If x 0, is |x|/x

Question

If x ≠ 0, is |x|/x < 1?

(1) x < 1
(2) x > −1

M36-114

Kulka123 · Answer

E because 
Modx/x is 1 for all positives and -1 for all negatives.

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Dragongirl24 · Answer

Statement 1: x<1
x can be any value from -1 and below as x cannot be zero
With the given condition, |x|/x<1, 
|-1|/-1= -1 <1 statement is true
|-10|/-1=-10<1, statement is true

Statement shall remain true for any value of x<1.

Hence 1 is sufficient

Statement 2: X>-1
X can be any value from 1

|1|/1= 1 , so the equation |x|/x<1, is not satisfied hence answer is false
|10|/10=1,the equation |x|/x<1, is not satisfied hence answer is false.
For any value of x, answer is false.
Hence statement 2 is sufficient.

Answer is D

ayushk09 · Answer

Please check as x can be fraction also....let x be -.1
Then |x| will be .1
|X|/x will be less than 1(-ve in this case)...however when x is positive function will be always 1....so no answer from 2 while 1 nullify as function will be always 1...so correct choice seems to be E

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Mo2men · Answer

Let's test some values

(1) x < 1

x=1/2.............Answer is No

x=-1/2.............Answer is Yes

Insufficient

2) x > −1

x=1/2.............Answer is No

x=-1/2.............Answer is Yes

Insufficient

combining 1 & 2

-1 < x <1..........We can use values above

Insufficient

Answer: E

GMATinsight · Answer

Question : is |x|/x < 1?

|x|/x can only be either +1 (if x is positive) or -1 (if x is Negative)
For |x|/x< 1, x must be negative

Question REPHRASED : is x < 0?

Statement 1 : x < 1

NOT SUFFICIENT

Statement 2 : x > -1

NOT SUFFICIENT

COmbining the statements

-1 < x < 1

Still x may be positive as well as Negative hence

NOT SUFFICIENT

Answer: Option E

GMATWhizTeam · Answer

Solution Step 1: Analyse Question Stem • x ≠ 0 • We need to find if \frac{|x|}{x} < 1 o Case 1: If x < 0 , then \frac{|x|}{x }= \frac{-x}{x }= -1 < 1 o Case 2: If x > 0 then \frac{|x|}{x} = \frac{x}{x} = 1 So, to find if \frac{|x|}{x} < 1 we actually need to find if x < 0. Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE Statement 1: x < 1 • We cannot be sure from this statement that x < 0. For example, x can be 0.5 or it can be -0.5 Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D. Statement 2: x > -1 • Here also, we cannot be sure from this statement that x < 0. For example, x can be 0.5 or it can be -0.5 Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B. Step 3: Analyse Statements by combining. • From statement 1: x < 1 • From statement 2: x > -1 • On combining both statements, we get, -1 < x < 1 o Still we cannot be sure that x < 0. For example, x can be 0.5 or it can be -0.5 Thus, the correct answer is Option E.

Bunuel · Answer

Official Solution: If x ≠ 0 , is \frac{|x|}{x} < 1 ? When x < 0 , then |x|=-x , and in this case \frac{|x|}{x}=\frac{-x}{x} = -1 . So, when x < 0 , the answer to the question is always YES. When x > 0 , then |x|=x , and in this case \frac{|x|}{x}=\frac{x}{x} = 1 . So, when x > 0 , the answer to the question is always NO. (1) x < 1 . Not sufficient. (2) x > −1 . Not sufficient. (1)+(2) We get -1 < x < 1 . We still cannot say whether x is negative or positive. Not sufficient. Answer: E

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

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