Yes/No DS questions - picking numbers for multiple variables

by **Guest** Sat Jun 07, 2008 12:42 pm

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

by **RonPurewal** Thu Jun 12, 2008 6:11 am

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.

by **Guest** Sat Aug 09, 2008 5:24 pm

How do we deal with the first inequality?

z<x-y-1

by **RonPurewal** Tue Sep 09, 2008 6:52 am

Anonymous Wrote: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