Week 5, Day 1: Quantitative Comparison

Chapter 16: Quantitative Comparisons

Quantitative Comparison questions include two mathematical expressions, usually following a question stem which applies to both expressions (quantity A and quantity B).

·       You usually don’t need to calculate a specific answer, just determine which is greater, whether they are equal, or if you need more information

·       Memorize these answer choices!

·       Do not rely on the calculator – avoid unnecessary computations

·       Be very careful with geometric figures, as they are not necessarily drawn to scale

·       The last answer choice D should ONLY be selected if no computation is possible OR if you can generate multiple different relationships (e.g., A is greater if x > 2, but A is lesser if x = 2)

·       Always simplify the expressions as much as possible

·       Remember to plug in easy and different numbers to test the values of algebraic expressions (FROZEN = fractions, repeats, ones, zero, extremes, negatives). IF you get different results depending on which value you plug in (e.g., B is greater with fractions, but A is greater with whole numbers), THEN the answer must be D.

 

ETS Strategy:

Use A ? B, and then try to figure out if ? = >, <, or =

 

Kaplan Method:

1.     Analyze the question stem

a.      Look at the information centered above the two quantities (if any)

b.     Look at the two quantities

                                                    i.     Are they numbers, variables, or both?

                                                  ii.     If there is a numerical value as one quantity, D will be wrong

2.     Approach strategically

a.      Process of Elimination

b.     Simplification

c.      Estimation

d.     Picking Numbers (FROZEN)

e.      Memorize the answer choices

                                                    i.     A = A is greater

                                                  ii.     B = B is greater

                                                iii.     C = A and B are equal

                                                iv.     D = not enough information

f.      When the quantities are variables, try to demonstrate that at least two different relationships are possible (so that the answer will be D)

g.     Try to make the two quantities look as similar as possible through eliminations and simplification

h.     Do the same thing to both quantities to reduce them and make comparison easier

i.       MAKE NO ASSUMPTIONS

                                                    i.     Diagrams are NOT to scale

                                                  ii.     NOT all variables are positive

                                                iii.     NOT all variables are integers or whole numbers

                                                iv.     Consider multiple possibilities: +/-, fractions, 1, 0, and -1

j.       Don’t fall for lookalikes:

                                                    i.     Ö5x + Ö5x = 2Ö5x, NOT Ö10x

                                                  ii.     Be very careful with radicals, exponents, parentheses, etc.