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Re: If a= -0.3, which of the following is true? [#permalink]

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10 Aug 2015, 23:30

Safe approach:

all options have a,a^2 and a^3

a^2 is positive. hence >a. Square of any number is greater than 0 (in GMAT) so a< a^2

just compare a and a^3 now. a^3 is negative as a is negative. And, on the negative side (left of zero) of the number line, the smaller is the magnitude of the negative numbers, the closer it is to zero and the greater it is. For example -0.00001 is greater than -0.1.

Re: If a= -0.3, which of the following is true? [#permalink]

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A. a < a^2 < a^3 B. a < a^3 < a^2 C. a^2 < a < a^3 D. a^2 < a^3 < a E. a^3 < a < a^2

We should keep in mind that when a negative number is raised to an even power, the result is positive, and when a negative number is raised to an odd power, the result is negative. Thus, a^2 is the largest among a, a^2, and a^3. Furthermore, we should keep in mind that when we raise a negative proper fraction to the third power, the result is a larger negative number. Thus, since a = -0.3:

a < a^3 < a^2, or -0.3 < -0.027 < 0.09

Answer: B
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