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A marketing firm found that, of 800 computer users surveyed, 280 were
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Updated on: 05 Jul 2018, 11:19
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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
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Originally posted by TippingPoint93 on 05 Jul 2018, 10:50.
Last edited by Bunuel on 05 Jul 2018, 11:19, 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
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05 Jul 2018, 11:24
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. P.S. You have to provide the OA's when posting questions.
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Re: A marketing firm found that, of 800 computer users surveyed, 280 were
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05 Jul 2018, 11:54
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
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05 Jul 2018, 23:22
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
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14 Jul 2018, 21:33
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
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25 Jul 2018, 02:37
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
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25 Jul 2018, 04:18
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=grpABoth=220 Or, grpA=220+both(2) Only grpB=grpBBothGiven,Only grpB=3*both Or, grpBBoth=3*both Or, grpB=4*both(3) substituting in (1), 800=220+both+4*bothboth+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=grp1both; now substituting in (a) Total=only grp1+only grp2+both grp1 & 2+neither grp1 nor grp2 Or, Total=(grp1both)+(grp2both)+both+neither Or, Total=grp1+grp22*both+both+neither Or, Total=grp1+grp2both+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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Re: A marketing firm found that, of 800 computer users surveyed, 280 were
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26 Jul 2018, 16:29
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
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03 Feb 2019, 22:18
Solution: The best way to solve the problem is by grid method. Attachment:
table1.PNG [ 10.23 KiB  Viewed 617 times ]
Let’s fill the grid by the information given the question. 280 were not familiar with either Website A or Website B, 220 were familiar only with Website A. For every 3 computer users who were familiar only with Website B, and one was familiar with both websites. Let “x” be the number of computer users who are familiar with both the websites and “3x” be the number of computer users who are familiar with only website B. Attachment:
table2.PNG [ 11.6 KiB  Viewed 617 times ]
So, from above grid it’s very much clear that; The number of computer users who are familiar with both the websites = 75. So, the correct answer option is “A”.
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Re: A marketing firm found that, of 800 computer users surveyed, 280 were
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05 Feb 2019, 11:38
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 My reasoning if it helps anyone: Every 3 computer users who were familiar only with Website B, one was familiar with both websites. This means Both : Only Website B is in a ratio of 1:3. If 280 were not familiar that means (800  280) 520 is the total group split between Website A/B/both. So total = Website A + Website B + Both A&B Website A = 220 Website B = B Both A&B = \(B/3\)\frac{[}{fraction] 520 = 220 + B + \([fraction]B/3}\) B = 225 Both A&B = 225/3 = 75 (Answer Choice A)




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