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Manager  Joined: 10 Nov 2010
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If a= -0.3, which of the following is true?  [#permalink]

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Question Stats: 59% (00:54) correct 41% (00:45) wrong based on 449 sessions

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If a= -0.3, which of the following is true?

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

Originally posted by GMATD11 on 13 Feb 2011, 09:53.
Last edited by Bunuel on 11 Aug 2015, 01:24, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If a= -0.3, which of the following is true?  [#permalink]

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a = -0.3 a^2 = 0.09 a^3 = -0.027

So a<a^3<a^2
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Re: If a= -0.3, which of the following is true?  [#permalink]

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a^2 will be highest, so it should be between b and e. and since -1<a<0 the cube will be more close to 0 than a, this gives b.
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Re: If a= -0.3, which of the following is true?  [#permalink]

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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.

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

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GMATD11 wrote:
If a= -0.3, which of the following is true?

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

As I just got reminded the hard way, I am most accurate with these problems when I use fractions and a number line.

a= -$$\frac{3}{10}$$

a$$^2$$ = (-$$\frac{3}{10})^2$$ = $$\frac{9}{100}$$, or, when the numbers are unwieldy, "some +"

a$$^3$$ = (-$$\frac{3}{10}$$)$$^3$$ = -$$\frac{27}{1000}$$

___-$$\frac{3}{10}$$ ___-$$\frac{27}{1000}$$__0___$$\frac{9}{100}$$___1_____

____$$a$$______$$a^3$$____|____$$a^2$$____|_____

$$a < a^3 < a^2$$

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

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GMATD11 wrote:
If a= -0.3, which of the following is true?

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

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

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_________________ Re: If a= -0.3, which of the following is true?   [#permalink] 02 Apr 2020, 05:37

# If a= -0.3, which of the following is true?  