Romil042 wrote:
Reni wrote:
Is |x| < 1 ?
(1) x/|x| < x
(2) x/|x| < 1
Hello,
Romil042. I just happened upon this question today and scrolled down to find your query. I think I can help clarify your confusion. I will respond inline below.
Romil042 wrote:
The statement asks whether the value of x is between -1 and 1.
So far, so good.
Romil042 wrote:
A:
x can fall into four domain,
x<-1
-1<x<0
0<x<1
1<x
for first and third the statement holds true, and not for second and fourth.
This statement at the end is inaccurate. Did you test values or make assumptions?
1) x < -1; test x = -2
\(\frac{x}{|x|} < x\)
\(\frac{(-2)}{|(-2)|} < (-2)\)
\(\frac{-2}{2} < -2\)
\(-1 < -2\)
XSince -1 is NOT less than -2, we know that
x CANNOT be less than -1.
2) -1 < x < 0; test x = -0.5
\(\frac{x}{|x|} < x\)
\(\frac{(-0.5)}{|(-0.5)|} < (-0.5)\)
\(\frac{-0.5}{0.5} < -0.5\)
\(-1 < -0.5\)
√We have found that
x CAN be between -1 and 0.
3) 0 < x < 1; test x = 0.5
\(\frac{x}{|x|} < x\)
\(\frac{(0.5)}{|(0.5)|} < (0.5)\)
\(\frac{0.5}{0.5} < 0.5\)
\(1 < 0.5\)
XSince 1 is NOT less than 0.5,
x CANNOT be between 0 and 1.
4) 1 < x; test x = 2
\(\frac{x}{|x|} < x\)
\(\frac{(2)}{|(2)|} < (2)\)
\(\frac{2}{2} < 2\)
\(1 < 2\)
√We have found that
x CAN be greater than 1. In short, we have two valid types of inputs based on Statement (1): x is either between -1 and 0 or it is greater than 1. Of course, we CANNOT answer the original question conclusively with this information.
a) If -1 < x < 0, |x| < 1
b) If x > 1, |x| > 1
Thus, Statement (1) on its own is NOT sufficient.
Romil042 wrote:
B:
It simply states that x<1.
Both the statement is insufficient. But by clubbing them still, we cannot say
because x<-1 satisfies and -1<x<0 too.
A bit confused why C is correct answer!
Of course, I hope you can see now that by combining the two statements, we can eliminate b) above, so it must be true that |x| < 1, and the answer is (C).
Good luck with your studies.
- Andrew