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

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

A. 5 
B. 10 
C. 15 
D. 20 
E. 25

Bunuel · Accepted Answer

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

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 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.

dauntingmcgee · Answer

My apologies, you are quite correct. I should not have doubted the awesome power of Bunuel

dauntingmcgee · Answer

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

Bunuel · Answer

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.

pavanpuneet · Answer

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?

Bunuel · Answer

For me the language is clear enough. It says "50% of those  asked ", so "50% of those  surveyed ".

summer101 · Answer

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

Bunuel · Answer

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

HKHR · Answer

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?

Bunuel · Answer

More than one means exactly 2 or exactly 3, regions e, d, f, and g in the diagram below:
 https://gmatclub.com/forum/download/file.php?id=18933

For more check  ADVANCED OVERLAPPING SETS PROBLEMS

Hope it helps.

kham71 · Answer

Please refer to the attached image. Thanks!

rishabhmishra · Answer

sir i am still unable to understand why we can't use total=A+B+C-(2 category)+3 category+neither as we need more than 1 category which mean 2 category+all 3 category and this formula will give us straight answer no need to add anything further please elaborate

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=18933

We need d + e + f + g.

The formula you mention will give  sum \ of \ 2-group \ overlaps=AnB+AnC+BnC=20 . Notice that AnB+AnC+BnC counts section g THREE times. We need to count it once. So, to get the answer we should subtract 2g from that: g = 5 --> 20 - 2g = 20 - 10 = 10.

Hope it's clear.

Robocopping · Answer

Hi Bunuel, 
"If 5% of the people in the survey  liked all three  of the products", doesn't that include the set of 2 overlaps? How do we know that liked all 3 translates to EXACTLY three products?

Bunuel · Answer

When you have 3 products {liked exactly three product} and {liked three product} are the same group.

firsttimenoob · Answer

I'm a little confused here - pls help

If 85% of those surveyed liked at least one of the products that means 15% did not like any of the products, hence none: 15%. When they say 50% of the people asked i.e. surveyed, or total people (right?), liked products 1, 30% liked prod. 2 and 20% liked prod. 3? How can 100% of the people like Product 1, 2 and 3 and still 15% of the people like none of the product? Is it because when they mention the 50%-30%-20% numbers it does not mean that 50% of the people only like product 1 and no other product?

Bunuel · Answer

Yes. For example, 50% of those asked liked product 1, does not mean that those 50% liked only product 1, some of them might also liked any of the other products.

ShubhamShekhar · Answer

In case anyone used the first formula and got 20% and started thinking what went wrong, below explanation can help:

Total=A+B+C−(sum of 2−group overlaps)+(all three)+NeitherTotal=A+B+C−(sum of 2−group overlaps)+(all three)+Neither.
100=50+30+20 -(sum of 2−group overlaps) +5+15
Solving :
 sum  of 2−group overlaps = 20

d+g+e+g+f+g=20
d+e+f+3g=20
d+e+f+3*5=20
d+e+f=5

More than one drink=(d+e+f)+g=5+5=10%

MHIKER · Answer

At least 85% liked product 1, 2, and 3 means 15% doesn't like anyone.

So, 100%= 50%+30%+20% - Exactly 2 -2(all the three)+ Neither

100=100 - Exactly 2 - 2*5+15

Exactly 2=5

More than 2=exactly 2 + all three =5+5=10

The answer is B

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

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