hey_thr67 wrote:In which quadrant of the coordinate plane does the point (x, y) lie?
(1) |xy| + x|y| + |x|y + xy > 0
(2) -x < -y < |y|
OA is D
How should I approach absolute questions, I took lot of time to conclude that -y < |y| is only true for y>0. Also what values to put confuses me.
4 quadrats ++ +- -+ --
1.|xy| + x|y| + |x|y + xy > 0
++ -> easy go satisfies the inequality
+- -> Will result in two -xy and two +xy = 0. Does not satisfy the inequality
-+ -> Same as above
-- -> Middle two will be -xy and end values will +xy, sum = 0
So point lies in Quadrant I. SUFF
(2) -x < -y < |y|
Break the inequality. -y < |y|, this will get satisfied only when y > 0, since -ve values will have both sides equal.
-x < -y => x > y => Multiplied by -1.
Now y > 0, and x > y so both are +ve. SUFF
IMO D.
Inequalities take a lot of time if you substitute values and check. Try approaching with general +ve, -ve values i.e +ve will satisfy this, -ve values will not.
I took lot of time to conclude that -y < |y| => Your query about this would also be easier if you had considered +ve or -ve value category of numbers. Test for values < 0, =0 and >0. Nothing more than that is needed. Do not substitute individual values and check. Always remember that when you have 0 in the inequality and no other numbers it tests for +ve -ve values as a whole and substituting individual numbers will slow you down.
