Mo2men wrote:What is the maximum value of −3x^2+12x−2y^2−12y−39?
A. −39
B. −9
C. 0
D. 9
E. 39
This type of question is typically solved by COMPLETING THE SQUARE -- a process that is beyond the scope of the GMAT.
Feel free to ignore this problem.
A GMAT-friendly approach:
Maximize the value of −3x² + 12x:
If x=0, then −3x^2 + 12x = 0.
If x=1, then −3x^2 + 12x = 9.
If x=2, then −3x^2 + 12x = 12.
If x=3, then −3x^2 + 12x = 9.
The results above indicate that the greatest possible value of −3x²+12x is 12.
Maximize the value of −2y² − 12y = -2(y² + 12y).
Here, the value will be maximized if the expression in red is NEGATIVE.
Test negative values in −2y²−12y.
If y=-1, then −2y² − 12y = 10.
If y=-2, then −2y² − 12y = 16.
If y=-3, then −2y² − 12y = 18.
If y=-4, then −2y² − 12y = 16.
The results above indicate that the greatest possible value of −2y²−12y is 18.
Thus:
The greatest possible value of −3x²+12x−2y²−12y−39 = (greatest possible value of −3x²+12x) + (greatest possible value of −2y²−12y) − 39 = 12 + 18 - 39 = -9.
The correct answer is
B.
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