Hi,

I often get stuck here or spend way too much time when going through the CLA process for DS questions - especially when it comes to listing numbers that meet the criterias of the question stem & statements that have multiple variables.

Here's an example:

x-y-z < 0 : is z < 1

(1) z < x-y-1
(2) x-y-1>0

Any help would be greatly appreciated.

Thanks

well, the first thing you should do is look for SUBSTITUTIONS or COMBINATIONS OF VARIABLES. if you look for those, then the resultant simplifications will greatly ease the amount of plugging/guessing required of you - or, if the transformation cancels out enough quantities, eliminate that plugging/guessing altogether.

for instance, take statement (2) here.
notice that there's the combination (x - y) in both statement (2) and the question prompt.
therefore, solve for this combination in both parts:
x - y < z (from the problem statement)
x - y > 1 (from statement 2)
since (x - y) is less than z but more than 1, it follows that z is greater than 1; this is sufficient.

you should ONLY look to plug in numbers if these sorts of manipulations fail; it's unlikely that a problem geared toward plugging in numbers would require the plugging in of LARGE quantities of numbers.

How do we deal with the first inequality?

z<x-y-1

it appears that that statement hasn't been transcribed correctly; see the result below. maybe the inequality sign was transcribed incorrectly, or ... ?

--

here's a useful general rule.

GENERAL RULE: YOU CAN ADD TWO INEQUALITIES IF THE INEQUALITY SIGNS FACE IN THE SAME DIRECTION.

the problem statement says that x - y - z < 0. since this one is also "less than", you can add them, giving
(x - y - z) + z < 0 + (x - y - 1)
x - y < x - y - 1
0 < -1
this is a contradiction, indicating that either the problem statement or statement 1 (or possibly both, but at least one of them) has been transcribed incorrectly.

whoops