CAT 2009 : Quant problem of the day

If positive real numbers a, b, c, d satisfy the following system of equations:
                 a + b + c + d = 12
                 abcd = 27 + ab + ac + ad + bc + bd + cd.
which option is correct ?

1.   a=2
2.   a=4
3.   a=3
4.   a=5

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[category quant]