Hi all,
I often come across a DS problem involving inequalities, and though I try to systematically solve it, I either find myself resorting to plugging in, or getting the problem wrong if I don't.
Here's an example: x does not equal -y, is (x-y)/(x+y)>1?
(1) x>0
(2) y<0
Seeing this setup, I would immediately try and simplify the expression. I would group the problem into two scenarios: either (x+y) is (a) positive or (b) negative.
(a) If (x+y) is positive, then you can multiply both sides by that term without flipping the sign, hence the question is asking: is (x-y)>(x+y)? This simplifies further to: is -y>y? I guess this would imply that y must be negative.
(b) If (x+y) is negative, then you must flip the sign after multiplying. The question becomes: is (x-y)<(x+y)? This simplifies to: is -y<y? I guess this would imply that y must be positive.
Statement (1) seems insufficient, since x cancels out in both scenarios. Statement (2) would seem to address both scenarios, and yield an answer.
However, checking by plugging in (as well as looking at the answer) indicates that the answer is E. I've decided maybe I'm forgetting something fundamental about simplifying algebraic inequalities, and so my systematic attempts (as opposed to plugging in) are faulty. Or, maybe Ive set it up correctly but my logic is faulty. Can anyone let me know how they would approach an inequalities problem where one might create "scenarios" based on an algebraic inequality?
Thanks, your help is appreciated.
I often come across a DS problem involving inequalities, and though I try to systematically solve it, I either find myself resorting to plugging in, or getting the problem wrong if I don't.
Here's an example: x does not equal -y, is (x-y)/(x+y)>1?
(1) x>0
(2) y<0
Seeing this setup, I would immediately try and simplify the expression. I would group the problem into two scenarios: either (x+y) is (a) positive or (b) negative.
(a) If (x+y) is positive, then you can multiply both sides by that term without flipping the sign, hence the question is asking: is (x-y)>(x+y)? This simplifies further to: is -y>y? I guess this would imply that y must be negative.
(b) If (x+y) is negative, then you must flip the sign after multiplying. The question becomes: is (x-y)<(x+y)? This simplifies to: is -y<y? I guess this would imply that y must be positive.
Statement (1) seems insufficient, since x cancels out in both scenarios. Statement (2) would seem to address both scenarios, and yield an answer.
However, checking by plugging in (as well as looking at the answer) indicates that the answer is E. I've decided maybe I'm forgetting something fundamental about simplifying algebraic inequalities, and so my systematic attempts (as opposed to plugging in) are faulty. Or, maybe Ive set it up correctly but my logic is faulty. Can anyone let me know how they would approach an inequalities problem where one might create "scenarios" based on an algebraic inequality?
Thanks, your help is appreciated.
