student22 wrote:My bad, by "!=" I mean not equal to. I don't know how to do the standard mathematical line through an equal sign, so I just used the programming version of "not equal to"
Even if it were a '!' (factorial) instead of '≠' (not equal to), there were many possibilities for x, y values apart from just 1 and -1. When x is 2, y is -2, x is 3, y is -6, x is 6, y is -720 etc. Nevertheless, you can copy the '≠' (not equal to) sign for future posts.
If x ≠-y, then x + y ≠0, and hence (x - y)/(x + y) is defined, and it would be greater than 1 in the following two cases, otherwise NOT:
Case 1: When each of (x - y) and (x + y) is positive and (x - y) > (x + y). This is possible only when x >0, x > -y, and y < 0.
Case 2: When each of (x - y) and (x + y) is negative and (x - y) < (x + y). This is possible only when x < y, x < 0, and few considerations for y as well.
A bird-eye-view now over the question can make us feel that no statement alone is sufficient. If taken together, we could tempt to the case 1 above and could say, YES, [spoiler]
C[/spoiler]; but NO! Case 1 also wants to corroborate whether x > -y or not. Hence, [spoiler]
still insufficient
E[/spoiler]
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
