Please post questions in the correct format. The prompt is missing in your post.gary391 wrote: A) x>1
(B) x>−1
(C) |x|<1
(D) |x|=1
(E) |x|^2>1
B
You should do this way:
We are given that X/|X| < X.gary391 wrote:
If X/|X| < X which of the following must be true about X?
(A) x>1
(B) x>−1
(C) |x|<1
(D) |x|=1
(E) |x|^2>1
B
This question is a good case for testing smart values.
We can pick values: -2, -1, -1/2, 0, 1/2, 1, and 2.
1. If X = -2, X/|X| = -2/|-2| = -1; -1 is NOT less than X =-2. Thus, -2 does not fit.
2. If X = -1, X/|X| = -1/|-1| = -1; -1 is NOT less than X =-1. Thus, -1 does not fit.
3. If X = -1/2, X/|X| = -1/2/(|-1/2|) = -1; -1 < X =-1/2. Thus, X=-1/2 fits. Or we can conclude that X > -1.
4. If X = 0, X/|X| = 0/|0| = Indeterminable. So far, we can conclude that 0 > X > -1.
5. If X = 1/2, X/|X| = 1/2/(|1/2|) = 1; 1 is NOT less than X =1/2. Thus, X=1/2 does not fit. However, we can still conclude that 0 > X > -1.
6. If X = 1, X/|X| = 1/|1| = 1; 1 is NOT less than X =1. Thus, 1 does not fit. We can still conclude that 0 > X > -1.
7. If X = 2, X/|X| = 2/(|2|) = 1; 1 < X =2. Thus, X=2 fits. Or we can conclude that X > 1.
So either it is: 0 > X > -1 or X > 1. The best way to satisfy both the ranges is x > -1. It does not mean that all the values lying in x > -1 must satisfy the inequality.
Answer: B
Let us analyze each option.
A. X > 1; It is partly correct. This option is a contender for 'Could be True' type of question, but this one is a 'Must be True' type. If X lies between 0 and -1, this option fails.
C. |X|<1: This means that -1 < X < 1. Like option A, it is partly correct for -1 < X.
D. |X|=1: This means that X is either -1 or 1. It is outrightly incorrect.
E. |X|^2>1: |X|^2>1 => |X| > 1 => X < -1 or X > 1. Again this option is partly correct for X > 1.
Hope this helps!
-Jay
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