Hi All,
Beyond the obvious algebra calculations that you could use to solve this DS question, you can actually avoid a "heavy" math approach if you recognize the algebra "patterns" at play here.
We're told that X^2 + BX + C = (X+D)^2 and that B, C and D are constants. We're asked for the value of C.
While the above equation certainly "looks" complex, you should recognize the "pieces":
1) (X+D)^2 is a Classic Quadratic
2) X^2 + BX + C is the "format" you get when you FOIL a Classic Quadratic
3) These two things are set EQUAL to one another, so one "restricts" the other.
eg
(X+5)^2 = X^2 + 10X + 25
This ultimately means that if you know ANY of the constants (B, C or D), then you can figure out ALL of the others:
If you know B, then D = B/2 and C = D^2
If you know C, then D = \sqrt{C} and B = 2D
If you know D, then B = 2D and C = D^2
This is all a really wordy way to point out that knowing your concepts can create "shortcuts"
Fact 1: D = 3
(X+3)^2 = X^2 + 6X + 9
We know B and C and can answer the question.
Fact 1 is SUFFICIENT
Fact 2: B = 6
X^2 + 6X + C = (X+D)^2
Since B = 6, and the middle term is the sum of the "O" and the "I" calculations in FOIL, the D = 3 and the C = 9.
Fact 2 is SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich