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# A factory manager estimated the average productivity (in widgets)

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Intern
Joined: 23 Jun 2023
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Location: Morocco
Concentration: Marketing, Nonprofit
Intern
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Given Kudos: 102
Location: Morocco
Concentration: Marketing, Nonprofit
Intern
Joined: 23 Jun 2023
Posts: 41
Own Kudos [?]: 86 [0]
Given Kudos: 102
Location: Morocco
Concentration: Marketing, Nonprofit
Tutor
Joined: 16 Oct 2010
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Location: Pune, India
Re: A factory manager estimated the average productivity (in widgets) [#permalink]
2
Kudos
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.

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.

Intern
Joined: 23 Jun 2023
Posts: 41
Own Kudos [?]: 86 [0]
Given Kudos: 102
Location: Morocco
Concentration: Marketing, Nonprofit
Re: A factory manager estimated the average productivity (in widgets) [#permalink]
KarishmaB wrote:
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.

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.

Thank you KarishmaB for your response.

Regarding statement 2 alone, when you say that we don't know what percentage 1000 widgets and 10 hrs represent of the total, that means they could also be above or below 10% of the total. Correct?
Tutor
Joined: 16 Oct 2010
Posts: 15153
Own Kudos [?]: 66872 [1]
Given Kudos: 436
Location: Pune, India
Re: A factory manager estimated the average productivity (in widgets) [#permalink]
1
Kudos
GianKR wrote:
KarishmaB wrote:
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.

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.