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# GRE Math Challenge #54-value of -3x^2 + 12x -2y^2 - 12y -39

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GRE Math Challenge #54-value of -3x^2 + 12x -2y^2 - 12y -39 [#permalink]  28 Feb 2015, 02:23
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Question Stats:

20% (00:15) correct 80% (02:51) wrong based on 5 sessions
What is the maximum value of $$-3x^2 + 12x -2y^2 - 12y -39$$ ?

A. -39
B. -9
C. 0
D. 9
E. 39
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #54 [#permalink]  25 Aug 2015, 20:31
Is there an efficient algebraic method for solving this problem?

I used calculus to find the maxima for the functions f(x) = -3x^2 + 12x [2] and g(y) = -2y^2 - 12 [-3]; then I plugged those numbers in to get -9.
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Re: GRE Math Challenge #54 [#permalink]  26 Aug 2015, 09:00
soumya1989 wrote:
What is the maximum value of $$-3x^2 + 12x -2y^2 - 12y -39$$ ?
A. -39
B. -9
C. 0
D. 9
E. 39

I don't think this is a GRE level question if this involves calculus... any algebraic way to solve...? please enlighten
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Re: GRE Math Challenge #54-value of -3x^2 + 12x -2y^2 - 12y -39 [#permalink]  16 Feb 2017, 01:02
Rearrange the expression to form -3*(x-2)^2-2*(y+2)^2-9.Now, the minimum value of the squares is zero, and also we should take their minimum not maximum because note that there is -3 and -2 multiplied with square expressions.So considering the square expressions zero, the final answer is -9.
Re: GRE Math Challenge #54-value of -3x^2 + 12x -2y^2 - 12y -39   [#permalink] 16 Feb 2017, 01:02
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