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 answersatishchandra 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
"Anyways, x>1 is not the only solution for this problem.kanwar86 wrote:IMO, C (my mistake...A seems correct here)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
"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: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.
"kanwar86 wrote: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: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.
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)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: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: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.
"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.
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.
We can solve this problem by picking numbers to eliminate 4 of the 5 choices.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
This clarifies my doubt about why Can't A be the answer.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.
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.
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.Stuart Kovinsky wrote: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.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
"
