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

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Joined: 22 Jul 2010
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In a consumer survey, 85% of those surveyed liked at least  [#permalink]

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26 Jul 2010, 02:53
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54% (02:10) correct 46% (02:21) wrong based on 678 sessions

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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
Math Expert
Joined: 02 Sep 2009
Posts: 62380
In a consumer survey, 85% of those surveyed liked at least  [#permalink]

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26 Jul 2010, 03:27
8
8
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[/quote]

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.

For more check ADVANCED OVERLAPPING SETS PROBLEMS

Hope it helps.
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Intern
Joined: 16 Jul 2010
Posts: 17
Re: Set theory-Need help in solving this  [#permalink]

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27 Jul 2010, 10:34
3
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.

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

Math Expert
Joined: 02 Sep 2009
Posts: 62380
Re: Set theory-Need help in solving this  [#permalink]

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27 Jul 2010, 10:47
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.

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

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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Joined: 16 Jul 2010
Posts: 17
Re: Set theory-Need help in solving this  [#permalink]

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27 Jul 2010, 10:50
1
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.

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

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
Manager
Joined: 26 Dec 2011
Posts: 89
Re: In a consumer survey, 85% of those surveyed  [#permalink]

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13 Jul 2012, 04:08
1
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?
Math Expert
Joined: 02 Sep 2009
Posts: 62380
Re: In a consumer survey, 85% of those surveyed  [#permalink]

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13 Jul 2012, 04:17
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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Joined: 06 Jun 2012
Posts: 112
Re: In a consumer survey, 85% of those surveyed  [#permalink]

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19 Mar 2013, 02:46
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?
Math Expert
Joined: 02 Sep 2009
Posts: 62380
Re: In a consumer survey, 85% of those surveyed  [#permalink]

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20 Mar 2013, 03:55
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?

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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Joined: 31 Mar 2013
Posts: 57
Location: India
GPA: 3.02
Re: Set theory-Need help in solving this  [#permalink]

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12 Sep 2013, 00:26
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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 62380
Re: Set theory-Need help in solving this  [#permalink]

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13 Sep 2013, 01:18
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.

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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Posts: 24
In a consumer survey, 85% of those surveyed liked at least  [#permalink]

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Updated on: 03 Jan 2016, 06:50
Please refer to the attached image. Thanks!
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Originally posted by kham71 on 03 Jan 2016, 06:40.
Last edited by kham71 on 03 Jan 2016, 06:50, edited 1 time in total.
Manager
Joined: 23 Sep 2016
Posts: 228
Re: In a consumer survey, 85% of those surveyed liked at least  [#permalink]

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05 Apr 2017, 22:27
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>
Math Expert
Joined: 02 Sep 2009
Posts: 62380
Re: In a consumer survey, 85% of those surveyed liked at least  [#permalink]

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05 Apr 2017, 23:01
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]

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24 Dec 2017, 03:48
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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 62380
Re: In a consumer survey, 85% of those surveyed liked at least  [#permalink]

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24 Dec 2017, 04:05
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.

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]

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