bubbliiiiiiii wrote:Q. X / |X| < X. Which of the following must be true about integer X? X is not equal to 0.
A. X > 1
B. X > -1
C. |X| < 1
D. |X| = 1
E.|X|^2 > 1
OA Later.
Please post explanations.
My working:
Q. X / |X| < X
Since X is there on both sides, irrespective of X being positive or negative we can cancel out X on both sides.
Question rephrased:
1/|X| < 1 which option must be true.
=> 1 < |X|
=> 1 < X or -1 > X
IMO A
The mistake is highlighted
above.
We have X/|X| < X
Since we have X on both sides, it's tempting to divide both sides by X (to get 1/|X| < 1).
HOWEVER, if X is negative, then we must reverse the direction of the inequality sign (to get 1/|X|
> 1).
So, a complete solution must consider the case where X is positive, and the case where X is negative.
Case where X is positive
Take: X/|X| < X
Divide both sides by X to get: 1/|X| < 1
Multiply both sides by |X| to get: 1 < |X|
This means that
X > 1 or
X < -1
IMPORTANT: We started with the premise that
X is positive, so we can rule out the possibility that
X < -1, which leaves us with only
X > 1
Case where X is negative
Take: X/|X| < X
Divide both sides by X to get: 1/|X| > 1
Multiply both sides by |X| to get: 1 > |X|
This means that
-1 < X < 1
IMPORTANT: There are no
integer values of X that satisfy this inequality.
So, all we can conclude here is that
X > 1
In other words,
integer x can equal 2, 3, 4, 5...
A. X > 1 This works (KEEP A)
B. X > -1 If X can be 2,3,4 etc, then X is definitely greater than -1 (KEEP B)
C. |X| < 1 this suggests that X must equal 0 - not true (ELIMINATE C)
D. |X| = 1 this suggests that X equals 1 or -1. not true (ELIMINATE D)
E.|X|^2 > 1 If X can be 2,3,4 etc, then |X| is definitely greater than 1 (KEEP E)
Looks like we have more than 1 correct answer:
A, B and E
Cheers,
Brent
