Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 26 May 2017, 12:07

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 22 Jul 2010
Posts: 32
Followers: 0

Kudos [?]: 35 [0], given: 94

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

### Show Tags

26 Jul 2010, 03:53
25
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

52% (02:35) correct 48% (01:57) wrong based on 644 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7739

Kudos [?]: 106226 [6] , given: 11618

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

### Show Tags

26 Jul 2010, 04:27
6
KUDOS
Expert's post
4
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%) 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.
_________________
Intern
Joined: 16 Jul 2010
Posts: 18
Followers: 1

Kudos [?]: 18 [1] , given: 9

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

### Show Tags

27 Jul 2010, 11:50
1
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%) 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
_________________

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

BSchool Forum Moderator
Joined: 27 Aug 2012
Posts: 1194
Followers: 134

Kudos [?]: 1617 [1] , given: 147

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

### Show Tags

09 Aug 2013, 08:28
1
KUDOS
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,
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?
_________________
Intern
Joined: 16 Jul 2010
Posts: 18
Followers: 1

Kudos [?]: 18 [0], given: 9

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

### Show Tags

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%) 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

_________________

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

Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7739

Kudos [?]: 106226 [0], given: 11618

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

### Show Tags

27 Jul 2010, 11:47
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.
_________________
Manager
Joined: 26 Dec 2011
Posts: 116
Followers: 1

Kudos [?]: 35 [0], given: 17

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

### Show Tags

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?
Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7739

Kudos [?]: 106226 [0], given: 11618

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

### Show Tags

13 Jul 2012, 05:17
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".
_________________
Manager
Joined: 06 Jun 2012
Posts: 142
Followers: 0

Kudos [?]: 208 [0], given: 37

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

### Show Tags

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?
_________________

Please give Kudos if you like the post

Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7739

Kudos [?]: 106226 [0], given: 11618

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

### Show Tags

20 Mar 2013, 04:55
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
_________________
Senior Manager
Joined: 10 Jul 2013
Posts: 334
Followers: 3

Kudos [?]: 363 [0], given: 102

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

### Show Tags

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%
_________________

Asif vai.....

Director
Joined: 03 Aug 2012
Posts: 896
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Followers: 24

Kudos [?]: 768 [0], given: 322

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

### Show Tags

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%) 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,

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

Rgds,
TGC !
Attachments

general.JPG [ 12.55 KiB | Viewed 7304 times ]

_________________

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

Manager
Joined: 31 Mar 2013
Posts: 72
Location: India
GPA: 3.02
Followers: 1

Kudos [?]: 27 [0], given: 109

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

### Show Tags

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%) 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: 38908
Followers: 7739

Kudos [?]: 106226 [0], given: 11618

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

### Show Tags

13 Sep 2013, 02:18
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.
_________________
Intern
Joined: 01 Apr 2013
Posts: 19
Followers: 0

Kudos [?]: 5 [0], given: 72

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

### Show Tags

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%) 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,
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?
Intern
Joined: 31 May 2014
Posts: 25
Followers: 0

Kudos [?]: 5 [0], given: 0

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

### Show Tags

31 May 2014, 12:42
Hi all, I use the 2nd formula and get the desired 5 and 5 for "like exactly 2 products" and "like exactly 3 products". My question: If the number of people who like 2 products equals the number of people who like 3 products, doesn't this mean that it must be the exact same five people? And hence the number of people who like more than 1 product is five, not ten?? Thx in advance.
Director
Joined: 10 Mar 2013
Posts: 597
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 17

Kudos [?]: 356 [0], given: 200

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

### Show Tags

14 Jun 2015, 05:27
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.

Hi Bunuel, I could be wrong, but the first formula is not wrong for this example either, it's just another approach:
First Formula: 100=50+30+20-X(Sum of 2Group overlaps)+5(all 3)+15(Neither)
X=20, but we have to substract 2*all 3 overlaps --> 20-2*5=10

_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Intern
Status: one month left...
Joined: 21 Jul 2015
Posts: 5
Location: China
Concentration: Accounting, Finance
GPA: 3.65
Followers: 0

Kudos [?]: 5 [0], given: 17

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

### Show Tags

20 Sep 2015, 00:33
Hi Bunuel, I am also confused with the language, and I know I am wrong, However, I failed to know what's wrong with my thought. here is my way of thinking. Could you please pinpoint the problem? Thanks.
I assume there are 100 people being surveyed, and 85 people like at least one of the product, accordingly, 15 people do not like any product. And then it said that 50% of those asked liked product 1. I decided to use 85 x 50% instead of 100 x 50% because I think the 50 % of people like product, so I should eliminate the 15 people who do not like any product. I just don't know what's wrong with my reasoning.
Intern
Joined: 31 Oct 2015
Posts: 37
Followers: 0

Kudos [?]: 2 [0], given: 53

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

### Show Tags

03 Jan 2016, 07:40
Please refer to the attached image. Thanks!
Attachments

SmartSelectImage_2016-01-03-09-27-24.png [ 104.72 KiB | Viewed 686 times ]

Last edited by kham71 on 03 Jan 2016, 07:50, edited 1 time in total.
Intern
Joined: 11 Jul 2016
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

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

### Show Tags

15 Oct 2016, 21:53
Why aren't we using the first formula in this?? the question states more than one product, so it should be 2 or more which requires the first formula? 10% is just "exactly two" products... Please help
Re: In a consumer survey, 85% of those surveyed liked at least   [#permalink] 15 Oct 2016, 21:53

Go to page    1   2    Next  [ 24 posts ]

Similar topics Replies Last post
Similar
Topics:
In a survey it was found that 95% of those surveyed liked mustard and 2 25 Dec 2016, 12:48
In a survey it was found that 75% of those surveyed liked mustard and 1 19 Dec 2016, 09:08
In a survey it was found that 84% of those surveyed liked mustard and 1 13 Dec 2016, 07:37
In a survey it was found that 60% of those surveyed liked honey and 40 3 08 Dec 2016, 08:24
1 In a consumer survey, 85% of those surveyed liked at least 6 21 Aug 2012, 08:05
Display posts from previous: Sort by