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For these questions the following functions have been defined.
$$la(x, y, z) = min (x+y, y+z)$$
$$le(x, y, z) = max(x -y, y-z)$$
$$ma (x, y, z) = \frac{1}{2} (le (x, y, z) + la (x, y, z))$$
Best approach to these type question remain assuming values and checking
Case - 1.x=8 ; y=7 ; z = 5
la (x,y,z) = 12
le (x,y,z) = 2
ma (x,y,z) = 7
Case -2: Let us try to find values for which la(x,y,z) and le(x,y,z) would be equal. In such a case, ma(x,y,z) would also be the same.
So max(x-y,y-z)= min(x+y, y+z)
As x>y>z>0, min(x+y, y+z) = y+z
So max(x-y, y-z) =y+z
Either x-y=y+z or y-z = y+z
So x=2y+z or z=0
But z cannot be 0 according to given condition.
So, x=2y+z
Let us assume y=2 and z=1
So x=5
la (x,y,z)= 3
le (x,y,z) = 3
ma (x,y,z)= 3
based on these two cases we can deduce that non of the given options holds true.
So the correct option to choose is D - None of these.
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