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

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A software programmer does 20% of the work in 80% of the [#permalink]  06 Mar 2011, 05:42
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71% (03:16) correct 28% (03:17) wrong based on 63 sessions
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
[Reveal] Spoiler: OA

Last edited by vivatran on 05 Nov 2012, 22:27, edited 3 times in total.
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Re: Work Problems [#permalink]  06 Mar 2011, 05:54
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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]  06 Mar 2011, 06:35
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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.

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Re: Work Problems [#permalink]  06 Mar 2011, 23:25
X lines - work
30 days - time

0.2x lines of code in 24 days

So in 1 day lines of code written = 0.2x/24

0.8x lines of code written in 6 days

So lines of code written in last 2 weeks = 0.2x/24 * 8 + 0.8x

= 0.2x/3 + 0.8x

= 0.2x( 1/3 + 4)

= 2/10 * 13/3 * x

= 13/15x
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Re: Work Problems [#permalink]  06 Mar 2011, 23:41
guys.. I think there are two answers to this problem ..

Solution 1: explained above: the dude works for 24 days and then 6 days..

Solution 2: he can also do 80% in first 6 days and then 20% in the next 24 days..

the last 2 weeks fall in 24 days..

24 days = 0.2 * X
14 days = 0.2 * X * 14 / 24 = 7 X/ 60
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Re: Work Problems [#permalink]  15 Sep 2011, 22:27
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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]  18 Sep 2011, 10:16
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]  18 Sep 2011, 21:06
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]  21 Sep 2011, 20:10
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]  22 Sep 2011, 20:51
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]  23 Sep 2011, 13:19
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,
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]  24 Sep 2011, 09:48
gmatyro wrote:

Hi,
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]  24 Sep 2011, 16:41
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]  29 Sep 2011, 03:23
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: Work Problems [#permalink]  04 Oct 2011, 10:01
There are two portion for this problem

I. First 80% of time - 24 days (20% work)
II. Remaining 20% time - 6 days (80% work)

The amount of work done in last two weeks(14 days) = 8 days of period 1 and 6 days of period 2
work done in 8 days of period 1 = 1/3(20%)
= 6.66%
Work done in last two days = 6.66 + 80 = 86.66 = 13/15
in terms of x
13x/15
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Re: A software programmer does 20% of the work in 80% of the [#permalink]  19 Feb 2012, 02:45
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prashantbacchewar 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) 7X/15
C) 7X/60
D) 2X/3
E) X/2

I somehow felt that something is missing in the problem

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Re: A software programmer does 20% of the work in 80% of the [#permalink]  13 Apr 2012, 04:21
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: A software programmer does 20% of the work in 80% of the [#permalink]  18 Jun 2012, 17:48
Just another way to look at it:

20% done in 80% of time
80% done in 20% of time

So we need the full "80% done in 20% time" -> 80% done of X -> 0.8(X)

Now the time where he was slacking in the beginning...
20% done in 80% time. We are only concerned with 30% of this time (50% was in the first half, we only want the duration that spills over into the second half. 80% -50% = 30% of the second half). So, 20% of 30% = 6% = .06(X)

Now we are done. Total of .86X was completed [add both portions, .06X+.8X] which is equal to 13(X)/15 (also easy to eyeball from the question answers).
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Re: A software programmer does 20% of the work in 80% of the   [#permalink] 18 Jun 2012, 17:48
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