Comparing relationship between variables

[mobenny]

Hi,

I was doing a few problems in the Green Quant book yesterday and I noticed that I have difficulty with a problem type where it is necessary to compare the relationship between multiple variables. i.e. the question may ask to rank in order from smallest to largest three variables. Each variable will be expressed algebraically in a different way. Or, another problem (data sufficiency) asked about the relationship of three variables and the value of the range.

I have trouble with these problems and I am wondering what is essential to understand about this problem type.

Thanks.

[JonathanSchneider]

Good question.

PS#Q83 is a good example (from the green book, Problem Solving). For that one, you simply need to determine all of the relationships. The easiest method would be to line up what you can in one long string. For example, you can say that "u > t > r > q." You don't know where the s fits in exactly, but it must be greater than t, so place that below the multiple inequality. From there make the proper determinations.

PS#Q122 is a very similar problem. This is again a Number Properties question. For such questions, you are best off using a conceptual approach (rather than picking numbers).

One final thought: most of these problems involve inequalities. When you are told that a certain variable is greater than, or less than, some number, you can insert that as "GT#" or "LT#" into the problem. For example, for PS#Q134, you can insert "GT0" for "d."