If ab > 0 then the two equations x + y = a and 1/x + 1/y = b have a unique simultaneous solution for x and y provided ab equals
(a) 1
(b) 2
(c) 4
(d) 8
(e) 9
(a) 1
(b) 2
(c) 4
(d) 8
(e) 9
a=1/x+1/y=(x+y)/xy
b=x+y
so ab = (x+y)*(x+y)/xy = (x+y)^2/xy
let ab = c for variable simplicity
c*xy = x^2 + 2xy + y^2
0 = x^2 + xy(2-c) + y^2
only form that will yield a valid solution is c=4 to give (C)
0=x^2 - 2xy + y^2 = (x-y)^2 and x=y
Seems more like a first year engineering question then a GMAT question
