GianKR wrote:
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.
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