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

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Manager
Joined: 06 Jul 2013
Posts: 51
Location: United States
A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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Updated on: 05 Jul 2018, 10:19
2
00:00

Difficulty:

55% (hard)

Question Stats:

59% (02:01) correct 41% (02:33) wrong based on 119 sessions

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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.
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Joined: 02 Sep 2009
Posts: 51071
Re: A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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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.

P.S. You have to provide the OA's when posting questions.
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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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05 Jul 2018, 10:54
1
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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Joined: 04 Jan 2015
Posts: 2269
A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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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.

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Joined: 05 Sep 2016
Posts: 29
Location: India
Concentration: General Management, Operations
WE: Engineering (Energy and Utilities)
Re: A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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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!!
Manager
Joined: 29 May 2017
Posts: 127
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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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
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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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.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: A marketing firm found that, of 800 computer users surveyed, 280 were  [#permalink]

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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

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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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