Normally a quadratic equation yields two possible answers, but not always. The exception is when the equation is a perfect square.
Statement 2 states:
x(x - 12) = -16 - 4x
Which becomes:
x^2 - 12x + 4x + 16 = 0
x^2 - 8x + 16 = 0
(x-4)(x-4)=0
So x must equal 4.
The problem, really, is statement 1.
X could equal 1, in which case 1(1-3) = (1-3) --> -2 = -2
OR
X could equal 4, in which case 4(4-4)=(4-4) --> 0 = 0
so you might be tempted to think that statement 1 is not sufficient because it yields two possible values for x.
However, 1^2 - 5(1) = -4 AND
4^2 - 5(4) = 16-20 = -4
What is the value of x^2 − 5x?
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Source: Beat The GMAT — Data Sufficiency |
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