Is x = √8 ? (1) x^2 − 4√2*x + 8 = 0 (2) x^2 + 2√2 *x − 16 = 0

Question

Is x = √8 ?

(1) x^2 − 4√2*x + 8 = 0 
(2) x^2 + 2√2 *x − 16 = 0

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v12345 · Answer

Statement 1: Sufficient 
 x^2 − 4√2*x + 8 = 0 
=>(x - √8)^2 = 0
=> x = √8, Yes
 Statement 2: Insufficient 
x^2 + 2√2 *x − 16 = 0
=> (x + 4√2)(x - 2√2) = 0
=> x = 2√2 or -4√2 , may be x = √8

Hence, OA is (A).

yashikaaggarwal · Answer

Is x = √8 ?

(1) x^2 − 4√2*x + 8 = 0
Compare to a^2+b^2-2ab = 0
(since 2√2x is negative)
A = x
B = 2√2 
(X-2√2)^2 = 0
X = 2√2 = √8 
Sufficient

(2) x^2 + 2√2 *x − 16 = 0
Compare to a^2+b^2+2ab = 0 (since 2√2x is positive)
x^2 + 2√2 *x +2 -2 − 16 = 0
A = x
B = √2

(X+√2)^2-(3√2)^2 = 0
A^2-B^2 = (A+B)(A-B)
(X+√2+3√2)(X+√2-3√2) = 0
(X+4√2)(x-2√2) = 0
X = √8 or x = -√32 
(Insufficient)

Answer is A

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sood1596 · Answer

Statement 1 is sufficient. 
Statement 2 returns two values for X.

Answer - A

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GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • We need to find if   x = \sqrt{8}

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:    x^2 − 4√2*x + 8 = 0  
 •   x^2 – 4\sqrt{2}*x + 8 = 0  
•  ⟹ x^2 – 2*2\sqrt{2} + (\sqrt{2})^2 = 0 
•  ⟹ (x – 2\sqrt{2})^2 = 0 
•   ⟹ x = 2\sqrt{2} = \sqrt{8}  
Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E.

Statement 2:    x^2 + 2√2 *x − 16 = 0  
 •   x^2 + 2√2 *x − 16 = 0  
•   ⟹ x^2 + 2*\sqrt{2}*x + 2 = 18  
•   ⟹ ( x + \sqrt{2})^2 = 18  
•   ⟹ x = -\sqrt{2} + 3\sqrt{2} \space or \space x = -\sqrt{2} - 3\sqrt{2}  
• Here we are getting two different values of x.
 o If   ⟹ x = 2\sqrt{2}⟹ x = \sqrt{8} 
o If   ⟹ x = -\sqrt{2} - 3\sqrt{2} = -4\sqrt{2} ⟹ x≠\sqrt{8}  
• The above two results are contradictory.  
Hence statement 2 is not sufficient.
Thus, the correct answer is  Option A.

GMATinsight · Answer

Question: Is x = √8 ?

STatement (1) x^2 − 4√2*x + 8 = 0

i.e.  (x- √8)^2 = 0 
 x = √8

SUFFICIENT  
 
 STatement (2) x^2 + 2√2 *x − 16 = 0

i.e.  (x+√2)^2 - 18 = 0

i.e.  (x+√2)^2 = 18

i.e.  x+√2 = 3√2  or  x+√2 = -3√2

i.e.  x = √8  YES or  x = -4√2  NO

NOT SUFFICIENT

Answer: Option A

KaramveerBakshi · Answer

We need to find if x = √8?

Statements:

(1) x^2 − 4√2*x + 8 = 0
Solving, we have
x^2 − (2)(x)(2√2) + (2√2)^2 = 0
(x-2√2)^2 = 0
Therefore, x = 2√2 = √8
  Sufficient

(2) x^2 + 2√2 *x − 16 = 0
Solving we get,
x^2 + (2)(√2)(x) − 16 = 0
x^2 + (2)(√2)(x) +2 - 2 - 16 = 0
(x+√2)^2 = 18
x+√2 = +-√18 = +-3√2
Therefore, x = 2√2 = √8 or x = -4√2
 Insufficient

Hence, the answer is Option (A)

Is x = √8 ? (1) x^2 − 4√2x + 8 = 0 (2) x^2 + 2√2 x − 16 = 0

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