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jain2016: Master | Next Rank: 500 Posts; Posts: 313; Joined: Tue Oct 13, 2015 7:01 am; Thanked: 2 times

by jain2016 » Wed Mar 23, 2016 11:01 am

If it takes 6 identical printing presses exactly 4 hours to print 5000 newspaper, how long would it take 3 of these presses to print 3000 newspapers ?

A) 3 hours, 20 minutes

B) 4 hours, 20 minutes

c) 4 hours, 48 minutes

D) 5 hours, 48 minutes

E) 6 hours, 50 minutes

OAC

Hi Experts ,

Please check and correct me.

We have that 6 presses printed 5000 newspaper in 4 hours.

So 1 printing press in 1 hours = 5000/24 = 625/3

So 3000 newspaper with 1 press in 1 hour = 3000/625/3, it becomes 3000*3/625

Now 3000 newspaper with 3 presses will be = 3000*3*3/625 right?

If I solve this, then I get the time, but I didn't get the answer.

Please correct if I am wrong.

Many thanks in advance.

SJ

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Source: Beat The GMAT — Problem Solving | Wed Mar 23, 2016 11:01 am

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

by GMATGuruNY » Wed Mar 23, 2016 11:27 am

jain2016 wrote:If it takes 6 identical printing presses exactly 4 hours to print 5000 newspaper, how long would it take 3 of these presses to print 3000 newspapers ?

A) 3 hours, 20 minutes

B) 4 hours, 20 minutes

c) 4 hours, 48 minutes

D) 5 hours, 48 minutes

E) 6 hours, 50 minutes

Use the following formula:
(workers)(time)/output = (workers)(time)/output

Since 6 presses require 4 hours to yield an output of 5000 newspapers, and we must determine the number of hours required for 3 presses to yield an output of 3000 newspapers, we get:

(6*4)/5000 = (3x)/3000
24/5 = 3x/3
24/5 = x
x = 24/5 = 4 + 4/5 hours = 4 hours, 48 minutes.

The correct answer is C.

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by [email protected] » Wed Mar 23, 2016 8:26 pm

Hi jain2016,

Since we have 6 machines working 4 hours each, we have 24 machine-hours of work being done. Those 24 hours of machine-work will produce 5,000 newspapers, so we can calculate what 1 hour of machine-work will produce:

5,000/24 = 2,500/12 = 1250/6 = 625/3 newspapers per machine-hour of work

With 3 machines, we have (625/3)(3) = 625 newspapers produced per hour. We're asked how many hours is takes to produce 3,000 newspapers under these conditions...

3,000/625 = 600/125 = 120/25 = 24/5 hours = 4 4/5 hours = 4 hours 48 minutes

Final Answer: C

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jain2016: Master | Next Rank: 500 Posts; Posts: 313; Joined: Tue Oct 13, 2015 7:01 am; Thanked: 2 times

by jain2016 » Thu Mar 24, 2016 6:18 am

Hi GMATGuruNY & Rich ,

Thank you so much for your reply, but can you please do let me know whats wrong with my method?

Many thanks in advance.

SJ

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

by GMATGuruNY » Thu Mar 24, 2016 6:46 am

jain2016 wrote:So 3000 newspaper with 1 press in 1 hour = 3000/625/3, it becomes 3000*3/625

Here, you correctly determine that the time for 1 press to produce 3000 newspapers = (3000*3)/625 hours.

Now 3000 newspaper with 3 presses will be = 3000*3*3/625 right?

This line of reasoning is incorrect.
Rate and time are RECIPROCALS.
Since 3 presses work at 3 TIMES THE RATE of 1 press, the time for 3 presses will be 1/3 THE TIME for 1 press.
Since the time for 1 press = (3000*3)/625 hours, the time for 3 presses = (1/3) * (3000*3)/625 = 3000/25 = 600/125 = 120/25 = 4 + 4/5 hours = 4 hours, 48 minutes.

The following approach might be easier:

Since in 1 hour each press produces 625/3 newspapers, the number of newspapers produced by 3 presses in 1 hour = (3)(625/3) = 625.
Since the rate for 3 presses = 625 newspapers per hour, the time for 3 presses to produce 3000 newspapers = w/r = 3000/625 = 600/125 = 120/25 = 4 + 4/5 hours = 4 hours, 48 minutes.

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by DavidG@VeritasPrep » Thu Mar 24, 2016 9:16 am

jain2016 wrote:If it takes 6 identical printing presses exactly 4 hours to print 5000 newspaper, how long would it take 3 of these presses to print 3000 newspapers ?

A) 3 hours, 20 minutes

B) 4 hours, 20 minutes

c) 4 hours, 48 minutes

D) 5 hours, 48 minutes

E) 6 hours, 50 minutes

OAC

SJ

You could also think about it like this: if it takes 6 presses 4 hours to do 5000 papers, it should take 3 presses 8 hours to do 5000 papers. (Half as many presses should take twice as much time.) If it takes 3 presses 8 hours to do 5000 papers, it should take them 8 *(.6) hours to do 3000 papers. (3000 is 60% or .6 of 5000.) 8 * .6 = 4.8 hours. Answer is C

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