Six computers, each working at the same constant rate . . .

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

Six computers, each working at the same constant rate . . .

by VJesus12 » Sat Jan 06, 2018 4:02 am

Six computers, each working at the same constant rate, together can process a certain amount of data in 15 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 10 days?

(A) 3
(B) 5
(C) 6
(D) 9
(E) 12

The OA is the option A.

What is the equation I should use? How can I know how much data process each computer? Experts, can you help me? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Sat Jan 06, 2018 4:02 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sat Jan 06, 2018 4:39 am

VJesus12 wrote:Six computers, each working at the same constant rate, together can process a certain amount of data in 15 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 10 days?

(A) 3
(B) 5
(C) 6
(D) 9
(E) 12

Use the following formula:
(workers)(time) = (workers)(time).

Since 6 computers take 15 days, we must determine how many computers are required to complete the job in 10 days, we get:
(6 computers)(15 days) = (x computers)(10 days)
6*15 = 10x
90 = 10x
x = 9.

Since 9 computers are required, the number of computers that must be added to the 6 original computers = 3.

The correct answer is A.

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by [email protected] » Sat Jan 06, 2018 11:32 am

Hi VJesus12,

We're told that 6 computers, each working at the same constant rate, together can process a certain amount of data in 15 days. We're asked how many ADDITIONAL computers, each working at the same constant rate, would be needed to process the SAME amount of data in 10 days.

In these types of 'work' questions, it often helps to start by calculating the total amount of unit-work that is needed to complete a task. Here, we have 6 computers that each work for 15 days to complete a task. This means:

(6 computers)(15 days of work each) = 90 computer-days of work needed to complete a task.

We're asked how many computers ADDITIONAL computers would be needed to complete the task in 10 days...

(X computers)(10 days of work each) = 90 computer-days of work needed
X = 90/10 = 9 total computers needed to complete the task in 10 days.

Since we already have 6 computers, 3 ADDITIONAL computers are needed.

Final Answer: A

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Aug 11, 2019 6:34 pm

VJesus12 wrote:Six computers, each working at the same constant rate, together can process a certain amount of data in 15 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 10 days?

(A) 3
(B) 5
(C) 6
(D) 9
(E) 12

The OA is the option A.

If 6 computers can process the data in 15 days, one computer can process the same data in 15 x 6 = 90 days.

To have the number of days reduced by a factor of 1/9 (i.e from 90 days to 10 days), we need to increase the number of computers by a factor of 9 (i.e. from 1 computer to 9 computers). Since we already have 6 computers at hand, we need 9 - 6 = 3 additional computers.

Alternate Solution:

The total number of computer-days required for this task is 6 x 15 = 90 computer-days.

The task could be accomplished by 1 computer in 90 days (since 1 x 90 = 90 computer-days), or by 2 computers in 45 days (since 2 x 45 = 90 computer-days), etc.

In this problem, we want the 90 computer-hours to be accomplished in 10 days, so we need 90/10 = 9 computers, which is 3 more than what we currently have.

Answer: A

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