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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?

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

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26 Jul 2010, 04:27

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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.

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

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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%)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 _________________

If you find my posts useful, please award me some Kudos!

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

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09 Aug 2013, 08:28

1

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Expert's post

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

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 _________________

If you find my posts useful, please award me some Kudos!

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

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27 Jul 2010, 11:47

Expert's post

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).

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 idea:

pick 100 and x= all set with exactly two items

85=30+50+20 -(X)-10

X=5

so the answer is 5+5/100= 10%

is it correct?because I downloaded that"must gmat problem.pdf" and the result is 20 according to that.

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 idea:

pick 100 and x= all set with exactly two items

85=30+50+20 -(X)-10

X=5

so the answer is 5+5/100= 10%

is it correct?because I downloaded that"must gmat problem.pdf" and the result is 20 according to that.

Merging similar topics. Please ask if anything remains unclear.

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?

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

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13 Jul 2012, 05:17

Expert's post

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". _________________

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

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10 Jan 2013, 10:33

Dear Bunuel, could you please explain the difference between the formula's that you state in the mathbook in a little bit more detail, Thanks in advance

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 _________________

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

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20 Mar 2013, 04:55

Expert's post

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.

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

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18 Apr 2013, 23:03

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.

Answer: B.

Hope it helps.

Hi Brunel,

I've been reading your posts and find your explanations very useful. However, for this question, im a little confused. From what part of the question do we derive "Exactly two and exactly three products"? why are we using "exactly" 2 overlaps instead of just 2 overlaps? is it because these numbers must be unique? I would really appreciate an elaboration on this.

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

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19 Apr 2013, 03:16

Expert's post

mokura 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.

Answer: B.

Hope it helps.

Hi Brunel,

I've been reading your posts and find your explanations very useful. However, for this question, im a little confused. From what part of the question do we derive "Exactly two and exactly three products"? why are we using "exactly" 2 overlaps instead of just 2 overlaps? is it because these numbers must be unique? I would really appreciate an elaboration on this.

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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Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

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?

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

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13 Sep 2013, 02:18

Expert's post

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%) 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...

This is also fine. Right?

gmatclubot

Re: Set theory-Need help in solving this
[#permalink]
18 Mar 2014, 21:21

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