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

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Math Expert
Joined: 02 Sep 2009
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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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09 Oct 2016, 23:42
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Difficulty:

55% (hard)

Question Stats:

68% (02:31) correct 32% (02:58) wrong based on 215 sessions

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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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10 Oct 2016, 01:17
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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10 Oct 2016, 04:26
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2
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
$$Or, V = 75$$

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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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02 Nov 2016, 07:52
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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29 Dec 2016, 02:30
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
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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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23 Apr 2017, 19:27
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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24 Apr 2017, 19:43
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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08 Mar 2018, 10:44
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.

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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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01 Jul 2020, 22:31
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

250=v( only virus)+ w ( only worm)+B..............(1)
"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=2.5B.................(2)
"If 50% of the files were not infected by a virus"
This means infected by only (W) i.e 50% of 250=125=======>125=2.5B
B=50 & So, only (W) =125
Putting the values in eq 1
250=V+125+50
V=75.
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Re: All 250 files on Sam's hard drive are infected by either a virus or a   [#permalink] 01 Jul 2020, 22:31