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Bunuel
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All 250 files on Sam's hard drive are infected by either a virus or a 25 Jul 2022, 08:30
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C
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45% (medium)

Question Stats:

73% (02:49) correct 27% (02:34) wrong based on 135 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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C
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azamatboden
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All 250 files on Sam's hard drive are infected by either a virus or a 26 Jul 2022, 09:20
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Can someone provide a solution please?
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av1901
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All 250 files on Sam's hard drive are infected by either a virus or a 26 Jul 2022, 10:07
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azamatboden
Can someone provide a solution please?
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Sure!
This is a question based on 2 overlapping sets and the formula for the same goes as

Total = A + B - Both + Neither

Now in this formula, A refers to all of A alone plus (A and B both) and the same goes for B which refers to all of B alone plus (A and B both)
This account for the both part to be counted twice and that is why it is subtracted once in the formula so as to include it only once

But this is a slight variation on the formula as it mentions only infected with virus and only infected with worms so that means its mentioning only all of A and all of B (without both parts) so in order to include the combination of both we need to add it here so the formula for this question is

Total = only Virus + only Worm + both + neither
Neither = 0 since all files are infected
Total = 250
Only Worm = 50 percent = 125
Only Worm = 2.5 x Both
Both = 50
250 = 125 + Only Virus+ 50 + 0
Only Virus= 75

Answer - C

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All 250 files on Sam's hard drive are infected by either a virus or a 19 Oct 2023, 01:13
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azamatboden
Can someone provide a solution please?

Sure!
This is a question based on 2 overlapping sets and the formula for the same goes as

Total = A + B - Both + Neither

Now in this formula, A refers to all of A alone plus (A and B both) and the same goes for B which refers to all of B alone plus (A and B both)
This account for the both part to be counted twice and that is why it is subtracted once in the formula so as to include it only once

But this is a slight variation on the formula as it mentions only infected with virus and only infected with worms so that means its mentioning only all of A and all of B (without both parts) so in order to include the combination of both we need to add it here so the formula for this question is

Total = only Virus + only Worm + both + neither
Neither = 0 since all files are infected
Total = 250
Only Worm = 50 percent = 125
Only Worm = 2.5 x Both
Both = 50
250 = 125 + Only Virus+ 50 + 0
Only Virus= 75

Answer - C

Please hit kudos if you like the solution

Posted from my mobile device
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Why is "both infected" 50?
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LucienH
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All 250 files on Sam's hard drive are infected by either a virus or a 19 Oct 2023, 06:47
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thelady02
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azamatboden
Can someone provide a solution please?

Sure!
This is a question based on 2 overlapping sets and the formula for the same goes as

Total = A + B - Both + Neither

Now in this formula, A refers to all of A alone plus (A and B both) and the same goes for B which refers to all of B alone plus (A and B both)
This account for the both part to be counted twice and that is why it is subtracted once in the formula so as to include it only once

But this is a slight variation on the formula as it mentions only infected with virus and only infected with worms so that means its mentioning only all of A and all of B (without both parts) so in order to include the combination of both we need to add it here so the formula for this question is

Total = only Virus + only Worm + both + neither
Neither = 0 since all files are infected
Total = 250
Only Worm = 50 percent = 125
Only Worm = 2.5 x Both
Both = 50
250 = 125 + Only Virus+ 50 + 0
Only Virus= 75

Answer - C

Please hit kudos if you like the solution

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Why is "both infected" 50?
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Let W be the number infected by worms
V be the number infected by a Virus
X the number infected by Both

you know that W = 0.5*250 = 125
This implies that V = 125 as well
you know that W = 2.5X
X = 125/2.5 = 50

Thus, the number NOT infected by a worm is 125 - 50 = 75

Hope it helps
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