Problem Solving

If x/lxl<x, which of the following must be true about x
(Note: Read lxl as modulus x)

A) x>1
B) x>-1
C) lxl<1
D) lxl = 1
E) lxl^2 > 1

plug in -> |x|, x<0, x=0, x>0
IOM a

satishchandra wrote:If x/lxl<x, which of the following must be true about x
(Note: Read lxl as modulus x)

A) x>1
B) x>-1
C) lxl<1
D) lxl = 1
E) lxl^2 > 1

satishchandra wrote:If x/lxl<x, which of the following must be true about x
(Note: Read lxl as modulus x)

A) x>1
B) x>-1
C) lxl<1
D) lxl = 1
E) lxl^2 > 1

IMO, C is the correct answer

kanwar86 wrote:

satishchandra wrote:If x/lxl<x, which of the following must be true about x
(Note: Read lxl as modulus x)

A) x>1
B) x>-1
C) lxl<1
D) lxl = 1
E) lxl^2 > 1

IMO, C (my mistake...A seems correct here)

Anyways, x>1 is not the only solution for this problem.
Consider, -1<x<0 (considering x is not an integer as it has not been mentioned in the question)
-0.5/|-0.5|=-1<-0.5
Hence, (-1<x<0 U x>1) is the complete solution of this question.
We can't just say x is always greater than 1 as is stated in the question (must be true about x)

*Kindly correct me if i am wrong.

Math takes patience to read the QUESTION carefully to answer what it ASKS - never get tired to repeat to myself

among choices listed A-E, A is "must" ans.

x can take values from (-1 to 0) and ( 1 to infinity)

Answer should be B

A does not cover the (-1 to 0) range.

shankar.ashwin wrote:x can take values from (-1 to 0) and ( 1 to infinity)

Answer should be B

A does not cover the (-1 to 0) range.

You have correctly reflected the solution on number line. However, option B) also includes the range 0<x<1, which is not a part of the solution. Hence, A is the only correct option left in this case.

The question asks which of the following is true of x and not for a value of x.

So any value of 'x' can be classified under x > -1. But when x = say -1/2, A does not define it. So A need not necessarily be valid ALWAYS.

Also x cannot take values from (0-1) but whatever values 'x' takes can be defined under x>-1 IMO.

kanwar86 wrote:

shankar.ashwin wrote:x can take values from (-1 to 0) and ( 1 to infinity)

Answer should be B

A does not cover the (-1 to 0) range.

You have correctly reflected the solution on number line. However, option B) also includes the range 0<x<1, which is not a part of the solution. Hence, A is the only correct option left in this case.

shankar.ashwin wrote:The question asks which of the following is true of x and not for a value of x.

So any value of 'x' can be classified under x > -1. But when x = say -1/2, A does not define it. So A need not necessarily be valid ALWAYS.

Also x cannot take values from (0-1) but whatever values 'x' takes can be defined under x>-1 IMO.

kanwar86 wrote:

shankar.ashwin wrote:x can take values from (-1 to 0) and ( 1 to infinity)

Answer should be B

A does not cover the (-1 to 0) range.

You have correctly reflected the solution on number line. However, option B) also includes the range 0<x<1, which is not a part of the solution. Hence, A is the only correct option left in this case.

The question already gives us a constraint that is If x/lxl<x. Whatever be the value of x, it must satisfy the given constraint. Under that constraint, the only range that satisfies the inequality for all its values is A) and not B)
Kindly correct me if i am wrong.

As you have previously mentioned if x was to take a value of -1/2. 'A' will not hold true and A cannot be the answer.

We just say x lies between (-1 and infinity) in B, ofcourse x cannot take (0-1), but whatever value 'x' takes is defined under x>-1.

We do not find the solution from options, solution is already found from the question, the answer choices just provide the range for the solution.

By choosing 'A' we restrict the range by 1.

kanwar86 wrote: The question already gives us a constraint that is If x/lxl<x. Whatever be the value of x, it must satisfy the given constraint. Under that constraint, the only range that satisfies the inequality for all its values is A) and not B)
Kindly correct me if i am wrong.

in order for us not to get stuck on this q., let's resume about "must" be cases
Can we define a value of x within the range x>1 which is not true for the given inequality x/|x|<x? ans. No - must be true for A)
Can we do so for the range x>-1, ans. Yes, 0 is not right fit (undefined denominator), the range 0<x<1 is outbound

a

and please post OA to conclude about this q.

shankar.ashwin wrote:As you have previously mentioned if x was to take a value of -1/2. 'A' will not hold true and A cannot be the answer.

We just say x lies between (-1 and infinity) in B, ofcourse x cannot take (0-1), but whatever value 'x' takes is defined under x>-1.

We do not find the solution from options, solution is already found from the question, the answer choices just provide the range for the solution.

By choosing 'A' we restrict the range by 1.

kanwar86 wrote: The question already gives us a constraint that is If x/lxl<x. Whatever be the value of x, it must satisfy the given constraint. Under that constraint, the only range that satisfies the inequality for all its values is A) and not B)
Kindly correct me if i am wrong.

satishchandra wrote:If x/lxl<x, which of the following must be true about x
(Note: Read lxl as modulus x)

A) x>1
B) x>-1
C) lxl<1
D) lxl = 1
E) lxl^2 > 1

We can solve this problem by picking numbers to eliminate 4 of the 5 choices.

First, let's pick a big positive number. If x=10, we get:

10/10 < 10,

which is certainly true. Therefore, x could be 10. Accordingly, we can eliminate (c) and (d).

We can now either pick another number to elminate (a) and (e); if x=1/2, then when we plug in we get:

(1/2)/(1/2) < 1/2,

which is also true. Since x could be 1/2, we can eliminate (a) and (e), leaving us with (b) as the correct choice.

No fancy algebra required!

It's also important to understand the question.

The question is NOT asking us "which of the following (in)equations defines all possible values of x"; it's simply asking us which of the following MUST be true given the constraint provided. Accordingly, even though (b) contains some numbers outside the range, it MUST be true that x is greater than -1.

Stuart Kovinsky wrote: It's also important to understand the question.

The question is NOT asking us "which of the following (in)equations defines all possible values of x"; it's simply asking us which of the following MUST be true given the constraint provided. Accordingly, even though (b) contains some numbers outside the range, it MUST be true that x is greater than -1.

This clarifies my doubt about why Can't A be the answer.
OA is indeed B

Stuart, when we substitute x = 1/2

We have (1/2)/(1/2) = 1

But 1 > 1/2, here. I think you meant to substitute x = -1/2, which helps us eliminate (a) and (e).

Stuart Kovinsky wrote:
We can now either pick another number to elminate (a) and (e); if x=1/2, then when we plug in we get:

(1/2)/(1/2) < 1/2,

which is also true. Since x could be 1/2, we can eliminate (a) and (e), leaving us with (b) as the correct choice.

Stuart Kovinsky wrote:

satishchandra wrote:If x/lxl<x, which of the following must be true about x
(Note: Read lxl as modulus x)

A) x>1
B) x>-1
C) lxl<1
D) lxl = 1
E) lxl^2 > 1

The question is NOT asking us "which of the following (in)equations defines all possible values of x"; it's simply asking us which of the following MUST be true given the constraint provided. Accordingly, even though (b) contains some numbers outside the range, it MUST be true that x is greater than -1.

Wow! That was enlightening and a good example of how doubts can be cleared by such healthy discussions. Thanks for bringing this problem on the forum.

Cheers team BTG!