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

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10 Jan 2014, 04:32

It's tricky. At first sight I thought hey this is easy, it can only be E. But i re-calculated and saw that -0.3^3 = -0.027 which is bigger than -0.3. So B. Hope I'm as smart in the GMAT and calculate first before picking an answer :D

When using an EVEN power, the negative terms "cancel out", so the result is always positive.

This holds true even when we use a negative power:

(-2)^(-2) = 1/(-2)(-2) = 1/4

The exception I mentioned earlier:

0^2 = (0)(0) = 0 Etc.

GMAT assassins aren't born, they're made, Rich

Thanks. I understood that. But the question says -0.3 and not (-0.3).

-0.3 = -1 * 0.3. Hence, whatever happens, it would be -1 * (0.3)^even number, hence the overall result would still be negative. Read this in the MGMAT Algebra book in the exponents chapter.

Before substituting in the value for 'A', let's look at 'A' to an even power:

A^2 = (A)(A) A^4 = (A)(A)(A)(A) Etc.

NOW, plug in the value for A.... (A = -0.3)....

A^2 = (-0.3)^2 = (-0.3)(-0.3) = +.09 Etc.

IF.... you were given -0.3^2 to start off with, then that calculation WOULD lead you to -.09 (since you have to use PEMDAS rules), but that is NOT what we were given in this question.

(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 are given that a = -0.3; what we must keep in mind in this problem is that we are really being tested on what happens when we raise a negative proper fraction to an exponent. We say negative proper fraction because -0.3 = -3/10.

The fact that a = -0.3 is not that important; in fact, we could use any negative proper fraction, such as -1/2 or -1/3 to obtain the correct answer.

Let's look at what happens when a negative proper fraction is raised to an even or odd power.

Rule: When a negative proper fraction is raised to an even-powered or odd-powered exponent, the value increases. If this rule is hard to see, let’s test -1/2. We can start by raising -½ to the even exponent of 2.

(-1/2)^2 =1/4

¼ > -1/2

Clearly, we can see that positive ¼ is greater than -½.

Let’s now check an odd-powered exponent; we can raise -1/2 to an exponent of 3.

(-1/2)^3 = -1/8

-1/8 > -1/2

Although both values are negative, -1/8 is greater than -½.

We can use these rules to answer the question. Since we are raising a negative base to a power, the largest value will be a^2, since that is positive, and a and a^3 are negative. That leaves us with answers B and E. Finally, we know a^3 must be greater than a, thus eliminating answer choice E.

The answer is B.
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GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

(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

Hello could you please tell me why answer D is incorrect.

D) 0.09 > -0.0027 > -0.3 B) -0.3 < -0.027 < 0.09

Aren't both of them same?

Hi nandetapuri,

It looks like you 'mixed up' the order of the three values. Notice that the largest term in Answer B is "a^2" (which equals +0.09), while the largest term in Answer D is "a" (which equals -0.3). So the answer to your immediate question is NO - Answers B and D are NOT the same.