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555-605 Level|   Algebra|      
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Bunuel
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Does x^2 + 4x + 4 = 10? 06 Jan 2017, 02:53
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25% (medium)

Question Stats:

76% (01:06) correct 24% (01:07) wrong based on 70 sessions

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

(1) x = 2

(2) \(\sqrt{x}=\sqrt{2}\)
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D
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rohit8865
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Does x^2 + 4x + 4 = 10? 06 Jan 2017, 07:46
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Bunuel
Does x^2 + 4x + 4 = 10?

(1) x = 2

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

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
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Does x^2 + 4x + 4 = 10? 29 Jan 2017, 10:40
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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
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Does x^2 + 4x + 4 = 10? 29 Jan 2017, 11:11
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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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Does x^2 + 4x + 4 = 10? 29 Jan 2017, 11:23
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pandeyamit07
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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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: \(i\sqrt{2}\neq \sqrt{2}\).
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Does x^2 + 4x + 4 = 10? 29 Jan 2017, 11:28
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[quote="pandeyamit07"]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.
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