Does x^2 + 4x + 4 = 10?

Question

Does x^2 + 4x + 4 = 10?
 
(1) x = 2

(2)  \sqrt{x}=\sqrt{2}

rohit8865 · Answer

is (x+2)^2=10

(1) x=2
(2+2)^2=16
suff

(2) sq both side IXI=2

x=2, -2
in both cases (x+2)^2 not equals 10
suff

Ans D

BloomingLotus · Answer

Statement 1: Putting direct value of X =2 we find x^2+4x+4 is not equal to 10. SUFFICIENT
Statement 2 : Squaring both sides we get x= -2 or +2 . Substituting both the values we find the equality equation is not true . Sufficient

Ans : D

pandeyamit07 · Answer

But by equation 2, we get 2 values ( 2 & -2) and one gives the value as 16 while other gives 0.

And both the equations can't contradict on value so 2nd equation is in sufficient.

And should be A

Pls correct me if am wrong

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Bunuel · Answer

Numbers on the GMAT are by default real numbers, thus for the GMAT even roots from negative numbers are not defined.

Even if that was not the case, still -2 does not satisfy the equation in (2).  \sqrt{-2}  is a complex number ( i\sqrt{2} ), while  \sqrt{2}  is an irrational real number:  i\sqrt{2}
eq \sqrt{2} .

BloomingLotus · Answer

But by equation 2, we get 2 values ( 2 & -2) and one gives the value as 16 while other gives 0.

And both the equations can't contradict on value so 2nd equation is in sufficient.

And should be A

Pls correct me if am wrong

Yes , you are right that Statement 2 will give either 16 or 0. In both the scenarios it answers the question that the equation given in question is not equal to 10 . So, we can consider the data given in Statement 2 as sufficient because we are able answer our question.

Does x^2 + 4x + 4 = 10?

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