly two products. More than one product liked is equivalent to those who liked exactly two products, (5%)plusthose who liked exactly three products (5%), so 5+5=10% liked more than one product.

Answer: B.

Bunuel, you are close but have a small error as highlighted in red above and fixed in green below.

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} + {liked exactly three product} + {liked none of three products}

100=50+30+20-x+5+15 --> x=15, so 15 people liked exactly two products. More than one product liked those who liked exactly two products, (15%)plusthose who liked exactly three products (5%), so 15+5=20% liked more than one product

In my post in the end of the first page I explain the difference in two formulas: the one I used (right one for THIS question) and the one you propose (wrong for THIS question).

Re: In a consumer survey, 85% of those surveyed [#permalink]

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13 Jul 2012, 05:08

Hi Bunuel...I was confused with the language..it says 50% of those.. is it 50% of 85% or 50% of whole? From your solution looks like latter..But do you agree that such language should be more clear? or am I missing something?

Hi Bunuel...I was confused with the language..it says 50% of those.. is it 50% of 85% or 50% of whole? From your solution looks like latter..But do you agree that such language should be more clear? or am I missing something?

For me the language is clear enough. It says "50% of those asked", so "50% of those surveyed".
_________________

Re: In a consumer survey, 85% of those surveyed [#permalink]

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19 Mar 2013, 03:46

Bunuel wrote:

pavanpuneet wrote:

Hi Bunuel...I was confused with the language..it says 50% of those.. is it 50% of 85% or 50% of whole? From your solution looks like latter..But do you agree that such language should be more clear? or am I missing something?

For me the language is clear enough. It says "50% of those asked", so "50% of those surveyed".

Hi Bunuel,

I was also confused with the language as it said 50% liked A, 30% liked B and 20% liked C, which means 100% liked atleast one of the 3 products. Whereas the question stated that 15% dint like any of the 3 products! Whats wrong with my reasoning? Thanks for your response
_________________

Hi Bunuel...I was confused with the language..it says 50% of those.. is it 50% of 85% or 50% of whole? From your solution looks like latter..But do you agree that such language should be more clear? or am I missing something?

For me the language is clear enough. It says "50% of those asked", so "50% of those surveyed".

Hi Bunuel,

I was also confused with the language as it said 50% liked A, 30% liked B and 20% liked C, which means 100% liked atleast one of the 3 products. Whereas the question stated that 15% dint like any of the 3 products! Whats wrong with my reasoning? Thanks for your response

50% liked product 1 does not mean that 50% liked ONLY product 1. 30% liked product 2 does not mean that 30% liked ONLY product 2. 20% liked product 3 does not mean that 20% liked ONLY product 3.

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

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09 Aug 2013, 13:43

mitmat wrote:

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

................. More than one = A+B+C- (A n B n C) - (A u B u C) = 50+30+20-5-85 = 10%
_________________

Re: Set theory-Need help in solving this [#permalink]

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17 Aug 2013, 05:01

Bunuel wrote:

mitmat wrote:

Can someone help me how to solve this question...thanks in advance...

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

As 85% of those surveyed liked at least one of three products then 15% liked none of three products.

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} - 2*{liked exactly three product} + {liked none of three products}

\(100=50+30+20-x-2*5+15\) --> \(x=5\), so 5 people liked exactly two products. More than one product liked those who liked exactly two products, (5%) plusthose who liked exactly three products (5%), so 5+5=10% liked more than one product.

When it says that 85% is to be distributed in 3 sets as per Venn diagram and 15% is not distributed among the 3 sets , it is understandable. However, when it says 50% for 1 , 30% for -2 and 20% for -3 it is confusing as to whether it says that 50% is only '1' or 50% is for FULL '1'.

Case 2: If 50% is distributed in FULL -1

As per diagram shown :

1=50%=a+e+d+g

Case1:

1=50%=a

Please advise !

Rgds, TGC !

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Re: Set theory-Need help in solving this [#permalink]

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12 Sep 2013, 01:26

Bunuel wrote:

mitmat wrote:

Can someone help me how to solve this question...thanks in advance...

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

As 85% of those surveyed liked at least one of three products then 15% liked none of three products.

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} - 2*{liked exactly three product} + {liked none of three products}

\(100=50+30+20-x-2*5+15\) --> \(x=5\), so 5 people liked exactly two products. More than one product liked those who liked exactly two products, (5%) plusthose who liked exactly three products (5%), so 5+5=10% liked more than one product.

I'm sorry to ask this in spite of so many explanations around. What does "more than 1 product" mean? Shouldn't it be the same as "2 group overlaps"? My understanding is that 2 group overlaps will include both 2 group and 3 group overlaps. Hence, formula 1 should be sufficient, right?

I know i am going wrong somewhere. Could you clarify please?

Can someone help me how to solve this question...thanks in advance...

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

As 85% of those surveyed liked at least one of three products then 15% liked none of three products.

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} - 2*{liked exactly three product} + {liked none of three products}

\(100=50+30+20-x-2*5+15\) --> \(x=5\), so 5 people liked exactly two products. More than one product liked those who liked exactly two products, (5%) plusthose who liked exactly three products (5%), so 5+5=10% liked more than one product.

I'm sorry to ask this in spite of so many explanations around. What does "more than 1 product" mean? Shouldn't it be the same as "2 group overlaps"? My understanding is that 2 group overlaps will include both 2 group and 3 group overlaps. Hence, formula 1 should be sufficient, right?

I know i am going wrong somewhere. Could you clarify please?

More than one means exactly 2 or exactly 3, regions e, d, f, and g in the diagram below:

Re: Set theory-Need help in solving this [#permalink]

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18 Mar 2014, 21:21

Thank you for providing this link bagdbmba. I tried using the other formula and, although I realize the one Bunnuel used is better for this problem, I was having trouble understanding how to link back to answer.

This makes perfect sense in terms of bridging the formulas!

bagdbmba wrote:

Bunuel wrote:

mitmat wrote:

Can someone help me how to solve this question...thanks in advance...

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

As 85% of those surveyed liked at least one of three products then 15% liked none of three products.

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} - 2*{liked exactly three product} + {liked none of three products}

\(100=50+30+20-x-2*5+15\) --> \(x=5\), so 5 people liked exactly two products. More than one product liked those who liked exactly two products, (5%) plusthose who liked exactly three products (5%), so 5+5=10% liked more than one product.

Hi Bunuel, Can you please clarify if we're to use first formula how the solution would look like?

If we consider '\(x=5\)' to be the overlaps of 3 sets A,B,C and overlaps of A&B, B&C, C&A; then eqn. should be\(100=50+30+20-x+5+15\) , So, x=20, now subtracting 2*5 (as 5 is taken thrice within x and qs demands 'at least one' so it should be considered once) So,x=20-10=10...

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

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31 May 2014, 12:42

Hi all, I use the 2nd formula and get the desired 5 and 5 for "like exactly 2 products" and "like exactly 3 products". My question: If the number of people who like 2 products equals the number of people who like 3 products, doesn't this mean that it must be the exact same five people? And hence the number of people who like more than 1 product is five, not ten?? Thx in advance.

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

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14 Jun 2015, 05:27

Bunuel wrote:

dauntingmcgee wrote:

Bunuel wrote:

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} - 2*{liked exactly three product} + {liked none of three products}

100=50+30+20-x-2*5+15 --> x=5, so 5 people liked exactly two products. More than one product liked is equivalent to those who liked exactly two products, (5%)plusthose who liked exactly three products (5%), so 5+5=10% liked more than one product.

Answer: B.

Bunuel, you are close but have a small error as highlighted in red above and fixed in green below.

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} + {liked exactly three product} + {liked none of three products}

100=50+30+20-x+5+15 --> x=15, so 15 people liked exactly two products. More than one product liked those who liked exactly two products, (15%)plusthose who liked exactly three products (5%), so 15+5=20% liked more than one product

In my post in the end of the first page I explain the difference in two formulas: the one I used (right one for THIS question) and the one you propose (wrong for THIS question).

Hope it helps.

Hi Bunuel, I could be wrong, but the first formula is not wrong for this example either, it's just another approach: First Formula: 100=50+30+20-X(Sum of 2Group overlaps)+5(all 3)+15(Neither) X=20, but we have to substract 2*all 3 overlaps --> 20-2*5=10

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

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20 Sep 2015, 00:33

Hi Bunuel, I am also confused with the language, and I know I am wrong, However, I failed to know what's wrong with my thought. here is my way of thinking. Could you please pinpoint the problem? Thanks. I assume there are 100 people being surveyed, and 85 people like at least one of the product, accordingly, 15 people do not like any product. And then it said that 50% of those asked liked product 1. I decided to use 85 x 50% instead of 100 x 50% because I think the 50 % of people like product, so I should eliminate the 15 people who do not like any product. I just don't know what's wrong with my reasoning.

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

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15 Oct 2016, 21:53

Why aren't we using the first formula in this?? the question states more than one product, so it should be 2 or more which requires the first formula? 10% is just "exactly two" products... Please help

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