Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In a consumer survey, 85% of those surveyed liked at least [#permalink]
26 Jul 2010, 02:53

10

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

52% (02:30) correct
48% (02:01) wrong based on 310 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

4

This post received KUDOS

Expert's post

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, 10:50

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!

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 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...

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).

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: 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 !

Attachments

general.JPG [ 12.55 KiB | Viewed 2714 times ]

_________________

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 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?

gmatclubot

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

Great to know you are joining Kellogg. A lot was being talked about your last minute interview on Pagalguy (all good though). It was kinda surprise that you got the...