list manipulation - Select/Delete with Sublist elements?

Probably easy and short question, I still didn't fully figure out how to easily select/delete sublists from a list. Example:

tt = {{2, 4}, {4, 8}};

I want to delete/select all the elements where the difference between them (Abs) is greater than four.

Answer

I would use either

Cases[data, {x_, y_} /; Abs[x - y] > 4]

or

With[{diff = Abs[data[[All, 1]] - data[[All, 2]]] - 4}, 
   Pick[data, UnitStep[diff]*Unitize[diff], 1]
]

The first clearly demonstrates what you are trying to do, the second is much faster...

data = RandomInteger[{0, 100}, {10^6, 2}];

(m1 =  Cases[data, {x_, y_} /; Abs[x - y] > 4]); // AbsoluteTiming

==> {2.8393092, Null}

(m2 = 
    With[{diff = Abs[data[[All, 1]] - data[[All, 2]]] - 4}, 
     Pick[data,UnitStep[diff]*Unitize[diff], 1]]); // AbsoluteTiming


==> {0.1248024, Null}

m1 == m2

==> True

Assuming you are working with random data and don't expect equality, the second method can be simplified to...

Pick[data, UnitStep[Abs[data[[All, 1]] - data[[All, 2]]] - 4], 1]

Edit:

Of course if you want to delete elements where Abs[x-y] > 4 you can modify the Cases definition as

Cases[data, {x_, y_} /; Abs[x - y] <= 4]

And the Pick method by swapping out the 1 in the last argument with 0.