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

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Intern
Joined: 23 Jan 2016
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Re: In a consumer survey, 85% of those surveyed liked at least  [#permalink]

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21 Oct 2016, 20:50
Adding in my thought process in case it helps anyone out

1. You have 85% like at least one of the three products. That includes those who liked 1,2,3 or three products.

2. 50% liked product 1, 30% product 2, and 20% product 3. That gives you a total of 100%. However, since only 85% liked at least one, you end up with 15% "too much".

3. The 15% is made up of those who liked either 2 or 3 products. Since 5% liked all three, you count that twice. That leaves 5% left over. So the total is 5% + 5% = 10% who liked more than one.
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Re: In a consumer survey, 85% of those surveyed liked at least  [#permalink]

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21 Oct 2016, 20:53
Nakul555 wrote:
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

I could be wrong Nakul555, but my thought process is that you don't know which ones like which two products. E.g., someone could like 1 and 2 or 2 and 3 or even 1 and 3. I think if you knew who liked what you might be able to use that first formula.
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Re: In a consumer survey, 85% of those surveyed liked at least  [#permalink]

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05 Apr 2017, 22:27
mathewmithun 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

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

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05 Apr 2017, 23:01
rishabhmishra wrote:
mathewmithun 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

<b>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</b>

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

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09 Jul 2017, 06:50
Hi Bunuel,

The place i got stuck in this question is "50% of those asked liked product 1"...now the asked % is given as 85%...so shouldn't that be 50% of 85 ?...rather than taking Product 1 as 50% directly....am i reading it wrongly ?

Best Regards,
Anup Kumar Patel
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Joined: 13 Mar 2017
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Re: In a consumer survey, 85% of those surveyed liked at least  [#permalink]

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24 Dec 2017, 03:48
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.

Hope it helps.

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?
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Joined: 02 Sep 2009
Posts: 53020
Re: In a consumer survey, 85% of those surveyed liked at least  [#permalink]

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24 Dec 2017, 04:05
Ahmedyali 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.

Hope it helps.

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?

When you have 3 products {liked exactly three product} and {liked three product} are the same group.
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Re: In a consumer survey, 85% of those surveyed liked at least  [#permalink]

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18 Dec 2018, 22:37
As 85% of those surveyed like atleast one of the three products, we can say that 15% of those surveyed didn’t like any of the three products.
Let total no of people surveyed be 100.
Total = {liked product 1} + {liked product 2} + {liked product 3} – {liked exactly two products} – 2 x {liked all products} + {liked none of the three products}
100 = 50 + 30 + 20 – a – 2 x 5 + 15
a = 5.
So, 5% people liked exactly 2 products and we know that 5% people liked all the three products.
Hence, 10% people liked more than one product.
Intern
Joined: 27 Nov 2015
Posts: 47
Re: In a consumer survey, 85% of those surveyed liked at least  [#permalink]

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13 Jan 2019, 07:05
Hi, I am not sure if this approach is correct. Kindly let me know

I used this formula

Total=A+B+C−(sum of 2−group overlaps)+(all three)+NeitherTotal=A+B+C−(sum of 2−group overlaps)+(all three)+Neither.

85=42.5+25.5+17-x+4.25

This gives me x=4.25 which is sum of 2−group overlaps. I add this to the all three sum which is 4.25, giving me 8.5.

This leads to 8.5/85*100 => 10%
Re: In a consumer survey, 85% of those surveyed liked at least   [#permalink] 13 Jan 2019, 07:05

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