What is the answer to this problem, and how do you solve it?

An insurance company keeps an electronic copy and a paper copy of
every policy they write.
3% of the policies have both inaccurate paper and electronic copies. 
Of the policies with inaccurate
electronic copies, 60% of those policies also have inaccurate paper
copies.  Of the policies with
inaccurate paper copies, 75% of those policies also have inaccurate
electronic copies.  What %
of policies have accurate electronic and paper copies?

Hello.

The answer is that 94% of policies have accurate electronic and paper copies.

We're told that 3% of policies have both inaccurate paper and
electronic copies. Of the policies with inaccurate electronic copies,
60% of those policies also have inaccurate paper copies.  Thus, the 3%
of policies with both inaccurate paper and electronic copies represent
60% of the total number of policies with inaccurate paper copies. 
From this, we can conclude that 5% of policies have inaccurate
electronic copies:

0.6 * (# of Inaccurate electronic copies) = 3%  of total policies
    # of Inaccurate electronic copies = 3% / 0.6 = 5%

Of the 5% with inaccurate electronic copies, 40% of those would have
accurate paper copies.

 .4 * 5% = 2%

Thus, 2% of total policies have inaccurate electronic copies but
accurate paper copies.


Again, we're told that 3% of policies have BOTH inaccurate paper and
electronic copies. Of the policies with inaccurate paper copies, 75%
of those policies also have inaccurate electronic copies.  Thus, the
3% of policies with both inaccurate paper and electronic copies
represent 75% of the total number of policies with inaccurate paper
copies.  From this, we can conclude that 4% of policies have
inaccurate electronic copies:

0.75 * (# of Inaccurate paper copies) = 3%
    # of Inaccurate electronic copies = 3% / 0.75 = 4%

Of the 4% with inaccurate paper copies, 25% of those would have
accurate electronic copies.

 .25 * 4% = 1%

Thus, 1% of total policies have inaccurate paper copies but accurate
electronic copies.

In summary...

3% of policies have both inaccurate paper and electronic copies. 
2% of policies have inaccurate electronic copies but accurate paper copies.
1% of policies have inaccurate paper copies but accurate electronic copies.

Thus, a total of 6% of policies have inaccurate paper copies or
inaccurate electronic copies or both.

From this, we can conclude that 94% of policies have accurate
electronic and paper copies.

I hope this helps.

I believe juggler got it!  Based on this question and the other, I
hope I don't need to take the GMAT anytime soon.  Sounds like
something for Marilyn Vos Savant.

They do a test book
- one gets used to answering slippery questions
- it is just practise

I took it in 1979 and was gratified to score pretty well
- but hacked off that two people I knew (and considered fairly thick) scored higher

What really amused me was that I was downgraded on the 'business
acumen' side, where I was precocious - the questions were wrong.

To give you an idea, one of the dim wits had taken it earlier, got the
80th percentile, but on the retake was in the 99th percentile.

In some ways such tests are not totally inane, somebody who passes one
with flying colours having never seen anything like it, is pretty
bright.

But, the person that /learns/ how to pass the thing, from crib books,
or practise is probably (but not certainly) brighter.

On the other hand, most people (in my time) used to take the GMAT to
get into Harvard Business School
- IMO Business Schools are not necessarily that good an idea
- people need experience first 
  - otherwise they are articulate and persuasive menaces
- and if they have experience, they are too valuable to lose

Get some crib books, take the (pseudo) test again
- it is quite amusing having a bit of paper that says that you are a genius
- rather like an expired, and unredeemed, lottery ticket

nilegarritson:
Thank you for the tip.
-juggler