Is x 4?

Question

Is x > 4?

(1) (x + 1)^2 > 4
(2) (x - 1)^2 > 4

Bunuel · Answer

Is x>4? (1) (x+1)^2>4 Approach #1: (x+1)^2>4 --> x+1<-2 or x+1>2 --> x<-3 or x>1 . Not sufficient. Approach #2: (x+1)^2>4 --> x^2+2x-3>0 --> (x+3)(x-1)>0 --> x<-3 or x>1 . Not sufficient. Graphic representation: statement 1.gif True range of x: statement 1+.gif (2) (x-1)^2>4 Approach #1: (x-1)^2>4 --> x-1<-2 or x-1>2 --> x<-1 or x>3 . Not sufficient. Approach #2: (x-1)^2>4 --> x^2-2x-3>0 --> (x+1)(x-3)>0 --> x<-1 or x>3 . Not sufficient. Graphic representation: statement 2.gif True range of x: statement 2+.gif (1)+(2) Intersection of the ranges from (1) and (2) is x<-3 or x>3 : (1)+(2).gif Not sufficient. Answer: E. P.S. Of course if you notice that some big enough positive number, for example y=10>4 , satisfies both statements and gives an answer YES and some small enough negative number, for example y=-10<4 , also satisfies both statements and gives an answer NO you'll get the answer E right away.

metallicafan · Answer

+1 E

Stmnt (1): (x+1)^2 > 4 -------> |x+1| > 2
There are two possibilities:
x > 1 or x < -3
INSUFF

Stmnt (2): (x-1)^2 > 4 -------> |x-1| > 2
There are two possibilities:
x > 3 or x < -1
INSUFF

Combining (1) and (2): INSUFF too

ANSWER: E

Apex231 · Answer

is x > 4 ( x + 1 ) ^ 2 > 4 |x+1| > 2 x > 1 or x< -3 Not sufficient. ( x - 1 ) ^ 2 > 4 |x-1| > 2 x>3 or x<-1 Not sufficient. (1) + (2) x < -3 or x >3 Two ranges, so Not sufficient

Bunuel · Answer

Bumping for review and further discussion.

stonecold · Answer

I see very long solutions above ...
Here was my approach
use the identity (a+b) * (a-b) = a^2-b^2
and finding the range we can see that x=100 and x=-100 satisfy both the statements.
hence E is sufficient

GGMU · Answer

Bunuel Though I got the ans correct, the solutions that I am getting are: x>3 or x>-1 and x>1 or x>-3
I am confused how everyone is getting x<−1 or x>3 and x<−3 or x>1. As far as I know we flip the signs when we multiply or divide. Am I missing some trick?

Bunuel · Answer

x > 3 and x > -1 does not make sense. What range are you getting with it?

Check below links:

Inequalities Made Easy!

Solving Quadratic Inequalities - Graphic Approach 
 Inequality tips

Hope it helps.

GGMU · Answer

Thanks  Bunuel

The links helped a lot..I understood my mistake...

ydmuley · Answer

Is x > 4?

(1) (x + 1)^2 > 4

x > 1
x>-3

As we are getting answer to the question x > 4 as YES and NO =====> (1) is  Not Sufficient

(2) (x - 1)^2 > 4

x>3
x>1

As we are getting answer to the question x > 4 as YES and NO =====>  (2) is Not Sufficient

Even after combining we get x > 3 as the maximum one, and again we get YES and NO answers to the question is x > 4.

Hence, Answer is E

harikrish · Answer

Statement 1: it is valid for all x>2 and x<-3. Therefore it is insufficient. Statement 2: It is valid for all x>3 and x<-2. Therefore it is insufficient. Combine: X can be -5,4 or 6 So we can't definitely tell if x>4 Therefore option E

Basshead · Answer

Is x > 4 ? (1) (x + 1)^2 > 4 | x + 1 | > 2 x > 1 x < -3 Insufficient. (2) (x - 1)^2 > 4 | x - 1 | > 2 x > 3 x < -1 Insufficient. (1+2) x > 3 or x < -3 Insufficient. Answer is E.

Is x > 4?

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GMAT Data Sufficiency (DS) Questions

Is x > 4?

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