McGraw-Hill Education GRE 2019

Quantitative Comparison Strategy: Exponents

When solving Quantitative Comparison questions that test exponents, it is

essential to recall both the rules discussed previously, and just as importantly, the

exceptions to these rules. Remember that success on Quantitative Comparison

questions often requires testing for Choice D, which requires challenging your

assumptions.

When solving a Quantitative Comparison question where either the exponent

or the base is a variable, always test 0, 1, and −1. For example:

QUANTITY A QUANTITY B

2 x 5 x

If x is positive, then Column B will always be greater. But remember that the

exponents 0, 1, and −1 have interesting properties, so make sure to test those cases

to see whether Column B is always greater.

■ If x = 0, then the two quantities are equal.

■ If x = 1, then Column B is greater.

■ If x = −1, then Column A becomes^12 and Column B becomes^15 , meaning that

Column A is greater.

These different values give you contradictory relationships, and the answer is

therefore D. When comparing numbers expressed as exponents, make sure to

express each column using the same base:

QUANTITY A QUANTITY B

1, 000600 10 1,800

Rewrite 1,000 using a base of 10: 1,000 = 10^3. Substitute 10^3 for 1,000 in Column A,

and compare the new expressions:

QUANTITY A QUANTITY B

(10^3 )^600                                 10 1,800

Use your exponent rules for Column A: (10^3 )^600 = 101,800. The two columns are

equal, and the answer is therefore Choice C.

276 PART 4 ■ MATH REVIEW

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