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

Question

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

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

davedekoos · Accepted Answer

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}

Answer: C

Kingsman · Answer

My answer is C.
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.

ali_aliyev · Answer

Bunuel  please review the question, I think "   must have been mistakenly written. Because when I ignored 3, I got answer C) 4/19. Can you please clarify the issue? Thanks.

Bunuel · Answer

_______________
Edited. Thank you.

EMPOWERgmatRichC · Answer

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).

GMAT assassins aren't born, they're made,
Rich

gracie · Answer

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

rohit8865 · Answer

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

energetics · Answer

1) Plug in easy numbers:
If #full time workers = 10, then #trainees 10*(2/5) = 4
If full time envelopes = 6, then trainee envelopes = 6*(2/3) = 4

2) Set up part/whole relationship: #trainees* t envelopes / #trainees * t envelopes + #full time *full time envelopes
16/(16+60) = 16/76 = 4/19

jfranciscocuencag · Answer

Any advice to know how plug in the correct numbers?

Kind regards!

jfranciscocuencag · Answer

Hello  gracie

What am i doing wrong here?

150 (Total workers)

T = 60
E = 90

One hour per full time employee so:

40 hours of T and 90 hours for E.

40/130 = 4/13

I am confussed =/

Kind regards!

EMPOWERgmatRichC · Answer

Hi jfranciscocuencag,

This prompt is perfect for TESTing VALUES, but you have to carefully read the prompt and choose values based on the given information. We're told that "there are 2/5 as many trainees as there are full-time workers." Thus, the number of trainees is 2/5 of the other group; NOT 2/5 of the total of all employees.

For example: If we had 5 full-time workers, then we would have (2/5)(5) = 2 trainees.

Next, we're told that a trainee can stuff 2/3 as many envelopes in one day as a full-time worker.

For example: If a full-time worker can stuff 3 envelopes in one day, then a trainee can stuff (2/3)(3) = 2 envelopes in a day.

Using the values in these examples, can you finish off this question?

GMAT assassins aren't born, they're made,
Rich

ScottTargetTestPrep · Answer

If we let the number of full time workers = 10, then there are 2/5 x 10 = 4 trainees. If we let the number of envelopes each full time worker can stuff a day = 3 envelopes, then each trainee can stuff 2 envelopes per day.

Thus, in one day, the trainees stuffed (4 x 2)/(4 x 2 + 10 x 3) = 8/38 = 4/19 of the envelopes.

Answer: C

satya2029 · Answer

Full time worker F , Trainee T
 F*Rf*t=Wf , where F total. full time workers, Rf rate of each worker, t is working time
 2/5F*2/3Rf*t=Wt 
So  Wt/(Wf+Wt) 
=  /  
=(4/15)/19/15
=4/19
C:)

WheatyPie · Answer

Bunuel, I'd recommend putting 4/15 in the answer choices as it's an easy mistake to make (trainees envelopes / full-time envelopes)

bumpbot · Answer

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