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Bunuel
If \(x^2 + 12x − k = 0\), is \(x = 4\)?

(1) \((x + 16)\) is a factor of \(x^2 + 12x − k\), where k is a constant, and x is a variable.

(2) \(x ≠ −16\)

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(1) \((x + 16)\) is a factor of \(x^2 + 12x − k\), where k is a constant, and x is a variable.
put x=-16 in the equation, we get k=64

The equation becomes: \(x^2 + 12x − 64 = 0\)
Solving this equation, we get \((x-4)(x+16)=0 \)
i.e, \(x=4\) or \(x=-16\)
We can't be sure what x is, as we have 2 values.
INSUFFICIENT.

(2) \(x ≠ −16\)
By itself, this option doesn't tell whether \(x=4\)
INSUFFICIENT

COMBINE 1) and 2):
From 1) we have \(x=4\) or \(x=-16\)
From 2) we have \(x ≠ −16\)

Therefore \(x=4\)
SUFFICIENT.

ANSWER C.
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If x^2+12x−k=0, is x=4?

Stat1: (x+16) is a factor of x^2+12x−k, where k is a constant, and x is a variable.

Putting x = -16 in the equation, x^2+12x−k= 0 or, 256- 192 -k =0 or, k= 64.
Now, equation, x^2+12x−64 =0so, x = -16 or 4. No idea, which is the value of x to consider. Not sufficient.

Stat2: x≠−16; But, we don't know value of k, so we can't be sure, if x = 4. Not sufficient.

Combining both, x = 4. Sufficient.

So, I think C. :)
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imo C
If \(x^2 + 12x − k = 0\), is \(x = 4\)?

(1) \((x + 16)\) is a factor of \(x^2 + 12x − k\), where k is a constant, and x is a variable.

\(x^2 + 12x − k\)
if X=-16 ,k =64
so X =4 as well .As we have 2 values of X
Not sufficient


(2) \(x ≠ −16\)
No idea about k .. or X ..
Not sufficient


Combinig .. we can get that
if \(x ≠ −16\)
x will be 4

sufficient
C is the ans
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