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In a consumer survey, 85% of those surveyed liked at least [#permalink]
26 Jul 2010, 02:53
13
This post was BOOKMARKED
00:00
A
B
C
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Difficulty:
75% (hard)
Question Stats:
50% (02:33) correct
50% (01:57) wrong based on 477 sessions
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]
26 Jul 2010, 03:27
6
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
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]
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%)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]
27 Jul 2010, 10:47
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).
Re: Set theory-Need help in solving this [#permalink]
27 Jul 2010, 10:50
1
This post received KUDOS
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!
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.
Re: overlapping sets [#permalink]
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.
Re: In a consumer survey, 85% of those surveyed [#permalink]
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?
Re: In a consumer survey, 85% of those surveyed [#permalink]
13 Jul 2012, 04:17
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]
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
Re: In a consumer survey, 85% of those surveyed [#permalink]
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 _________________
Re: In a consumer survey, 85% of those surveyed [#permalink]
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.
Re: Set theory-Need help in solving this [#permalink]
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%) 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]
19 Apr 2013, 02:16
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: Set theory-Need help in solving this [#permalink]
09 Aug 2013, 07:28
1
This post received KUDOS
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: In a consumer survey, 85% of those surveyed liked at least [#permalink]
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% _________________
Re: Set theory-Need help in solving this [#permalink]
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%) 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]
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%) 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]
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%) 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]
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%) 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, 20:21
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