GRE-Style: Quantitative Comparison — Number Properties

GRE Quantitative · Axiom Academy

EXAMPLE GRE-Style: Quantitative Comparison — Number Properties Solve a Quantitative Comparison question by reasoning about number properties instead of pure computation. Given n = -3 , compare the two columns below. Choose whether Column A is greater, Column B is greater, the columns are equal, or the relationship cannot be determined. Nice work — you solved a Quantitative Comparison question by computing both columns and reasoning about number properties. A few principles worth keeping for every QC question: Even vs. odd powers of a negative: raising a negative number to an EVEN power always gives a positive result, while an ODD power keeps the negative sign. That single fact is why Column A beat Column B here — (-3)^2 = 9 is positive, but (-3)^3 = -27 is still negative. Squaring a proper fraction shrinks it: for , . So ends up bigger than — squaring doesn't always mean "bigger." A bigger number doesn't mean more prime factors: and both have exactly 3 distinct prime factors, even though — always factor completely rather than assuming. Result: with n=-3 , Column A ( n^2=9 ) is greater than Column B ( n^3=-27 ), so the answer is Column A is greater . On Quantitative Comparison questions, compute both columns carefully before choosing — number-property traps like sign, size, and parity are exactly what the GRE is testing.

This is the written version of the interactive lesson above. See the full GRE Quantitative course.