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Intern  Joined: 18 Sep 2010
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A software programmer does 20% of the work in 80% of the  [#permalink]

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Question Stats: 70% (03:02) correct 30% (02:58) wrong based on 494 sessions

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A software programmer does 20% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X?

A. 13x /15
B. 15x/15
C. 7x/15
D. 2x/30
E. 13x/30

Originally posted by vivatran on 06 Mar 2011, 05:42.
Last edited by vivatran on 05 Nov 2012, 22:27, edited 3 times in total.
Veritas Prep GMAT Instructor V
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Re: Work Problems  [#permalink]

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6
shuwa wrote:
A software programmer does 20% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X?

A) 13x /15

B) 15x/15

C) 7x/15

D) 2x/30

E) 13x/30

Another thing you might want to note here is that he does 80% of the work in the last 20% of time i.e. in last 6 days. So the work he does in last 14 days is more than 4X/5 but less than X. Only option (A) lies in this range.
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Re: Work Problems  [#permalink]

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10
30 days- X lines

80% of 30
24 days; 0.2X lines

Remaining 6 days:
0.8X lines

Need to find out for last 14 days;
We know the number of lines for last 6 days: 0.8X

How about 8 days before that;
24 days- 0.2X
1 day - 0.2X/24 lines
8 days - (0.2X/24)*8 lines = (1/15)X lines

Total number of lines in last 14 days

(1/15)x + 0.8X = (1/15)x + (8/10)X = (52/60)X = (13/15)X lines of codes
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Re: Work Problems  [#permalink]

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1
shuwa wrote:
A software programmer does 20% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X?

It's better to plug the numbers for this question let x=30 lines;

20% of the work in 80% of the time --> 0.2*30 lines=6 lines in the first 0.8*30 days=24 days and the remaining 24 lines in last 6 days;

Last 14 days = last 6 days (stage 2) + previous 8 days (part of stage 1): 24 lines in last 6 days + 1/3*6=2 lines in previous 8 days (as 8 is 1/3 of 24 days in stage 1) = 26 lines in the last 14 days, which is 26/30=13/15 part of the whole job.

P.S. Please provide answer choices for PS problems.
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Re: Work Problems  [#permalink]

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work - time

1 t
20/100 80t/100
80/100 20t/100

30 days - x lines

20x/100 will be finished in (80/100)*30 days ( i.e 24 days)

80x/100 in (20/100)*30 days (i.e 6 days)

work done in last two weeks = last 6 days work + last 8 days work

= 80x/100 + (20x/100)(8/24)
= 13x/15

(one flaw i see in the question is that it does not say the programmer works initial 20% of work in 80% time. so if you take it as initial 80% of work in 20% time, answer would be different)
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Re: Work Problems  [#permalink]

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Spidy001 wrote:

(one flaw i see in the question is that it does not say the programmer works initial 20% of work in 80% time. so if you take it as initial 80% of work in 20% time, answer would be different)

I did notice the same thing and therefore, read the question stem carefully. Notice that it says 'does 20% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time.'
Important is the use of the word 'remaining' which implies that he does 20% of the work in the first 80% of time and 80% in the leftover 20% time. Therefore, the intent of the question is quite clear.
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Re: Work Problems  [#permalink]

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Hi,
I'm trying to plug in for Question # 138 in OG 12. Could anyone point out where i'm going wrong in my reasoning?
No. of Boxes loaded by Night workers = 3/4 of Day workers
No. of Night workers = 4/5 of Day workers.

Let the number of Day workers = 100 and they load a total of 100 boxes.
No. of boxes loaded by Night workers = 3/4 x 100 = 75
No. of Night workers = 4/5 x 100 = 80

total no. of boxes loaded by both workers = 175
total no. of boxes loaded by day workers = 100

fraction of boxes loaded by day workers out of the total = 100/175 = 4/7
The closest answer is 4/5 which is D.

But the correct answer is 5/8 which is E.
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Re: Work Problems  [#permalink]

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gmatyro wrote:
Hi,
I'm trying to plug in for Question # 138 in OG 12. Could anyone point out where i'm going wrong in my reasoning?
No. of Boxes loaded by Night workers = 3/4 of Day workers
No. of Night workers = 4/5 of Day workers.

Let the number of Day workers = 100 and they load a total of 100 boxes.
No. of boxes loaded by Night workers = 3/4 x 100 = 75
No. of Night workers = 4/5 x 100 = 80

total no. of boxes loaded by both workers = 175
total no. of boxes loaded by day workers = 100

fraction of boxes loaded by day workers out of the total = 100/175 = 4/7
The closest answer is 4/5 which is D.

But the correct answer is 5/8 which is E.

You need to make a new thread for a new question, put down the question and your method.
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Re: Work Problems  [#permalink]

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VeritasPrepKarishma wrote:
gmatyro wrote:
Hi,
I'm trying to plug in for Question # 138 in OG 12. Could anyone point out where i'm going wrong in my reasoning?
No. of Boxes loaded by Night workers = 3/4 of Day workers
No. of Night workers = 4/5 of Day workers.

Let the number of Day workers = 100 and they load a total of 100 boxes.
No. of boxes loaded by Night workers = 3/4 x 100 = 75
No. of Night workers = 4/5 x 100 = 80

total no. of boxes loaded by both workers = 175
total no. of boxes loaded by day workers = 100

fraction of boxes loaded by day workers out of the total = 100/175 = 4/7
The closest answer is 4/5 which is D.

But the correct answer is 5/8 which is E.

You need to make a new thread for a new question, put down the question and your method.

Hi,
There was a thread already and have posted the question on that thread. [url]help-me-with-the-answer-rates-ratio-question-102404.html[/url]
I went thru the answers posted which i understand but i can't see why my reasoning is wrong. Appreciate your response
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Re: Work Problems  [#permalink]

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gmatyro wrote:

Hi,
There was a thread already and have posted the question on that thread. [url]help-me-with-the-answer-rates-ratio-question-102404.html[/url]
I went thru the answers posted which i understand but i can't see why my reasoning is wrong. Appreciate your response

Have posted the issue in your solution in that thread itself. If you want me to look at a particular question or your solution, just put it down in the corresponding thread and send me a pm. I will look into it.
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Re: Work Problems  [#permalink]

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Hi,

Is there a way to solve the problem by solving for the portion of X done in the first 14 days and subtract the result from X? I keep getting the wrong answer with the following:

X/5 = R*4T/5
R = X/(4T)
14 days later.. or T/2
X/(4T)*T/2 = X/8
So for the remainder period...
X-X/8 = 7X/8

would appreciate any help that would pinpoint where this fails.
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Re: Work Problems  [#permalink]

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syh244 wrote:
Hi,

Is there a way to solve the problem by solving for the portion of X done in the first 14 days and subtract the result from X? I keep getting the wrong answer with the following:

X/5 = R*4T/5
R = X/(4T)
14 days later.. or T/2
X/(4T)*T/2 = X/8
So for the remainder period...
X-X/8 = 7X/8

would appreciate any help that would pinpoint where this fails.

Sure you can do it that way too.

The error is that the month consists of 30 days (given) so you need to find the work done in 16 days (so that 2 weeks i.e. 14 days are leftover) and subtract that from X.

(X/4T) * 16T/30 = 2X/15

X - 2X/15 = 13X/15
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Re: A software programmer does 20% of the work in 80% of the  [#permalink]

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taking into account the assumptions about 20% of work during the 80% of time and vice versa we get

(1)
30 days*80%=24days
X work *20%=x/5
(2)
30*20%=6 days
X*80%=4x/5

we need to find out the amount of work, done during the last 14 days
according to the (2) we already have the amount of work, done in last 6 days - 4x/5

rest will be calculated based on the data from (1)
knowing that during each stage work was done at constant rate, we can set a proportion
(x/5)/24*8=x/15

and now we just sum up two pieces of work
x/15+(4x)/5=13x/15
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Re: Work Problem - Need help on this.  [#permalink]

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4
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manukumar wrote:
A software programmer does 20% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X?

1) 13x/15
2) 7x/15
3) 7x/60
4) 2x/3
5) x/2

Pick nos. Take x = 60
1st stage -> 20% of the work in 80% of the time
So 20% of 60 = 12
and 80% of 30 (nos of days) = 24
So he writes 12 lines of code in 1st 24 days

2nd stage -> 80% of the work in the remaining 20% of the time
so he writes 48 lines of code in last 6 days.

The 2 boldface are your rates.
In the last 14 days comprises of both the stages.
in the 1st 8 days he writes at the rate of$$\frac{12}{24} \frac{lines}{days}$$ so he writes 4 lines ( $$8 * \frac{12}{24}$$)
in the last 6 days he writes at the rate of$$\frac{48}{6}$$ lines / days so he writes 48 lines ($$6 *\frac{48}{6}$$)

totally he writes 52 lines. This is the final value / target value.
Substitute X = 60 and check which one results in 52.

Only option A gives 52 when x = 60.

Cheers
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Re: A software programmer does 20% of the work in 80% of the  [#permalink]

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1
Total work - x lines
Total time - 30 days

20% work done in 80% time... given
20% of work= x/5
80% of time=30*0.8=24 days
Therefore rate for first 24 days=(x/5)/24=x/120

We have been asked to compute work completed in last 2 weeks, i.e. last 14 days
Work done in last 14 days=Total work-work done in first 16 days
= x-[(x/120)*16]
= x-(2x/15)
= 13x/15
Ans= A
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A software programmer does 20% of the work in 80% of the  [#permalink]

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This question can be answered without any computation.
As the 80% of work is done in the last 6 days( 20% of 30 days). Then the work done in the last 14 days must be more than 80% i.e. 4/5 (For the possible answer the numerator must be greater than half of the denimenator) and there are two possible options A (13x/15 ) and D (2x/3 ) Clearly D is just 66.67% and the obvious choice is answer choice A.

Or, if we want to kill some time and do the tedious job of computing, we can do the same as follows :
For first part, the time spent is is 80% of 30 days = 30*0.8 =24 days ( Here the programmer does 20% of the work (x) i.e. 1x/5)

For the second part, the time spent is 20% of 30 days= 30*0.2= 6 days ( Here the programmer does 80% of work (x) i.e. 4x/5)

Now lets see, what part of work the programmer does in last 14 days.

Last 14 days= 8 days + 6 days (last 6 days)
= [(1x/5)*(1/24)]*8 + 4x/5
=1x/15 +4x/5
=13x/15
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GMAT 1: 720 Q50 V38 Re: A software programmer does 20% of the work in 80% of the  [#permalink]

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Here is the pictorial representation of the situation:

Work = X Time = 30 days Last 15 days work
1) 20% = 1/5X 80% = 24 days 8 days of work = 24 days of work/3 = 1/3*1/5x = 1/15*x
2) 80% = 4/5X 20% = 6 days 6 days of work = 4/5*x

Last 15 days will be 8 days from the 1) and 6 days from 2) = (4/5+1/15)*x = 13/15*x
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Re: A software programmer does 20% of the work in 80% of the time, and 80%  [#permalink]

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Bunuel wrote:
A software programmer does 20% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, what fraction of the work did he complete in the last two weeks, in terms of X?

A. 13x/15
B. 7x/15
C. 7x/60
D. 2x/3
E. x/2

Total Work = X lines

20% Total Work = (20/100)X = X/5 lines
80% Total Work = (80/100)X = 4X/5 lines

20% Total Time = (20/100)30 = 6 Days
80% Total Time = (80/100)30 = 24 Days

Last two weeks = 2*7 = 14 days

Amount of work done done in last 6 of these 14 days = 80% Total Work = 4X/5 Lines
Amount of work done done in First 8 of these 14 days = (8/24)*(X/5 lines) = X/15 Lines

Total Work done in last 14 days = (4X/5) +(X/15) Lines = 13X/15 Lines

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A software programmer does 20% of the work in 80% of the  [#permalink]

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vivatran wrote:
A software programmer does 20% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X?

A. 13x /15
B. 15x/15
C. 7x/15
D. 2x/30
E. 13x/30

I had the same approach as VeritasPrepKarishma had.

we can easily eliminate B, C, D, and E right away.

in the last 6 days, he did 80% of the job. therefore, in last 2 weeks, he finished more than 80% of the work.
B = X, or 100% - CLEARLY not
C = slightly more than 50%. 9x/15 = 3x/5 = 60%. but this is way more than 7x/15
D = way too small
E = way too small

now..to verify
we know that in first 24 days, he did x/5 work. each day, he did x/120 work. in 8 days, he did 8x/120 work, or 4x/60 or x/15.
in last 6 days, he did 4x/5 work.
total work done in last 2 weeks:
4x/5 + x/15
multiply first one by 3:
12x/15 + x/15 = 13x/15

I believe it should be a sub-600 level question, if the answer choices are not changed so that to not eliminate incorrect ones so easy.
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