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# At a local office, each trainee can stuff 2/3 as many envelopes per

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Math Expert
Joined: 02 Sep 2009
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At a local office, each trainee can stuff 2/3 as many envelopes per  [#permalink]

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03 Jan 2016, 12:58
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15
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Difficulty:

45% (medium)

Question Stats:

73% (02:08) correct 27% (03:16) wrong based on 224 sessions

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At a local office, each trainee can stuff 2/3 as many envelopes per day as a full time worker. If there are $$\frac{2}{5}$$ as many trainees as there are full time workers, then what fraction of all the envelopes stuffed in a day did the trainees stuff?

A. 2/19
B. 2/17
C. 4/19
D. 4/17
E. 14/15

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Posts: 1
Re: At a local office, each trainee can stuff 2/3 as many envelopes per  [#permalink]

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04 Jan 2016, 05:29
1
Bunuel please review the question, I think "[3][2/5] must have been mistakenly written. Because when I ignored 3, I got answer C) 4/19. Can you please clarify the issue? Thanks.
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Re: At a local office, each trainee can stuff 2/3 as many envelopes per  [#permalink]

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04 Jan 2016, 06:09
ali_aliyev wrote:
Bunuel please review the question, I think "[3][2/5] must have been mistakenly written. Because when I ignored 3, I got answer C) 4/19. Can you please clarify the issue? Thanks.

_______________
Edited. Thank you.
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Re: At a local office, each trainee can stuff 2/3 as many envelopes per  [#permalink]

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04 Jan 2016, 14:13
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3
To know the fraction of all envelopes stuffed by trainees, we need to know how many envelopes were stuffed by trainees and how many were stuffed in total.

let $$x=$$number of envelopes a full-time worker can stuff in a day
Then the number of envelopes a trainee can stuff in a day is $$\frac{2}{3}x$$

(Note that we don't really need the variable, but for visualization purposes, it can sometimes make it easier to understand and follow what is going on.)

It is given that the number of trainees to full-time workers is 2:5, and since we are only concerned with the ratio envelopes stuffed by trainees, then we can assume that there are 5 full time workers and 2 trainees.

Total number of envelopes stuffed = (all envelopes stuffed by full-time workers) + (all envelopes stuffed by trainees)
$$T=5x + 2*\frac{2}{3}x$$

What we're asked to find is the fraction of envelopes stuffed by trainees =
(all envelopes stuffed by trainees)/(Total amount of envelopes stuffed) =

$$=\frac{(2*\frac{2}{3}x)}{(5x+2*\frac{2}{3}x)}$$

$$= \frac{\frac{4}{3}x}{\frac{19}{3}x}$$

$$=\frac{4}{19}$$

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Re: At a local office, each trainee can stuff 2/3 as many envelopes per  [#permalink]

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06 Jan 2016, 22:18
Hi All,

This question is essentially a 'lift' of an OG question.

In the GMAT2016: PS Question 175 (page 177).
In the GMAT2015/OG13: PS Question 151 (page 173).

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At a local office, each trainee can stuff 2/3 as many envelopes per  [#permalink]

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07 Jan 2016, 03:11
2
1
Simple solution is considered Full time and trainee employees separately. We have a table:
We plugged in the number of full time employees is 5.

No of people | Work rate | Time(1 day) | The amount of work
Trainee 2 | 2/3 | 1 | 4/3
Full time 5 | 1 | 1 | 5
|
The fraction amount of work done by trainee to total: 4/3 : (4/3+5) = 4/19.
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Re: At a local office, each trainee can stuff 2/3 as many envelopes per  [#permalink]

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07 Jan 2016, 11:31
let 5 and 2=number of full time workers and trainees respectively
let 3 and 2= respective daily rates of each
(5)(3)=15 total daily full time worker envelopes stuffed
(2)(2)=4 total daily trainee envelopes stuffed
4/(4+15)=4/19=fraction of total daily envelopes stuffed by trainees
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At a local office, each trainee can stuff 2/3 as many envelopes per  [#permalink]

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05 Mar 2017, 07:41
Bunuel wrote:
At a local office, each trainee can stuff 2/3 as many envelopes per day as a full time worker. If there are $$\frac{2}{5}$$ as many trainees as there are full time workers, then what fraction of all the envelopes stuffed in a day did the trainees stuff?

A. 2/19
B. 2/17
C. 4/19
D. 4/17
E. 14/15

Let 1 full time worker do x envelops
then 1 trainee = 2x/3

suppose there are 50 full time worker ...then they do 50x envelopes
then 20 trainee (2*50/5= 20) will do 20*2x/3 = 40x/3 envelops
together((envelops done by 20 trainees + envelops done by 50 full time workes)) they do 50x+ 40x/3 = 190x/3

required fraction = envelops done by 20 trainees / (envelops done by 20 trainees + envelops done by 50 full time workes)
40x/3 / 190x/3 == 4/19

Ans C
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Re: At a local office, each trainee can stuff 2/3 as many envelopes per  [#permalink]

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27 Jul 2018, 10:32
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