The minimum resistance i.e., 3 ohms can be obtained only by connecting the two coils in parallel.
So, xy/x+y =3
or, xy=3x+3y

and the maximum resistance can be obtained by series
Hence x=4 and y=12

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With two resistances R1 and R2 we have the 4 following combinations possible:

R1  or  R2 if they are used individually. 
   let R2  be the larger of the two.

R1 R2 / (R1 + R2)  if used in parallel.      
     -- This is the smallest value.  It is  < R1 and < R2.

R1 + R2  if used in series.    This is the largest value.  SO it is  > R1 and > R2.

Hence, from the given values,
      R1 + R2 = 16 Ω
       R1 R2 / (R1 + R2) =  3 Ω

So, R1 and R2 are 4 Ω and 12 Ω respectively.

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