A furniture manufacturer has two machines, but only one can

Bunuel.... please could you point out anymore questions of this type ? Thanks for all your help.

viewforumtags.php look in PS or/and DS Work Problems.

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Let us look for LCM f 15 and 12. Say 60 is total work.
A completes in 12 days 2 shifts which means it works 2.5 hrs per shift. (60/12 = 5 hrs two shifts)
Similarly B completes in 15 days or works 2 hrs per shift.
Now, per day work as per shift plan 2.5 (A) + 2 (B) + (2.5 + 2)/2 (A and B combined) = 6.75 hrs per day
Total time = 60/6.75 which comes around 9 days.

machine A finish the job in 2*12 shifts = 24 shifts
machine B finish the job in 2*15 shifts = 30 shifts

Lets assume total work require 120 shifts

Therefore,
rate of A = 5 shifts/day
rate of B = 4 shifts/day
rate of (A+B) = 9 shifts/day

According to current schedule work complete in a day = 5+4+(9/2) =13.5 shifts/day

Therefore, Time required to finish 120 shifts = (120/13.5) = 8.88.. days ~ 9 days

Machines A & B work for 1.5 shifts a day.
So, in 2 days 3 shifts.(imagine 2 days=1 schedule)

A's production rate 12 days 2 shifts, so in 1 schedule rate is 8.
B's production rate 15 days 2 shifts, so in 1 schedule rate is 10

This implies: T=8*10/8+10 = 80/18 (for 1 schedule)
and we know 1 schedule is of 2 days,

(80/18)*2 = 9days (Approx)

Hence D.

I actually got one of these right!!!!!!!!!!!!!!!! First time in about 80 attempts at a work rate problem! I'm so happy

So based on the info given, it takes 24 shifts for A to complete the job, and 30 shifts for B to complete the job, if they each worked independently. So the rate for A is 1/24 and for B 1/30. If each day they're working 1.5 shifts, then each day A completes 1.5/24 (which equals 1/16) and B is completing 1.5/30 (which equals 20). Finding a common denominator of 80, their total work per day combined is 9/80. Thus after working 1.5 shifts each per day for 9 days they'll have completed the whole job (8/9ths through the 9th day).

curious why some questions will specify an "approx" solution and provide rounded answer choices, others will not, however provide fractional answers (when applicable), and then others, such as above, will do neither/both? I understand the above job wasn't done until partly into the 8th day, so it did take 9 days to complete...

Bunuel, is a question such as the above fair game on the test? I have been under the impression that the answer choices will be exact, unless the question specifies an "approx" solution or the answer choices are based on objects that can't be physically split (people, cars, etc)...isn't a day an interval and/or unit of measure? thank you.

Let us say that the total work is of 240 units

A ---- 12 days ---- 2 shifts ----- 10 units per shift

B ---- 15 days ---- 2 shifts ----- 8 units per shift

When they work together A + B + (A+B)/2 = 10 + 8 + 9 = 27 units per shift

Every 3 shifts ---- 27 units
x 8 x 8

Every 24 shifts ---- 216 units

26 shifts ----- 216 + 18 = 234

In 27th shift the work will get finishe

1 Day ---- 3 shifts hence total days taken = 27/3 = 9 days

Pushpinder Gill

The clause "while both work half of the third shift" is confusing. The phrase "each work half of the third phrase" would have had more clarity.

This question should have asked "approximately" how many days will it take for the machines to do the job.

'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days.

To finish a work say you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully.

in one shift, A can do 1/24 of the work
in one shift, B can do 1/30 of the work
no of days required for the completion of the task by A and B together in the current schedule is (3/2)*((1/24)+(1/30))*t=1
t=8.888=9

1 .Each machine works 1.5 shifts a day
2. Machine A can do the job in 24 shifts or 16 days
3. Machine B can do the job in 30 shifts or 20 days.
4. Both together can do the job in 1/ (1/16 + 1/20) = 80/9= 9 days

Hi, if the GMAT says "how many days will it take to do the job" shouldn't the answer choices be exact? Otherwise it would say "approximately" correct? This is confusing me big time. I'll be grateful if someone could help me clarify! Thanks!

A requires 12 days working 2shifts.
So working one shift it requires 24 days. Similarly b requires 30 days.
Also together they work half shift so further divide by 2.

The equation becomes 1/24+1/30+9/240

Which gives 27/240.
Reciprocal gives 9days

Machine A does 1/24 per day
Machine B does 1/30 per day
Combined does 1/27 per day

Rates are very close to each other so I thought that the shifts must all account for 1/3 of the job.

1/3 is done in 8, 9 and 10 days respectively. Again the median value seems like the perfect compromise.

So 9 days.

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