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# If x/|x| < x, which of the following must be true about

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18 Sep 2010, 04:56
gurpreetsingh wrote:
x>-1 and x not equal to 0 and 1 - This is given. => x could be 2 , 3, 4,5,6,7----- so on
Every value of x should satisfy the answer.

Q1. Which of the following is always true.

1. X>2 -> is this always true? -> This is always true expect for x = 2.

If I take x = 2 using the inequality x/|x| < x , x =2 does not satisfy x>2.

I hope it makes sense.

Bunnel my point is every value that satisfy x/|x| < x should satisfy the answer choice.

Since 2 satisfies x/|x| < x but no x>2, x>2 can not be the answer...

Subset reason : All the values of x that satisfy x/|x| < x should be a subset of x>2
=> if x/|x| < x satisfy n values, then all those n values should be satisfied by x>2.

gurpreet I said that options B and E are always true. Option B says x>-1 and not x>2. x>2 is option A, which is not always true.
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18 Sep 2010, 05:01
oh I m sry ! my bad !! I apologize

but x =1 also does not satisfy x/|x| < x ...which is part of x>-1

if x>-1 then x=1 must satisfy x/|x| < x
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18 Sep 2010, 05:14
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gurpreetsingh wrote:
oh I m sry ! my bad !! I apologize

but x =1 also does not satisfy x/|x| < x ...which is part of x>-1

if x>-1 then x=1 must satisfy x/|x| < x

No-no-no-no. It should be vise-versa. As I said it seems that you are confused with the logic of the question, please see the examples in the end of my first post for examples.

If the solutions of $$\frac{x}{|x|}< x$$ satisfy a statement than it would mean that this statement is always true.

For ANY $$x$$ from the set {2, 3, 4, ...} (which is the solution) statements B ($$x>-1$$) and E ($$|x|^2>1$$) are TRUE or in other words solutions satisfy both B and E.

As I wrote in my previous post:
The question asks which of the following MUST be true, or which of the following is ALWAYS true. For such kind of questions if you can prove that A STATEMENT is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

So can you give me an example of $$x$$ which satisfies $$\frac{x}{|x|}< x$$ and is not more than -1?
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18 Sep 2010, 05:44
Check similar question about the same concept: inequality-87922.html#p783945
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18 Sep 2010, 06:09
Thanks Bunnel for your Patience. +1

I got it now !!

the initial given statement itself says that x can not be equal to 0 and 1 and is > -1.

so all the other numbers will be >-1.

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Re: If x/|x| < x, which of the following must be true about [#permalink]

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25 Feb 2015, 23:41
tkarthi4u wrote:
If x/|x| < x, which of the following must be true about integer x? (x is not equal to 0)

A. x > 2
B. x > -1
C. |x| < 1
D. |x| = 1
E. |x|^2 > 1

Please change the OA to E
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Re: If x/|x| < x, which of the following must be true about   [#permalink] 25 Feb 2015, 23:41

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