If x 0, is x^2/x

Question

If x ≠ 0, is x^2/x < 1 ?

(1) x < 1
(2) x > −1

M36-113

Bunuel · Accepted Answer

Official Solution:

If  x ≠ 0 , is  \frac{x^2}{x} < 1  ? 
 
First of all, notice that  "is  \frac{x^2}{x} < 1  ?"  is equivalent to  "is  x < 1  ?"  because  \frac{x^2}{x} =x  for all  x .
 
(1)  x < 1 
 
Directly answers the question. Sufficient.
 
(2)  x > −1  
 
 x  can be less (for example, 1/2) as well as more than 1 (for example, 2). Not sufficient.

Answer: A

GMATinsight · Answer

Question:  is x^2/x < 1 ?

Sign of x^2/x will always assume the sign of x

Question REPHRASED:  is x < 1 ?

Statement 1 : x < 1

SUFFICIENT

Statement 2 : x > −1

x may be less than 1 or greater than 1 hence

NOT SUFFICIENT

Answer: Option A

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 •  x ≠ 0 
• We need to find if  \frac{x^2}{x }< 1 
 o Or,  \frac{x^2}{x }– 1 < 0 ⟹\frac{ x(x-1)}{x} < 0 
o If we represent the above inequality on number line, we will get below ranges.
 https://www.dropbox.com/s/jl8mvh9miyr40ic/quadratic.png?dl=1 
o Thus, on combining the ranges of x and x(x -1), we get,  \frac{x(x-1)}{x} < 0 ⟹ x < 1   
Therefore, we only need to find if x < 1.
 Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  x < 1
 • This is exactly same as our analysis. 
Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E.
 Statement 2:  x > -1
 • However, we cannot be sure if x < 1 or not. For example x can be -0.5 which is less than 1 but x can also be 2 which is greater than 1. 
Hence, statement 2 is NOT sufficient and we can eliminate answer Option D.
Thus, the correct answer is  Option A.

Gokul20 · Answer

Hi  Bunuel ,
Can you please post the solution to this problem. I got the answer wrong

Bunuel · Answer

The solutions above are correct, the OA is A. Do you have any specific question?

Gokul20 · Answer

Oh ! Sorry for the confusion. I remember seeing the Answer as E !! May be I missed it !

sampad · Answer

I think when x(x-1)<0 then the value of x will be the range of 0<x<1. In this case the answer should be E. Because ST 1 is only satisfying one condition. Not the second one.

Bunuel · Answer

\frac{x^2}{x} < 1 is equivalent to \frac{x(x - 1)}{x} < 0 , not to x(x-1)<0 , and \frac{x(x - 1)}{x} < 0 ( \frac{x^2}{x} < 1 ) is true for x < 1, so (1) is sufficient. You cannot multiply \frac{x^2}{x} < 1 by x to get x^2 < x, because you don't know the sign of x: if x > 0, yes, you get x^2 < x but if x < 0, then you get x^2 > x (flip the sign when multiplying by a negative value).

bumpbot · Answer

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If x 0, is x^2/x < 1 ? (1) x < 1 (2) x > 1

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