Absolute

[MBA.Aspirant]

If x/||x||< x , which of the following must be true about x , (x is not 0)

(A)|x|=1
(B)|x|<1
(C)x>2
(D)x>-1

[Anurag@Gurome]

If x/||x||< x , which of the following must be true about x , (x is not 0)

(A)|x|=1
(B)|x|<1
(C)x>2
(D)x>-1

If x is positive, x/||x|| < x ----> x/x < x ----> x > 1
If x is negative, x/||x|| < x ----> x/(-x) < x ----> x > -1

Thus we see that if x satisfies the given condition then x > 1 if x is positive and x > -1 if x is negative. In any of the cases x is greater than -1.

The correct answer is D.

[abhi0697]

x>1 and x>-1 => In both cases, x>1

So IMO it should be C where it says x>2.

[Anurag@Gurome]

x>1 and x>-1 => In both cases, x>1

So IMO it should be C where it says x>2.

Hi,

The problem says if x satisfies the condition then which of the options must be true about x. Note that x = -0.5 satisfies the given condition, but according to your solution x = -0.5 is not greater than 2.[/b]