According to a recent magazine article, of those office employees who typically work 8 hours at the office each day but sometimes say that they will work at home on a particular day, 25 percent actually work less than one hour. At the same time, over 90 percent of those same office employees believe they are more productive working at home than working in their office.

The statements above, if true, best support which of the following conclusions about the office employees discussed in the article?

A) On average, the office employees working at home for a day work fewer hours than office employees working at the office.
B) 10 percent of the office employees are less productive working from home than working in their office.
C) At least 15 percent of the office employees do not define productivity exclusively in terms of the number of hours worked.
D) At least 25 percent of the office employees can complete the same amount of work in one hour at home as in 8 hours at the office.
E) Some of the office employees make statements regarding their productivity that are not in fact true.



It said the answer is "C" but I cannot understand how the figure 15 percent comes. Can anybody help throw me a light? Thank you!

I love it when math questions are buried within CR questions...

Suppose there are 100 employees. We're told that 90 out of the 100 people believe they are more productive at home than they are at work. We're also told that 25 out of the 100 people work less than one hour on the day they work from home.

The smallest possible overlap between these two subgroups of people is 15. That is, there must be at least 15 people who are described by both statements. Why 15? Subtract from 25 the 10 people who do not believe they are more productive at home.

So, among that overlap group, we have people who work less than one hour when at home, and yet also feel more productive. This group of people certainly does not define productivity strictly by the number of hours worked.

Define set A as set of people who feel they are more productive at home
Define set B as set of people who work less than 1 hour at home

P(A) = 90%
P(B) = 25%

So P(A union B) = P(A) + P(B) - P(A intersect B) <= 1.0

So P(A intersect B) >= .9 + .25 - 1.0 = .15

This is to say the group of people who work less than 1 hour and feel they are more productive are of 15% of the population sampled.

So far I agree with the number 15%. But exactly because of the fact that these guys work fewer hours and claim they are more productive, they basically equate productivity with amount of work divided by number of working hours. They have fewer hours -> higher productivity, and correlate productivity with number of hours worked.

This is in fact what answer C says to the contrary. I do not see any answer as a good inference from the evidence.

What is my flaw of argument here?

Thanks!

So at least 15% of people measure productivity this way:

Productivity = (Work Completed/Number of Hours)*constant
[This is just the math version of what you said.]

Then isn't it true that "At least 15 percent of the office employees do not define productivity exclusively in terms of the number of hours worked"? (Italics added by me, as I think this one word is the clincher. Clearly, the amount of work accomplished has to factor into it.)

Also, I'd argue that someone who did define productivity exclusively in terms of number of hours worked would do so with a direct proportionality: Productivity = Number of Hours * constant, such that more hours ==> greater productivity. You argued above that at least 15% of people view the relationship as inversely proportional: more hours to do the same amount of work ==>lower productivity. Even if you accept that these 15% could define productivity exclusively as a function of hours, the relationship would likely be the inverse!

_________________
Emily Sledge
Instructor
ManhattanGMAT

I have seen above explanation but, I could not arrive to OA.

My understanding is as below

A = 90 percent of the office employees believe that they are more productive at home than at work.
B = 25 percent of the office employees actually work fewer hours (<1 hr) when they work at home than when they work at the office (8 hrs).
A intersection B = 100 - (90+25) = 15

15 percent of the office employee believe they are more productive at home than at work and work fewer hours (<1 hr) at home than at office (8 hrs).
So such argument is not possible. Is this lead to answer? I could not understood.

What could be the definition of productivity?

Productivity = const * (work / time) OR const * (work * time)

Hi,

I have a question here:-

Is this really a question about Resolving a problem in the argument rather than "Support Conclusion"? I can really solve the problem better this way as the correct answer resolves the conflict in the premise.

Thanks!

akhp, the whole issue in this problem is that these workers may be defining productivity in an unconventional way. Our job then is not to speculate on what their definition of productivity is, but rather to acknowledge that they are probably defining it in a way that we wouldn't anticipate..

Arjun, it is usually a good idea to approach the problem based on the constraints the question provides. Although you may get some traction on the problem by using an alternate approach, this is dangerous and should be used sparingly..

_________________
Tim Sanders
Manhattan GMAT Instructor

Hi,
I was trying to understand this question & dont understand why should the overlap be 15%. Can it not be greater as shown below.....

w<1hr w>1hr
---------------------------------------------------------
25% 65% Pr@home
---------------------------------------------------------
0% 10% nP@home
---------------------------------------------------------



Am I not seeing something ?

Forgive me, but I find the wording of this question somewhat ambiguous.

The argument says "of those office employees who work from home…". The OA shifts to all "the office employees" (i.e. all employees).

While the question stem mentions "which of the following about the office employees discussed" this does not make it clear whether we're talking about all the office employees or the office employees who work from home. I would argue that both are discussed. With the former interpretation, we cannot infer "At least 15 percent of the office employees…[opt C]" as the percentage of the employees who work from home is unknown.

I think use of the word 'discussed' creates unnecessary ambiguity as to which set is being considered.

Did you read Emily's explanation above? She lays this out pretty well. Let us know if you need more help.

_________________
Jamie Nelson
ManhattanGMAT Instructor

"discussed" has got to refer to the people we just talked about in the argument. Who are they? People who typically work eight hours in the office but sometimes work from home, as stated in the passage.

_________________
Jamie Nelson
ManhattanGMAT Instructor