beeparoo wrote:Searched, but could not find this question in the forum...
If a > 0, b > 0, and (b + y) does not = 0, is
(a + y)/(b + y) < a/b ?
1) a < b
2) y < 0
with a problem like this, it's probably best to go with strategic number picking, UNLESS you are ABSOLUTELY AMAZING at algebra - meaning that you can manipulate variables flawlessly, and you are possessed of an equally flawless understanding of signs, inequalities, and the like (and the way they transform under different operations).
if you're going to pick numbers here, then, as with other number-picking operations, you should
pick numbers that are relevant to the operations at the heart of the problem. in other words, you should NOT pick numbers at random.
here, the problem is centered around an inequality involving two ratios. such inequalities differ from other inequalities principally in that their behavior changes radically according to the
signs of the numerators and denominators.
therefore, you want to pick numbers that will mess with the signs of those numerators/denominators in different ways.
to wit:
taking both conditions together,
let a = 2, b = 4
(a) take y = -1. then a+y and b+y are still positive.
this yields 1/3, which IS less than 2/4.
(b) take y = -3. then a+y is negative, but b+y is still positive.
this yields -1/1, which IS less than 2/4 (because it's negative).
(c) take y = -5. then both a+y and b+y are negative.
this yields -3/-1 = 3, which is NOT less than 2/4.
insufficient
answer = e
there it is, folks: even number picking is decidedly
nonrandom. it depends almost entirely on the
context of the problem; the more you understand about the underlying number properties, the more likely you are to nail the number picking.