Good questions, I'm trying...
1) rephrase: x/a = (x-b)/a + b/a and x/b = (x-a+2)/b + (a-2)/b
this gives us at least that x-b is divisible by and x-a+2 is divisible by b
trying answers:
E and D give nothing being substitued in either of equations
C and B could be tested only in the first equation
So A is left (not sure)
2) x-y should be greater than x+y, could be true if y is negative only, so B
3) If we deal with positive numerator and denominator and add the same number to each of them the value of the fraction will always decrease - we divide on greater number both parts of a new numerator (2 is sufficient, answer is no). If a fraction is less than 1, by adding the same number the new fraction will always be greater than original (1 is sufficient, answer yes). So D.
4) The inequality is true only if y
5. (1) is insufficient, because for x+y to be greater than 0 both can be greater or smaller one another. (2) is insufficient too, y^x is less 0, only when y is negative and x is odd. So inequality is true for x,y being either 3,-2 or -3, -2. Answer is E.