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Brian has to clean 675 beer glasses. If he cleans 16% of the glasses i

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Brian has to clean 675 beer glasses. If he cleans 16% of the glasses i  [#permalink]

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New post 15 May 2015, 03:11
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Question Stats:

65% (02:51) correct 35% (02:56) wrong based on 223 sessions

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Brian has to clean 675 beer glasses. If he cleans 16% of the glasses in the first 88 minutes, then which of the following is closest to the number of hours Brian has to work at double his initial speed, to finish cleaning the rest of the glasses?

A. 4.1
B. 7.8
C. 8
D. 8.2
E. 3.9

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Re: Brian has to clean 675 beer glasses. If he cleans 16% of the glasses i  [#permalink]

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New post 15 May 2015, 05:15
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Hi reto,

Presenting the detailed solution below:

Given
We are given the initial rate at which Brian works and are asked to find the time taken by Brian to complete the rest of the work at double his initial rate.

Approach
We know that Work = Rate * Time. Since we are given the initial amount of work done we can find out the balance amount of work to be done(i.e. cleaning the glasses). Also we know the initial rate of Brian which can be used to calculate his final rate to do the work. Since we know the amount of work to be done and the rate at which Brian will be working, we can find out the time taken by him.

Working Out
Initial no. of glasses cleaned by Brian = 16% of 675 = \(\frac{16}{100} * 675\)

Time taken by Brian for cleaning glasses = 88 minutes

Brian's rate of cleaning glasses \(=\frac{16*675}{100*88}\) glasses/minute


His rate for cleaning the remaining glasses = 2 * Initial Rate = \(2 * \frac{16*675}{100*88}\)

Number of remaining glasses to be cleaned = (100-16)% of 675 glasses = \(\frac{84}{100} * 675\)

Time taken by Brian to clean the remaining glasses \(= \frac{84}{100} * 675 * \frac{100* 88}{16* 675 * 2}\) = 231 minutes = ~ 3.9 hours

Hope its clear :)

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Re: Brian has to clean 675 beer glasses. If he cleans 16% of the glasses i  [#permalink]

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New post 15 May 2015, 08:09
reto wrote:
Brian has to clean 675 beer glasses. If he cleans 16% of the glasses in the first 88 minutes, then which of the following is closest to the number of hours Brian has to work at double his initial speed, to finish cleaning the rest of the glasses?

A. 4.1
B. 7.8
C. 8
D. 8.2
E. 3.9



is this really a sub 600? I got it right but the calculations took me just over 3 mins. The process is very simple, but the numbers are not the best.
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Re: Brian has to clean 675 beer glasses. If he cleans 16% of the glasses i  [#permalink]

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New post 15 May 2015, 08:47
Wofford09 wrote:
reto wrote:
Brian has to clean 675 beer glasses. If he cleans 16% of the glasses in the first 88 minutes, then which of the following is closest to the number of hours Brian has to work at double his initial speed, to finish cleaning the rest of the glasses?

A. 4.1
B. 7.8
C. 8
D. 8.2
E. 3.9



is this really a sub 600? I got it right but the calculations took me just over 3 mins. The process is very simple, but the numbers are not the best.


Im actually not sure what level it is because it was not stated. I would try like that:

Brian's rate of cleaning glasses is \(=\frac{0.16*675}{88}\) glasses/minute
For the remaining glasses he has the double rate: \(2 * \frac{0.16*675}{88}\)

Now all you have to do is divide the remaining classes through the new double rate (don't calculate the exact number but use 0.84*675 for the remaining glasses) like that:

\(\frac{0.84*675*88}{2*0.16*675}\)

Then cancel out as much terms as possible (675 cancels, 88 cancels with the 2 in the denominator and 0.84 divided with 0.16 is approx 5 times). This leaves you with a nice approximation of 5*44 minutes = 220min = 3.6 hours. I think that should be enough.

If you want to be more precise look at the solution from EgmatQuantExpert and do it with the whole percent numbers.

Does this help?
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Re: Brian has to clean 675 beer glasses. If he cleans 16% of the glasses i  [#permalink]

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New post 15 May 2015, 11:17
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Wofford09 wrote:
reto wrote:
Brian has to clean 675 beer glasses. If he cleans 16% of the glasses in the first 88 minutes, then which of the following is closest to the number of hours Brian has to work at double his initial speed, to finish cleaning the rest of the glasses?

A. 4.1
B. 7.8
C. 8
D. 8.2
E. 3.9



is this really a sub 600? I got it right but the calculations took me just over 3 mins. The process is very simple, but the numbers are not the best.


Hi Wofford09,

You do not need to do the calculations at every step. Such questions also tests how well you interpret numbers. If you avoid calculations till the last step you would get the fraction as \(\frac{84}{100} * 675 * \frac{100* 88}{16* 675 * 2}\).

The larger terms would cancel out to give you a straightforward fraction \(\frac{84*88}{16*2} = 21 * 11 = 231\) minutes.

The numbers are given in a manner so that it cancels out at the end and the calculation becomes pretty straightforward.

Hope this helps :)

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Harsh
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Re: Brian has to clean 675 beer glasses. If he cleans 16% of the glasses i  [#permalink]

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New post 15 May 2015, 15:29
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Hi reto,

This question can be solved with a bit of estimation and some basic calculations.

To start, the fact that there are 675 beer glasses is actually irrelevant.

We know that Brian cleaned 16% of the glasses in 88 minutes. That's about 1/6 of the glasses in about 1.5 hours.

To clean the remaining 5/6 of the glasses at this same rate would take about 5(1.5) = 7.5 hours....

HOWEVER, we're told that Brian will work at DOUBLE his initial rate, so we have to divide that time in HALF:

7.5/2 = 3.75 hours

Now, given that 16% is NOT exactly 1/6 and that 88 minutes is LESS than 1.5 hours, our estimate is pretty close....

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Re: Brian has to clean 675 beer glasses. If he cleans 16% of the glasses i  [#permalink]

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New post 28 May 2016, 04:37
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There's a simple way to go about it. First, as the question is all about Percentages, forget about the number of glasses. We will use percentages and the good old unitary method to do this.

Lets start :)

Point 1

16% in 88 mins at normal speed.
So, at double the speed...? it will take half the time to do the same work

Thus, at double speed --> 16% in 44 mins.

Point 2

Work already done --> 16%
Work left --> 100-16 --> 84% (and this has to be done at double the speed)

Applying unitary method

\(16%\) ---------- \(44 mins\)

\(1%\) ------------ \(\frac{44}{16}\)

\(84%\) ---------- \(\frac{44}{16} * 84\)

Converting the above result into hours by dividing by 60 will give you the answer as 3.85...which is closest to 3.9 and Voila :)


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Re: Brian has to clean 675 beer glasses. If he cleans 16% of the glasses i  [#permalink]

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New post 24 Jul 2017, 08:32
reto wrote:
Brian has to clean 675 beer glasses. If he cleans 16% of the glasses in the first 88 minutes, then which of the following is closest to the number of hours Brian has to work at double his initial speed, to finish cleaning the rest of the glasses?

A. 4.1
B. 7.8
C. 8
D. 8.2
E. 3.9


In 88 mins Brian cleans \(108\) beer glasses...
In 1 min Brian cleans \(\frac{108}{88}\) beer glasses...

Twice initial efficiency is \(\frac{108}{88}\) \(*2\) = \(\frac{108}{44}\) glasses...

Glasses remaining is \(675 - 108 = 567\)

Time required to clean those is \(\frac{567*44}{108*60}\) = \(3.85\) Hours

Thus, the answer must be (E) 3.9 Hours...
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Re: Brian has to clean 675 beer glasses. If he cleans 16% of the glasses i  [#permalink]

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New post 26 Jul 2017, 16:39
reto wrote:
Brian has to clean 675 beer glasses. If he cleans 16% of the glasses in the first 88 minutes, then which of the following is closest to the number of hours Brian has to work at double his initial speed, to finish cleaning the rest of the glasses?

A. 4.1
B. 7.8
C. 8
D. 8.2
E. 3.9


We are given that Brian has to clean 675 beer glasses. If Brian cleans 16% (or 0.16 x 675 = 108) of them in 88 minutes, his rate in minutes is 108/88 = 27/22. If his speed is doubled, his new rate is 54/22 = 27/11. Since he has 567 glasses left to clean, the time in minutes is:

567/(27/11) = (567 x 11)/27 = 21 x 11 = 231 minutes or 231/60 = 3.85 hours.

Answer: E
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Brian has to clean 675 beer glasses. If he cleans 16% of the glasses i  [#permalink]

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New post 30 Jul 2017, 09:48
My 2 cents -

NOTE - 21/60 ~ 1/3 because we can approximate it as 20/60 = 1/3.
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Re: Brian has to clean 675 beer glasses. If he cleans 16% of the glasses i  [#permalink]

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Re: Brian has to clean 675 beer glasses. If he cleans 16% of the glasses i   [#permalink] 24 Sep 2018, 10:07
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