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by karthikpandian19 » Tue Nov 22, 2011 2:50 pm
How many of the 60 cars sold last month by a certain dealer had neither power windows nor a stereo?

1. Of the 60 cars sold, 20 had a stereo but not power windows

2. Of the 60 cars sold, 30 had a power windows and stereo
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by GMATGuruNY » Tue Nov 22, 2011 3:01 pm
karthikpandian19 wrote:How many of the 60 cars sold last month by a certain dealer had neither power windows nor a stereo?

1. Of the 60 cars sold, 20 had a stereo but not power windows

2. Of the 60 cars sold, 30 had a power windows and stereo
60 = Only stereo + Only power windows + Both stereo and power windows + Neither.

Statement 1: Only stereo = 20.
No way to solve for Neither.
INSUFFICIENT.

Statement 2: Both stereo and power windows = 30.
No way to solve for Neither.
INSUFFICIENT.

Statements 1 and 2 combined:
60 = 20 + Only power windows + 30 + Neither.
Only power windows + Neither = 10.
No way to solve for Neither.
INSUFFICIENT.

The correct answer is E.
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by chieftang » Tue Nov 29, 2011 11:34 pm
karthikpandian19 wrote:How many of the 60 cars sold last month by a certain dealer had neither power windows nor a stereo?

1. Of the 60 cars sold, 20 had a stereo but not power windows

2. Of the 60 cars sold, 30 had a power windows and stereo
PW == power windows
S == stereo

Possibilities:

PW && S (30 from statement 2)
!PW && S (20 from statement 1)
PW && !S
!PW && !S

Of the 10 remaining we don't have sufficient info to determine which of the two remaining PW/S combinations they had.

Insufficent info.
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by shekhar.kataria » Thu Dec 01, 2011 9:47 am
60 = Only stereo + Only power windows + Both stereo and power windows + Neither.
Hi Mitch

I think that the Quotes formula will have negative both stereo and power windows value.

Correct formula for 2 option sets are

Total - Neither = Only A + Only B - Both A&B...
this is because of the fact the last value is added twice... Please correct me if i am going wrong somewhere.
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by GMATGuruNY » Thu Dec 01, 2011 12:20 pm
shekhar.kataria wrote:
60 = Only stereo + Only power windows + Both stereo and power windows + Neither.
Hi Mitch

I think that the Quotes formula will have negative both stereo and power windows value.

Correct formula for 2 option sets are

Total - Neither = Only A + Only B - Both A&B...
this is because of the fact the last value is added twice... Please correct me if i am going wrong somewhere.
When two sets overlap, there are two equations that can be used to represent the sum of all the elements.

Equation 1:
Total = (everyone in A) + (everyone in B) - both + neither.

In the equation above, when we count (everyone in A) and (everyone in B), the OVERLAP -- everyone in BOTH A and B -- gets counted twice. Thus, we SUBTRACT the overlap -- everyone in BOTH A and B -- so that it is not double-counted.

Equation 2:
Total = Only A + Only B + Both + Neither.

In the equation above, when we count everyone ONLY in A and everyone ONLY in B, we DON'T count the overlap between the two groups. Thus, we need to ADD IN the overlap -- everyone in BOTH A and B -- so that it is included in the total.

In my solution above, I used the latter equation.
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