I29-166

Question

Umbrella Corporation monitors a network of 6,000 computers. At the start of the virus outbreak, 4 of these computers get infected. The infection weakens with each round of spreading:
 
• In the first iteration, each of the 4 initially infected machines infects 8 others.
 
• In the second iteration, each machine infected in the first iteration infects 4 others.
 
• In the third iteration, each machine infected in the second iteration infects 2 others.
 
• In the fourth iteration, each machine infected in the third iteration infects 1 other.
 
Select for  2 iterations  the number of computers that remain uninfected after two iterations are completed, and select for  4 iterations  the number of computers that remain uninfected after four iterations are completed. Make only two selections, one in each column.

Bunuel · Answer

Official Solution:

The network contains 6,000 computers in total, and the outbreak begins with 4 of them infected.
 
 Iteration 1 : Each of the 4 infects 8 others, producing 32 new infections. Adding these to the initial 4 gives 36 infected computers.
 
 Iteration 2 : The 32 from the first round each infect 4 others, producing 128 new infections. Adding this to the 36 infected so far gives a cumulative total of 164 after two iterations. The number of unaffected computers is 6,000 − 164 =  5,836 .
 
 Iteration 3 : The 128 from the second round each infect 2 others, producing 256 new infections. Cumulative total = 164 + 256 = 420.
 
 Iteration 4 : The 256 from the third round each infect 1 other, producing 256 new infections. Cumulative total = 420 + 256 = 676 after four iterations. The number of unaffected computers is 6,000 − 676 =  5,324 .

Correct answer:

2 iterations  "5,836"

4 iterations  "5,324"

RightChip · Answer

I like the solution - it’s helpful.

PastCreek · Answer

I like the solution - it’s helpful.

Username1512 · Answer

I did not quite understand the solution. I'm a little confused here. When we multiply the initial 4 with 8, aren't they aalready included in the 32 and so on...? Why o we need to add them again making them 36? 
And in such questions how do we identify when it needs to be successively added?

Bunuel · Answer

4 * 8 = 32 means 32 new computers infected by the original 4.

The original 4 are not included in those 32.

So after iteration 1, total infected = original infected + newly infected = 4 + 32 = 36.

shailjamendi1 · Answer

I like the solution - it’s helpful.

SportEarth · Answer

I did not quite understand the solution. In the second iteration, why are we considering infected devices as 32 and not 36. Aren't a total of 36 computers infected before second iteration.

Bunuel · Answer

Check the question:

• In the first iteration, each of the 4 initially infected machines infects 8 others.

• In the second iteration,  each machine infected in the first iteration  infects 4 others.

• In the third iteration,  each machine infected in the second iteration  infects 2 others.

• In the fourth iteration,  each machine infected in the third iteration  infects 1 other.

There are  36 infected computers in total , but only the  32 computers infected during the first iteration  spread the virus in the second iteration.

The original 4 computers spread the virus only in the first iteration, so they are not counted again.

UltraBeam · Answer

I like the solution - it’s helpful.

Memer · Answer

I like the solution - it’s helpful.

Janejane02 · Answer

I like the solution - it’s helpful.

ADikshita · Answer

I don’t quite agree with the solution. What happened to initial 4 computers which infected 32. Total infected are now 32 + 4 = 36. 
In Iteration 2 - 36 will infect 4 each, total 36*4 = 144
total after this is 144+ 36 = 180. 
Similarly we will go for the other rounds.

Bunuel · Answer

Please review the question again and check this post: https://gmatclub.com/forum/i29-450217.html#p3811561 Hope this helps.

I29-166

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My Rewards

2 iterations	4 iterations
		5,260
		5,324
		5,452
		5,488
		5,836
		5,872

2 iterations	4 iterations
		5,260
		5,324
		5,452
		5,488
		5,836
		5,872