keats wrote:

Did anyone tried solving this problem with double matrix? One of the guys did, but looks like his excel is incomplete

Yes, i was at the beginning a bit confused. But finally got it:

Here is a general formula:

A + B - Both + Neitherfrom question:

48 + S - Both + Neither = 75

Statement 1

38 have patio but no swimming pool

then formula becomes:

(48-38) + S - Both + Neither = 75

10 + S - Both + Neither = 75 ----> Is this sufficient to find S? No, therefore not sufficient. Why? because you are left with three variables - S,Both and Neither with one equation

Statement 2

Both = Neither

this means either we can replace from formula Both or Neither like this:

from question:

48 + S - Both + Neither = 75

Replacing "Both"

48 + S - Neither + Neither = 75 -----> you can see that Neither cancels out

then you are left with 48 + S = 75, from here you don't need to solve it since you can find the value of S Sufficient

Replacing "Neither"

48 + S - Both + Both = 75 -----> you can see that "Both" cancels out

then you are left with 48 + S = 75 same outcome as above.

My point is either way will eliminate both and neither in the formula.