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

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

A. 5
B. 10
C. 15
D. 20
E. 25
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In a consumer survey, 85% of those surveyed liked at least [#permalink] New post   26 Jul 2010, 04:27
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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

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 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%) plus those who liked exactly three products (5%), so 5 + 5 = 10% liked more than one product.

Answer: B.

For more check ADVANCED OVERLAPPING SETS PROBLEMS

Hope it helps.
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Re: Set theory-Need help in solving this [#permalink] New post   27 Jul 2010, 11:34
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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%) plus those 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%) plus those 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] New post   27 Jul 2010, 11:47
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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%) plus those 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%) plus those who liked exactly three products (5%), so 15+5=20% liked more than one product

Answer: D


Please follow this link: formulae-for-3-overlapping-sets-69014.html

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.
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Re: Set theory-Need help in solving this [#permalink] New post   27 Jul 2010, 11:50
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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%) plus those 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%) plus those who liked exactly three products (5%), so 15+5=20% liked more than one product

Answer: D


Please follow this link: formulae-for-3-overlapping-sets-69014.html

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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Re: In a consumer survey, 85% of those surveyed [#permalink] New post   13 Jul 2012, 05:08
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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?
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Re: In a consumer survey, 85% of those surveyed [#permalink] New post   13 Jul 2012, 05:17
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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".
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Re: In a consumer survey, 85% of those surveyed [#permalink] New post   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
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Re: In a consumer survey, 85% of those surveyed [#permalink] New post   20 Mar 2013, 04:55
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summer101 wrote:
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


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.

Check the link provided here: in-a-consumer-survey-85-of-those-surveyed-liked-at-least-98018.html#p754585
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Re: Set theory-Need help in solving this [#permalink] New post   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%) plus those who liked exactly three products (5%), so 5+5=10% liked more than one product.

Answer: B.

For more check ADVANCED OVERLAPPING SETS PROBLEMS

Hope it helps.


Hi Bunuel,

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?
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Re: Set theory-Need help in solving this [#permalink] New post   13 Sep 2013, 02:18
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emailmkarthik 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%) plus those who liked exactly three products (5%), so 5+5=10% liked more than one product.

Answer: B.

For more check ADVANCED OVERLAPPING SETS PROBLEMS

Hope it helps.


Hi Bunuel,

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:


For more check ADVANCED OVERLAPPING SETS PROBLEMS

Hope it helps.
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In a consumer survey, 85% of those surveyed liked at least [#permalink] New post   Updated on: 03 Jan 2016, 07:50
Please refer to the attached image. Thanks!
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Originally posted by kham71 on 03 Jan 2016, 07:40.
Last edited by kham71 on 03 Jan 2016, 07:50, edited 1 time in total.
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Re: In a consumer survey, 85% of those surveyed liked at least [#permalink] New post   05 Apr 2017, 23:27
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mathewmithun 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

<b>sir i am still unable to understand why we can't use total=A+B+C-(2 category)+3 category+neither as we need more than 1 category which mean 2 category+all 3 category and this formula will give us straight answer no need to add anything further please elaborate</b>
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Re: In a consumer survey, 85% of those surveyed liked at least [#permalink] New post   06 Apr 2017, 00:01
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rishabhmishra wrote:
mathewmithun 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

<b>sir i am still unable to understand why we can't use total=A+B+C-(2 category)+3 category+neither as we need more than 1 category which mean 2 category+all 3 category and this formula will give us straight answer no need to add anything further please elaborate</b>




We need d + e + f + g.

The formula you mention will give \(sum \ of \ 2-group \ overlaps=AnB+AnC+BnC=20\). Notice that AnB+AnC+BnC counts section g THREE times. We need to count it once. So, to get the answer we should subtract 2g from that: g = 5 --> 20 - 2g = 20 - 10 = 10.

Hope it's clear.
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Re: In a consumer survey, 85% of those surveyed liked at least [#permalink] New post   24 Dec 2017, 04:48
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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%) plus those who liked exactly three products (5%), so 5+5=10% liked more than one product.

Answer: B.



Hope it helps.


Hi Bunuel,
"If 5% of the people in the survey liked all three of the products", doesn't that include the set of 2 overlaps? How do we know that liked all 3 translates to EXACTLY three products?
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Re: In a consumer survey, 85% of those surveyed liked at least [#permalink] New post   24 Dec 2017, 05:05
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Ahmedyali 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%) plus those who liked exactly three products (5%), so 5+5=10% liked more than one product.

Answer: B.



Hope it helps.


Hi Bunuel,
"If 5% of the people in the survey liked all three of the products", doesn't that include the set of 2 overlaps? How do we know that liked all 3 translates to EXACTLY three products?


When you have 3 products {liked exactly three product} and {liked three product} are the same group.
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Re: In a consumer survey, 85% of those surveyed liked at least [#permalink] New post   28 Jun 2020, 20:37
mathewmithun 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


I'm a little confused here - pls help :please: :cry:

If 85% of those surveyed liked at least one of the products that means 15% did not like any of the products, hence none: 15%. When they say 50% of the people asked i.e. surveyed, or total people (right?), liked products 1, 30% liked prod. 2 and 20% liked prod. 3? How can 100% of the people like Product 1, 2 and 3 and still 15% of the people like none of the product? Is it because when they mention the 50%-30%-20% numbers it does not mean that 50% of the people only like product 1 and no other product?
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Re: In a consumer survey, 85% of those surveyed liked at least [#permalink] New post   29 Jun 2020, 00:08
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firsttimenoob wrote:
mathewmithun 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


I'm a little confused here - pls help :please: :cry:

If 85% of those surveyed liked at least one of the products that means 15% did not like any of the products, hence none: 15%. When they say 50% of the people asked i.e. surveyed, or total people (right?), liked products 1, 30% liked prod. 2 and 20% liked prod. 3? How can 100% of the people like Product 1, 2 and 3 and still 15% of the people like none of the product? Is it because when they mention the 50%-30%-20% numbers it does not mean that 50% of the people only like product 1 and no other product?


Yes. For example, 50% of those asked liked product 1, does not mean that those 50% liked only product 1, some of them might also liked any of the other products.
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Re: In a consumer survey, 85% of those surveyed liked at least [#permalink] New post   22 Jul 2020, 01:36
In case anyone used the first formula and got 20% and started thinking what went wrong, below explanation can help:

Total=A+B+C−(sum of 2−group overlaps)+(all three)+NeitherTotal=A+B+C−(sum of 2−group overlaps)+(all three)+Neither.
100=50+30+20 -(sum of 2−group overlaps) +5+15
Solving :
sum of 2−group overlaps = 20

d+g+e+g+f+g=20
d+e+f+3g=20
d+e+f+3*5=20
d+e+f=5

More than one drink=(d+e+f)+g=5+5=10%
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Re: In a consumer survey, 85% of those surveyed liked at least [#permalink] New post   13 Jan 2021, 15:58
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mathewmithun 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


At least 85% liked product 1, 2, and 3 means 15% doesn't like anyone.

So, 100%= 50%+30%+20% - Exactly 2 -2(all the three)+ Neither

100=100 - Exactly 2 - 2*5+15

Exactly 2=5

More than 2=exactly 2 + all three =5+5=10

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