24 computer hackers can scan and infect 10 computers in 5 hours. If th

Question

24 computer hackers can scan and infect 10 computers in 5 hours. If this group of hackers wants to scan and infect 20 computers in 8 hours, how many new computers hackers do they need to recruit and join their team in order to accomplish this task, assuming all hackers work at the same rate?

A) 0
B) 6
C) 8
D) 10
E) 16

Source- Barron Gmat

I got a

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B, but apparently it is D

but isn't correct. Please kindly explain. Thank you

A) 0
B) 6
C) 8
D) 10
E) 16

Source- Barron Gmat

I got a  B, but apparently it is D  but isn't correct. Please kindly explain. Thank you

ksingh16 · Answer

Here the quantum of work is getting doubled so we have to equate man-hour accordingly.Therefore the equation would be:

24*5/10={(24+x)*8}/20.

Solving this will give x=6

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generis · Answer

I think you're right, and Barron is not.

Work = ( N umber of workers) x (individual  R ate) x ( T ime), or

W = (N)(R)(T)

So the individual rate of the original 24 hackers (N) who take 5 hours (T) to hack 10 computers (W) is

10/(5*24) =  \frac{10}{120}  or  R =  \frac{1}{12}

At that rate, to hack 20 computers in 8 hours, the number of hackers needed would be

(\frac{1}{12} )*(8)*(N)= 20

\frac{2}{3} N = 20

N = 30. There are already 24. The hackers need 6 more people.

I think the answer is B.

ydmuley · Answer

Great Question and my answer is similar to  ksingh16

24 * 5/10 = ((24+x)*8)/20

Simplifying this we get:
 
 x = 6

Hence B, is he answer.

ydmuley · Answer

ssr300  Request you to EDIT the OA, as it is not D, it is B

pushpitkc · Answer

Let the number of units of work done(to hack one system) is  120 units. 
Since 24 hackers, infect  10 computers, they do 1200 units of work . This work takes these hackers 5 hours.
So, in essence,  1 hacker does  1200 / (5*24) which is  10 units of work/hour

Now we have to infect 20 computers, making the units of work to do 2400 units.
It has been given that there are 24 hackers, and we are asked to find 
how many additional hackers are required to pull this work in 8 hours.

No of hackers = 2400/ (8*10) = 30
 Since they have 24 hackers, they will need to recruit 6 additional hackers to pull this job off(Option B)

utkarshthapak · Answer

I too agree with everyone here that OA should be B. No wonder that only a few answered it right.

Bunuel , could you shed some light on this question please?

Bunuel · Answer

_____________________
Edited the OA. Thank you.

MvArrow · Answer

I solved it in a different way... please tell me if my way of reasoning is not flawed...

24 Hackers works at a Rate of 10/5 --> R=2

X Hackers works at a Rate of 20/8 --> R=5/2

So I set up a proportion:

(2/1)/24 = (5/2)/X
1/12 = 5/2x

Cross multiplying we get X=30 and Number Of Additional Hackers would be 30-24 = 6 thus B

Abhishek009 · Answer

Use Shortcut formula -

\frac{M_1*T_1}{W_2} = \frac{M_2*T_2}{W_1}

So,  \frac{24*5}{20} = \frac{(24 + m)*8}{24}

Or,  6 = \frac{(24 + m)}{3}

Or,  18 = 24 + m

So,  m = 6

Thus, the answer will be (B)

MvArrow · Answer

Can you please explain me how it work or give me a link to the detailed explanation about how to use it? Thanks

Abhishek009 · Answer

Please go through the following link - https://gmatclub.com/forum/understandin ... 69681.html Hope the discussion here, helps..

ScottTargetTestPrep · Answer

We are given that the rate of 24 computer hackers is 10/5 = 2.

We need the new rate to be 20/8 = 5/2. We can let x = the number of computer hackers needed to achieve that rate and create the following proportion:

24/2 = x/(5/2)

12 = x/(5/2)

12 = 2x/5

60 = 2x

x = 30

So, the number of new hackers needed is 30 - 24 = 6.

Answer: B

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