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

Question

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

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

Bunuel · Answer

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.

PKN · Answer

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)

EgmatQuantExpert · Answer

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

swagatamoitra · Answer

Of the three approaches listed by three users i found yours to be the simplest!!

Mansoor50 · Answer

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

PKN · Answer

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.

JeffTargetTestPrep · Answer

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

KrishnakumarKA1 · Answer

Solution:
The best way to solve the problem is by grid method.

Attachment:

table1.PNG [ 10.23 KiB | Viewed 5051 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 5061 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”.

NinetyFour · Answer

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{

520 = 220 + B +   B/3}

B = 225

Both A&B = 225/3 = 75 (Answer Choice A)

bumpbot · Answer

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

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