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All 250 files on Sam's hard drive are infected by either a virus or a

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All 250 files on Sam's hard drive are infected by either a virus or a [#permalink]

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New post 10 Oct 2016, 00:42
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All 250 files on Sam's hard drive are infected by either a virus or a worm or both. The number of files that are infected only by a worm is 2.5 times the number of files that are infected by both a virus and a worm. If 50% of the files were not infected by a virus, how many of Sam's files were NOT infected by a worm?

A. 50
B. 70
C. 75
D. 100
E. 125

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Re: All 250 files on Sam's hard drive are infected by either a virus or a [#permalink]

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New post 10 Oct 2016, 02:17
Given data
n(Total) = 250
n(only worm) = 125(50% of total)
n(only worm ) = 2.5 * n(both worm and virus)
So,
n(both worn and virus) = 125/2.5 = 50

n(Total) = n(only worm) + n(both worm and virus) + n(only virus)
n(only virus) = 250-125-50 = 75

Hence, the files not infected by worm is n(Only virus) = 75(Option C)
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All 250 files on Sam's hard drive are infected by either a virus or a [#permalink]

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New post 10 Oct 2016, 05:26
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Bunuel wrote:
All 250 files on Sam's hard drive are infected by either a virus or a worm or both. The number of files that are infected only by a worm is 2.5 times the number of files that are infected by both a virus and a worm. If 50% of the files were not infected by a virus, how many of Sam's files were NOT infected by a worm?

A. 50
B. 70
C. 75
D. 100
E. 125

Let no of files infected by Virus be \(" V "\) and Number of files infected by Worm be \("W"\) and files infected by both a virus and a worm be \("VW"\)
Quote:
The number of files that are infected only by a worm is 2.5 times the number of files that are infected by both a virus and a worm

Total Infected Files = Files Infected only by Virus + Files Infected only by Worm - Files Infected by both Worm & Virus

\(250 = V + W + VW\)
Quote:
If 50% of the files were not infected by a virus

So, We get \(W = 125\)
Quote:
The number of files that are infected only by a worm is 2.5 times the number of files that are infected by both a virus and a worm.

\(W = \frac{5}{2}VW\)
Or, \(125 = \frac{5}{2}VW\)
So, \(VW = 50\)

We know - \(250 = V + W + VW\)
So, 250 = V + 125 + 50
Or, V = 250 - 125 - 50
\(Or, V = 75\)

Hence answer will be (C)
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Re: All 250 files on Sam's hard drive are infected by either a virus or a [#permalink]

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New post 02 Nov 2016, 08:52
Abhishek009 - VW = 50
Only W (i.e. W-VW) = 2.5x = 125
Only V (i.e. V-VW) = V-50

V+VW+W = 250
V-50 + 50 + 125 = 250
Hence, V = 125.

Am i missing something?
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Re: All 250 files on Sam's hard drive are infected by either a virus or a [#permalink]

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New post 29 Dec 2016, 03:30
Let
infected by virus and worm= x
so infected only by worm in 2.5x
as 50% is not infected by virus so 50% is infected by worm
so 125 is infected by worm
as 2.5x=125
x= 50 (infected by both virus and worm.
so lastly infected not by worm means infected only by virus
so 250-125(worm only)-(50 both virus and worm)
75 is correct
answer is C
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Re: All 250 files on Sam's hard drive are infected by either a virus or a [#permalink]

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New post 23 Apr 2017, 20:27
Vishvesh88 wrote:
Abhishek009 - VW = 50
Only W (i.e. W-VW) = 2.5x = 125
Only V (i.e. V-VW) = V-50

V+VW+W = 250
V-50 + 50 + 125 = 250
Hence, V = 125.

Am i missing something?


From your solution, we need to find files not affected by a worm - which should be (V-50). You stopped at finding just V (which includes some common files affected by worm).
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Re: All 250 files on Sam's hard drive are infected by either a virus or a [#permalink]

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New post 24 Apr 2017, 20:43
Is my method wrong?

V = 125

now we know that

w = 2.5 (v+w)
= 2.5 v + 2.5 w

1.5 w = 2.5 v

3w = 5v

we know that v=125 so w=75.
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Re: All 250 files on Sam's hard drive are infected by either a virus or a [#permalink]

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New post 08 Mar 2018, 11:44
Bunuel wrote:
All 250 files on Sam's hard drive are infected by either a virus or a worm or both. The number of files that are infected only by a worm is 2.5 times the number of files that are infected by both a virus and a worm. If 50% of the files were not infected by a virus, how many of Sam's files were NOT infected by a worm?

A. 50
B. 70
C. 75
D. 100
E. 125


Letting b = the number of files infected by both a virus and a worm, we can create the equation:

Total = worm only + virus only + both + neither

250 = 2.5b + [0.5(250) - b] + b + 0

250 = 2.5b + 125

125 = 2.5b

50 = b

The files that were not infected by a worm were those that were infected by a virus only, so there were 0.5(250) - 50 = 125 - 50 = 75 files infected by virus only.

Answer: C
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Re: All 250 files on Sam's hard drive are infected by either a virus or a   [#permalink] 08 Mar 2018, 11:44
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