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A marketing firm found that, of 800 computer users surveyed, 280 were

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A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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New post Updated on: 05 Jul 2018, 10:19
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A marketing firm found that, of 800 computer users surveyed, 280 were not familiar with either Website A or Website B, 220 were familiar only with Website A, and for every 3 computer users who were familiar only with Website B, one was familiar with both websites. How many of the 800 computer users were familiar with both websites?

(A) 75
(B) 100
(C) 135
(D) 150
(E) 200

Originally posted by TippingPoint93 on 05 Jul 2018, 09:50.
Last edited by Bunuel on 05 Jul 2018, 10:19, edited 1 time in total.
Added the OA.
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Re: A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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New post 05 Jul 2018, 10:24
TippingPoint93 wrote:
A marketing firm found that, of 800 computer users surveyed, 280 were not familiar with either Website A or Website B, 220 were familiar only with Website A, and for every 3 computer users who were familiar only with Website B, one was familiar with both websites. How many of the 800 computer users were familiar with both websites?

(A) 75
(B) 100
(C) 135
(D) 150
(E) 200


Total = A + B - Both + Neither.

Total = 800
280 were not familiar with either Website A or Website B: Neither = 280
220 were familiar only with Website A: A - Both = 220
For every 3 computer users who were familiar only with Website B, one was familiar with both websites: B - Both = 3*Both --> B = 4*Both.

800 = A + B - Both + 280.
Since A - Both = 220, then 800 = 220 + B + 280.
B =300.

B = 4*Both --> 300 = 4*Both --> Both = 75.

Answer: A.

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Re: A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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New post 05 Jul 2018, 10:54
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1
TippingPoint93 wrote:
A marketing firm found that, of 800 computer users surveyed, 280 were not familiar with either Website A or Website B, 220 were familiar only with Website A, and for every 3 computer users who were familiar only with Website B, one was familiar with both websites. How many of the 800 computer users were familiar with both websites?

(A) 75
(B) 100
(C) 135
(D) 150
(E) 200


Please refer the affixed Venn diagram,
800 computer users surveyed, T=800
280 were not familiar with either Website A or Website B, n=280
220 were familiar only with Website A, a=220
for every 3 computer users who were familiar only with Website B, one was familiar with both websites; if c=x then b=3x.
Question stem:- c=x=?

We have a+c+b+n=T=800
Or, 220+x+3x+280=800
Or,4x=300
or, x=\(\frac{300}{4}\)=75

Ans. (A)
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A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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New post 05 Jul 2018, 22:22
2

Solution


Given:
    • Number of computer users surveyed = 800
    • Number of users not familiar with either Website A or Website B = 280
    • Number of users familiar with only Website A = 220
    • For every 3 computer users who were familiar only with Website B, one was familiar with both websites

To find:
    • Number of computer users familiar with both the websites

Approach and Working:
    • Let us assume,
      o Number of users surveyed as U
      o Number of users familiar with Website A as A, and
      o Number of users familiar with Website B as B
    • From the given information,
      o U = 800
      o U - (A ⋃ B) = 280 => (A ⋃ B) = U - 280 ……………………….. (1)
      o A – (A ⋂ B) = 220 => A = 220 + (A ⋂ B) ……………………… (2)
      o B - (A ⋂ B) = 3(A ⋂ B) => B = 4(A ⋂ B)………………………………. (3)
    • (A ⋃ B) = A + B - (A ⋂ B)
    • Substituting (1), (2) and (3) in the above equation, we get
      o U - 280 = 220 + (A ⋂ B) + 4(A ⋂ B) - (A ⋂ B)
      o Implies, 4(A ⋂ B) = 800 – 280 -220
      o Thus, (A ⋂ B) = 300/4 = 75

Therefore, number of computer users familiar with both the websites = 75

Hence, the correct answer is option A.

Answer: A
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Re: A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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New post 14 Jul 2018, 20:33
PKN wrote:
TippingPoint93 wrote:
A marketing firm found that, of 800 computer users surveyed, 280 were not familiar with either Website A or Website B, 220 were familiar only with Website A, and for every 3 computer users who were familiar only with Website B, one was familiar with both websites. How many of the 800 computer users were familiar with both websites?

(A) 75
(B) 100
(C) 135
(D) 150
(E) 200


Please refer the affixed Venn diagram,
800 computer users surveyed, T=800
280 were not familiar with either Website A or Website B, n=280
220 were familiar only with Website A, a=220
for every 3 computer users who were familiar only with Website B, one was familiar with both websites; if c=x then b=3x.
Question stem:- c=x=?

We have a+c+b+n=T=800
Or, 220+x+3x+280=800
Or,4x=300
or, x=\(\frac{300}{4}\)=75

Ans. (A)


Of the three approaches listed by three users i found yours to be the simplest!! :-)
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Re: A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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New post 25 Jul 2018, 01:37
PKN wrote:
TippingPoint93 wrote:
A marketing firm found that, of 800 computer users surveyed, 280 were not familiar with either Website A or Website B, 220 were familiar only with Website A, and for every 3 computer users who were familiar only with Website B, one was familiar with both websites. How many of the 800 computer users were familiar with both websites?

(A) 75
(B) 100
(C) 135
(D) 150
(E) 200


Please refer the affixed Venn diagram,
800 computer users surveyed, T=800
280 were not familiar with either Website A or Website B, n=280
220 were familiar only with Website A, a=220
for every 3 computer users who were familiar only with Website B, one was familiar with both websites; if c=x then b=3x.
Question stem:- c=x=?

We have a+c+b+n=T=800
Or, 220+x+3x+280=800
Or,4x=300
or, x=\(\frac{300}{4}\)=75

Ans. (A)


I got the answer by the double matrix method but the Venn approach gave me a wrong answer:

the formula is: total grp 1+ grp 2 - both + neither.

why are you using +c and not -c?

thanks
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Re: A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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New post 25 Jul 2018, 03:18
Mansoor50 wrote:
PKN wrote:
TippingPoint93 wrote:
A marketing firm found that, of 800 computer users surveyed, 280 were not familiar with either Website A or Website B, 220 were familiar only with Website A, and for every 3 computer users who were familiar only with Website B, one was familiar with both websites. How many of the 800 computer users were familiar with both websites?

(A) 75
(B) 100
(C) 135
(D) 150
(E) 200


Please refer the affixed Venn diagram,
800 computer users surveyed, T=800
280 were not familiar with either Website A or Website B, n=280
220 were familiar only with Website A, a=220
for every 3 computer users who were familiar only with Website B, one was familiar with both websites; if c=x then b=3x.
Question stem:- c=x=?

We have a+c+b+n=T=800
Or, 220+x+3x+280=800
Or,4x=300
or, x=\(\frac{300}{4}\)=75

Ans. (A)


I got the answer by the double matrix method but the Venn approach gave me a wrong answer:

the formula is: total grp 1+ grp 2 - both + neither.

why are you using +c and not -c?

thanks

Hi Mansoor50,
Let's apply your formula :-total= grp 1+ grp 2 - both + neither------------(1)
Given total=800, neither=280,
Only groupA=grpA-Both=220
Or, grpA=220+both-------------------------------------------------------------------(2)
Only grpB=grpB-Both
Given,Only grpB=3*both
Or, grpB-Both=3*both
Or, grpB=4*both-----------------------------------------------------------------------(3)
substituting in (1), 800=220+both+4*both-both+280
Or, 800=500+4*both
Or, \(both=\frac{300}{4}=75\)
We have arrived at the solution using your formula and concepts.
(The notations A , B denoted for website A & Website B)

P.S:-
We need to understand the nomenclatures a,b, and c.(As per my approach)
a=only grp1
b=only grp2
c=both grp1 & 2
n=neither grp1 nor grp2
T=Total group
So, Total=only grp1+only grp2+both grp1 & 2+neither grp1 nor grp2----------------(a)

We can transform the above deduction into your formula:-
since grp1=only grp1+both, So, only grp1=grp1-both; now substituting in (a)

Total=only grp1+only grp2+both grp1 & 2+neither grp1 nor grp2
Or, Total=(grp1-both)+(grp2-both)+both+neither
Or, Total=grp1+grp2-2*both+both+neither
Or, Total=grp1+grp2-both+neither-------------------------------------------------------------(b)

So, basically, both the formula and the deduction are the the same. The only difference is method of consideration of "only" or "only+both".

Hope it helps.
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Regards,

PKN

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Re: A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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New post 26 Jul 2018, 15:29
TippingPoint93 wrote:
A marketing firm found that, of 800 computer users surveyed, 280 were not familiar with either Website A or Website B, 220 were familiar only with Website A, and for every 3 computer users who were familiar only with Website B, one was familiar with both websites. How many of the 800 computer users were familiar with both websites?

(A) 75
(B) 100
(C) 135
(D) 150
(E) 200


Let’s denote the number of users who are familiar with both websites as x. Then, the number of users who are familiar with only website B is 3x.

We can use the formula:

Total = only A + only B + both + neither

800 = 220 + 3x + x + 280

800 = 500 + 4x

300 = 4x

75 = x

Answer: A
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Re: A marketing firm found that, of 800 computer users surveyed, 280 were &nbs [#permalink] 26 Jul 2018, 15:29
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