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20 Jul 2023, 14:51
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
52% (02:20) correct
48%
(02:12)
wrong
based on 320
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A factory manager estimated the average productivity (in widgets) of factory employees by dividing their estimated daily total output (in widgets) by their estimated daily total hours. Was the manager's estimate within 10% of the actual productivity?
1) The daily total output estimate and the daily total hour estimate were each within 10% of the actual totals.
2) The manager overestimated the daily total output by 1000 widgets and underestimated the daily total hours by 10 hours.
1) The daily total output estimate and the daily total hour estimate were each within 10% of the actual totals.
2) The manager overestimated the daily total output by 1000 widgets and underestimated the daily total hours by 10 hours.
20 Jul 2023, 17:41
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GianKR
We are told that the Av. productivity (rate) = Daily output (work)/ Daily total hours (time).
And we are asked whether the estimated average productivity is within 10% of the actual average productivity (maximum 10% more or maximum 10% less than the actual average productivity).
Statement 1 tells us that the daily total output estimate and the daily total hour estimate were each within 10% of the actual totals.
Case 1: If the total output and the total hour were both increased by 10%, the estimated average productivity would be equal to the actual average productivity; and the answer will be YES.
Case 2: On the other hand, if for example the total output was decreased by 10% and the total hour was increased by 10%, the estimated average productivity would be nearly 20% less than the actual average productivity; and the answer in this case will be NO.
Therefore, Statement 1 is not sufficient.
Statement 2 tells us that the manager overestimated the daily total output by 1000 widgets and underestimated the daily total hours by 10 hours.
Which translates to the following:
Actual productivity= (Estimated output - 1000) / (Estimated total hours + 10)
Case 1: If for example the estimated output equals 2000 and the estimated total hours equals 20; the estimated average would equal 100 which is not within 10% of the actual average that is in this case 100/3 (10% more or 10% less than 100/3, will put us in values between 30 and 36 for tha actual average). The answer in this case is NO.
Case 2: If for example both the estimated output and the estimated total hours equal 1 billion, subtracting 1000 from the numerator and adding 10 to the denominator are insignificant and would not change much in the value of the fraction that is the actual productivity; hence the estimated productivity will be surely within 10% of the actual productivity. The answer in this case is YES.
Therefore, statement 2 is not sufficient.
Now combining both statements:
Case 1: If the total output and the total hour were both increased by 10%, the estimated average productivity would be equal to the actual average productivity; and the answer will be YES.
Case 2:
If 10% of the actual output equals 1000, the actual output would equal 10000
And if 10% of the actual total hours equal 10, the actual total hours would equal 100
Leading for the actual average to equal: 10000/100= 100
While the estimated average would equal: (10000+1000)/ (100-10)= 11000/90= 1100/9= 122,22
122,22 is not within 10% of 100 (that is something between 90 inclusive and 110 inclusive).
The answer in this case is NO.
Therefore, both statements together are not sufficient.
Correct answer is E
20 Jul 2023, 19:33
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GianKR
This is what we are given:
\(Productivity (P) = \frac{Output}{Hours}\)
IS \(\frac{9}{10} *\frac{Actual-Output}{Actual-Hours} < \frac{Estimate-Output}{Estimate-Hours} < \frac{11}{10} * \frac{Actual-Output}{Actual-Hours}\)?
Statement 1:
Think what happens in the extreme case if Estimate Output is 10% more than Actual and Estimate Hours is 10% less than Actual.
Your Estimate Productivity becomes\( = \frac {(11/10) * Actual-Output}{(9/10) * Actual-Hours} = \frac{11}{9} * Actual-Productivity\)
So your Estimate could vary by as much as 22% or the manager could be on target and have 0% error in the Estimate (since errors are WITHIN 10% so they could be 0% errors too). Hence this statement alone is not sufficient.
Statement 2: Since we don't have any total number of widgets and hours, we cannot say what these numbers of 1000 and 10 represent. What percentage are they of the total?
Is error of 1000 widgets 1% of total actual output or 5% or 10%? Similarly is error of 10 hrs 1% of total actual hours or 5% or 10%.
Based on what % errors they represent, they could lead to very small errors to 22% as discussed above.
Not sufficient alone.
Both statements: All we know is that his Output and Hours Estimates were within 10% and we don't know what percentage 1000 widgets and 10 hrs represent so the data is not sufficient.
Answer (E)
