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

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In a consumer survey, 85% of those surveyed liked at least [#permalink] New post 26 Jul 2010, 02:53
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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
[Reveal] Spoiler: OA
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Re: Set theory-Need help in solving this [#permalink] New post 26 Jul 2010, 03:27
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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%) 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, 10:34
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%) 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, 10:47
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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, 10:50
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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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overlapping sets [#permalink] New post 12 Jan 2012, 03:14
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.
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Re: overlapping sets [#permalink] New post 12 Jan 2012, 03:19
Expert's post
mushyyy 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

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.

Please follow the link for detailed explanation of the concept tested in this question: formulae-for-3-overlapping-sets-69014.html#p729340
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Re: In a consumer survey, 85% of those surveyed [#permalink] New post 13 Jul 2012, 04:08
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?
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Re: In a consumer survey, 85% of those surveyed [#permalink] New post 13 Jul 2012, 04:17
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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?


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 liked at least [#permalink] New post 10 Jan 2013, 09:33
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
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Re: In a consumer survey, 85% of those surveyed [#permalink] New post 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?
Thanks for your response
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Re: In a consumer survey, 85% of those surveyed [#permalink] New post 20 Mar 2013, 03:55
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.

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 18 Apr 2013, 22:03
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%) plus those 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.

Thanks and kudos!
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Re: Set theory-Need help in solving this [#permalink] New post 19 Apr 2013, 02:16
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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%) plus those 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.

Thanks and kudos!


Check this post: ADVANCED OVERLAPPING SETS PROBLEMS

Hope it helps.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Set theory-Need help in solving this [#permalink] New post 09 Aug 2013, 07:28
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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.

For more check ADVANCED OVERLAPPING SETS PROBLEMS

Hope it helps.


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 be100=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?
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Re: In a consumer survey, 85% of those surveyed liked at least [#permalink] New post 09 Aug 2013, 12:43
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%
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Re: Set theory-Need help in solving this [#permalink] New post 17 Aug 2013, 04:01
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%) 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,

Somehow I am unable to get the question itself.

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 !

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TGC !
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Re: Set theory-Need help in solving this [#permalink] New post 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.

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, 01:18
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%) 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:
Image

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 18 Mar 2014, 20:21
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%) 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,
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 be100=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?
Re: Set theory-Need help in solving this   [#permalink] 18 Mar 2014, 20:21
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