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A certain computer virus replicates itself across the Internet such th

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Manager
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Joined: 26 Dec 2018
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A certain computer virus replicates itself across the Internet such th  [#permalink]

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New post 15 Jan 2019, 03:37
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A certain computer virus replicates itself across the Internet such that the number of infected computers quadruples every 5 minutes. Two-thirds of a certain company's 3,000 computers have anti-virus software that protects against this virus while the rest are vulnerable to infection. If one computer on that company's network has become infected, approximately how long will it take before all unprotected computers on the network are infected?

A) 20 minutes

B) 25 minutes

C) 30 minutes

D) 35 minutes

E) 40 minutes

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Joined: 05 Jan 2018
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A certain computer virus replicates itself across the Internet such th  [#permalink]

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New post 15 Jan 2019, 08:01
1
Speed of viral infection = 4^n per 5 mins

1/3rd of 3000 computers will get infected = 1000 computers
If we start counting from 0 mins when the first computer gets infected
Time line:
Minutes----------0------------5------------5*2-----------5*3............................. 5*n
Computers--------1----------- 4------------4^2----------4^3.............................1000(~4^5)

=> n=5
and so total time taken to infect all computers 25 minutes.
Answer B
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A certain computer virus replicates itself across the Internet such th  [#permalink]

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New post 15 Jan 2019, 08:24
UB001 wrote:
A certain computer virus replicates itself across the Internet such that the number of infected computers quadruples every 5 minutes. Two-thirds of a certain company's 3,000 computers have anti-virus software that protects against this virus while the rest are vulnerable to infection. If one computer on that company's network has become infected, approximately how long will it take before all unprotected computers on the network are infected?

A) 20 minutes

B) 25 minutes

C) 30 minutes

D) 35 minutes

E) 40 minutes


Here is my approach, Let me know, if this can be optimized further

1/3 doesn't have antivirus software= 1000

the rate becomes 4 times in 5 minutes, initially it was 1
5---10---15---20---25
4---16---64---256--1024

Answer B
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Re: A certain computer virus replicates itself across the Internet such th  [#permalink]

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New post 15 Jan 2019, 08:43
UB001 wrote:
A certain computer virus replicates itself across the Internet such that the number of infected computers quadruples every 5 minutes. Two-thirds of a certain company's 3,000 computers have anti-virus software that protects against this virus while the rest are vulnerable to infection. If one computer on that company's network has become infected, approximately how long will it take before all unprotected computers on the network are infected?

A) 20 minutes

B) 25 minutes

C) 30 minutes

D) 35 minutes

E) 40 minutes


Unprotected computers in the company is \(\frac{1}{3}*3000 = 1000\)

Since the virus Quadruples every 5 minutes we have -

\(4^1 = 4\)

\(4^2 = 16\)

\(4^3 = 64\)

\(4^4 = 256\)

\(4^5 = 1024\)

Thus, we have within 5*5 = 25 minutes all the unprotected computers of the company will get infected, Answer must be (B) 25
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Re: A certain computer virus replicates itself across the Internet such th   [#permalink] 15 Jan 2019, 08:43
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