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# If (a,b)=(9,8), the expression 2(a^3-b^3)/(a(a+b)+b^2) is:

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GMATH Teacher
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Joined: 12 Oct 2010
Posts: 935
If (a,b)=(9,8), the expression 2(a^3-b^3)/(a(a+b)+b^2) is:  [#permalink]

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03 Mar 2019, 15:46
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Difficulty:

15% (low)

Question Stats:

79% (01:47) correct 21% (01:22) wrong based on 33 sessions

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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

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Re: If (a,b)=(9,8), the expression 2(a^3-b^3)/(a(a+b)+b^2) is:  [#permalink]

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03 Mar 2019, 16:14
Keep in mind that:

$${a^3} - {b^3} = (a - b) ({a^2} + ab + {b^2})$$

Hence:

$$2 \frac{(a^3 - b^3)}{a (a + b) + b^2} = 2 (a - b) \frac{(a^2 + ab + b^2)}{a^2 + ab + b^2} = 2 (9 - 8) = 2$$

Thus, the correct answer is C.
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MEMENTO AUDERE SEMPER
GMATH Teacher
Status: GMATH founder
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If (a,b)=(9,8), the expression 2(a^3-b^3)/(a(a+b)+b^2) is:  [#permalink]

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03 Mar 2019, 16:39
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

$$?\,\, = \,\,\frac{{2\left( {{a^3} - {b^3}} \right)}}{{a\left( {a + b} \right) + {b^2}}}\,\,\,\,\,{\text{for}}\,\,\,\,\left( {a,b} \right) = \left( {9,8} \right)$$

$$\left. \matrix{ 2\left( {{a^3} - {b^3}} \right) = 2\left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right)\,\,\, \hfill \cr a\left( {a + b} \right) + {b^2} = {a^2} + ab + {b^2} \hfill \cr} \right\}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,{{2\left( {{a^3} - {b^3}} \right)} \over {{a^2} + ab + {b^2}}} = 2\left( {a - b} \right)\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {a,b} \right) = \left( {9,8} \right)} \,\,\,\,\,? = 2$$

$$\left( * \right)\,\,{\rm{when}}\,\,\,{a^2} + ab + {b^2} \ne 0$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
If (a,b)=(9,8), the expression 2(a^3-b^3)/(a(a+b)+b^2) is:   [#permalink] 03 Mar 2019, 16:39
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