A certain work plan for September requires that a work team, working

We have no of days=30

Let the required no of items be x.

We have \(\frac{15*150+15*x}{15+15}=200\)
Or, 2250+15x=200*30
Or, 15x=6000-2250=3750
Or, \(x=\frac{3750}{15}=250\)

Ans. (B)

September has 30 Days so -

\(30* 200 = 15*150 + 15k\)

Or, \(6000 = 2250 + 15k\)

So, k = 250, Answer must be (B)

using the weighted average to get the combined rate:

150*0.5+0.5*x=200
75+0.5*x=200
0.5*x=125
x=250

Posted from my mobile device

We can create the equation:

200 = (150 x 15 + n)/30

6000 = 2,250 + n

3,750 = n

So per day, 3,750/15 = 250 items must be produced

Alternate Solution:

For the first half of the month, the team was 50 items below the daily goal each day. Thus, for the second half of the month, the team must produce the required 200 daily units each day, plus 50 extra units each day (to make up for the earlier deficit). Thus, the team must have a daily average of 250 units for the second half of the month..

Answer: B

Alternate Solution:

We see that 150/200 = 3/4 = 0.75 or 25 percent less of the average was produced per day for the first 15 days.

To produce the average for the 25 percent more than the average must be produced or 1.25 x 200 = 250 items per day.

Bunuel

For the sake of simplicity, would you recommend the following approach for this question?

(150+n)/2=200
150+n=400
n=250

Thank you in advance.

This works because the time period is split in half: For the first half of the month, the team produced an average of 150 items per day. How many items per day must the team average during the second half of the month if it is to attain the average daily production rate required by the work plan?

However if it were: For the first third of the month, the team produced an average of 150 items per day. How many items per day must the team average during the remaining two thirds of the month if it is to attain the average daily production rate required by the work plan? Then this approach won''t give the correct answer.

September month has 30 days.

Ideal avg. production=200/day
For first 15 days item production-150/day
Difference/day=200-150=>50 items/day (produced less per day for 15 days)
That implies to maintain avg. item production =200/day, we should get 50 item production extra/day in addition to 200/day (50+200) for next 15 days=250/day

(B)

Number sense approach would be to realize that it is 50 units below the target for half of the month so it must be be compensated by an addition of 50 for the other half of the month.

200 + 50 = 250

The other way is

\(30 * 200 = 15 * 150 + 15 * x\)

This can be rewritten as \(30 * 200 = 15 (150+x)\)

\(2 * 200 = (150+x)\)


\(400 = 150 + x\)

\(x = 400 - 150 = 250\)

Answer choice B

This would be a much simpler approach:
since the question clearly talks about half and a half month,
i would just pick 2days, rather than 30days/2 .. 15 and 15 days.. to simplify the calculation.
for 2 days, the productivity would be 200*2= 400 units total.
with 150 units/day produced for half a month, in our case 1 day.. so 150 units..
so we are lagging behind by 400-150=250 units.
250 units need to be produced to catch up.

One can use the concept of weighted average to get to the answer in less than 30 seconds..

150 is average for the 1st 15 days(given), total average/weighted average is 200(given). Now we know that the weight is the same—1st half is 15 days, next half is 15 days. This means that the overall average or the weighted average should be midway between the average for the 1st 15 days and average for the next 15 days. So therefore [150+x(average of the last 15 days)]/2 = 200—> x=250

Posted from my mobile device

this is a weird question by the GMAT. What if I was not aware how many days in September? some months have 31 days....

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