fskilnik wrote:
GMATH practice exercise (Quant Class 3)
If \(\left( {a,b} \right) = \left( {9,8} \right)\) , the expression \({{2\left( {{a^3} - {b^3}} \right)} \over {a\left( {a + b} \right) + {b^2}}}\) is:
(A) negative
(B) zero
(C) between 0 and 3
(D) between 3 and 6
(E) greater than 6
\(?\,\, = \,\,\frac{{2\left( {{a^3} - {b^3}} \right)}}{{a\left( {a + b} \right) + {b^2}}}\,\,\,\,\,{\text{for}}\,\,\,\,\left( {a,b} \right) = \left( {9,8} \right)\)
\(\left. \matrix{
2\left( {{a^3} - {b^3}} \right) = 2\left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right)\,\,\, \hfill \cr
a\left( {a + b} \right) + {b^2} = {a^2} + ab + {b^2} \hfill \cr} \right\}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,{{2\left( {{a^3} - {b^3}} \right)} \over {{a^2} + ab + {b^2}}} = 2\left( {a - b} \right)\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {a,b} \right) = \left( {9,8} \right)} \,\,\,\,\,? = 2\)
\(\left( * \right)\,\,{\rm{when}}\,\,\,{a^2} + ab + {b^2} \ne 0\)
The correct answer is (C).
We follow the notations and rationale taught in the
GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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