Problem Solving

sam2304 wrote:If x ≠ 0 and x/|x| < x, which of the following must be true ?

A.x > 1
B.x > −1
C.|x| < 1
D.|x| > 1
E.−1 < x < 0

Anurag@Gurome wrote:

sam2304 wrote:If x ≠ 0 and x/|x| < x, which of the following must be true ?

For x > 0, |x| = x ---> x/|x| = x/x = 1

• Now if |x|/x < x, then 1 < x

For x < 0, |x| = -x ---> x/|x| = x/(-x) = -1

• Now if |x|/x < x, then -1 < x. Hence, -1 < x < 0

Therefore, either -1 < x < 0 or x > 1.

In both cases, x > -1

The correct answer is B.

sam2304 wrote:If x ≠ 0 and x/|x| < x, which of the following must be true ?

A.x > 1
B.x > −1
C.|x| < 1
D.|x| > 1
E.−1 < x < 0

Anurag@Gurome wrote: B. x > -1 ---> This is true about x for both the ranges.

Keep in mind that what the question have asked is not same as "For what range of values of x, x/|x| < x?"

Anurag@Gurome wrote:

sam2304 wrote:How is it, x > -1 from both the statements ?

Because x > 1 means x is greater than -1. Also -1 < x < 0 means x greater than -1.

The question asked which of the following must be true for x. None of the options other than C, i.e. x > -1 is true about x. To make it more clear,

• A. x > 1 ---> If -1 < x < 0, then this is not true about x.
  B. x > -1 ---> This is true about x for both the ranges.
  C. |x| < 1 ---> If x > 1, then this is not true about x.
  D. |x| > 1 ---> If -1 < x < 0, then this is not true about x.
  E. -1 < x < 0 ---> If x > 1, then this is not true about x.

Keep in mind that what the question have asked is not same as "For what range of values of x, x/|x| < x?"

Hope that helps.

bubbliiiiiiii wrote: What if x = 1? This does not fit into the statement! Could you please help me what am I missing?