If a = -0.3, which of the following is true? : GMAT Problem Solving (PS)
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# If a = -0.3, which of the following is true?

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

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12 Dec 2012, 08:05
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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
[Reveal] Spoiler: OA
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Re: If a = -0.3, which of the following is true? [#permalink]

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12 Dec 2012, 08:07
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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

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

Thus, 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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10 Jan 2014, 03:32
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
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Re: If a = -0.3, which of the following is true? [#permalink]

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11 Sep 2014, 12:22
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

since a is -ive , square value will have +ive & will be greater than a & a^3

a has also decimal point a^3>a

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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07 Oct 2015, 02:15
a^2 is the only positive number, so A,C and D are out. As a is a negative number a^3>a
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Re: If a = -0.3, which of the following is true? [#permalink]

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22 Dec 2015, 04:41
Can someone please explain this ? Read it in the MGMAT Algebra book (Page 39).

-2^4 = Negative

(-2)^4 = Positive

So, how is it that -0.3^even number is even ?
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Re: If a = -0.3, which of the following is true? [#permalink]

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24 Dec 2015, 17:37
Can someone please explain this ? Read it in the MGMAT Algebra book (Page 39).

-2^4 = Negative

(-2)^4 = Positive

So, how is it that -0.3^even number is even ?

(-.3)^(even) would NOT end in an even number. It would be a POSITIVE number though.

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Intern Joined: 01 Jul 2015 Posts: 38 WE: Investment Banking (Investment Banking) Followers: 1 Kudos [?]: 2 [0], given: 1 Re: If a = -0.3, which of the following is true? [#permalink] ### Show Tags 24 Dec 2015, 22:12 EMPOWERgmatRichC wrote: torreadortorment wrote: Can someone please explain this ? Read it in the MGMAT Algebra book (Page 39). -2^4 = Negative (-2)^4 = Positive So, how is it that -0.3^even number is even ? Hi torreadortorment, (-.3)^(even) would NOT end in an even number. It would be a POSITIVE number though. GMAT assassins aren't born, they're made, Rich Sorry my bad. I meant, how is it that -0.3^even number is positive ? I know why (-2)^4 = Positive. However, isn't -2^4 = Negative> EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8572 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 400 Kudos [?]: 2564 [0], given: 166 Re: If a = -0.3, which of the following is true? [#permalink] ### Show Tags 25 Dec 2015, 10:49 Hi torreadortorment, This is actually a Number Property Rule. Almost any number, when raised to an even power, will end in a positive number (the exception is 0). For example: 2^2 = (2)(2) = 4 (-2)^2 = (-2)(-2) = +4 3^4 = (3)(3)(3)(3) = 81 (-3)^4 = (-3)(-3)(-3)(-3) = 81 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 _________________ Contact Rich: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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

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25 Dec 2015, 11:14
EMPOWERgmatRichC wrote:

This is actually a Number Property Rule. Almost any number, when raised to an even power, will end in a positive number (the exception is 0).

For example:

2^2 = (2)(2) = 4
(-2)^2 = (-2)(-2) = +4

3^4 = (3)(3)(3)(3) = 81
(-3)^4 = (-3)(-3)(-3)(-3) = 81

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.

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

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25 Dec 2015, 11:32

You've misinterpreted the question.

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.

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

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25 Dec 2015, 22:43
Understood. Thank you so much.
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Re: If a = -0.3, which of the following is true? [#permalink]

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11 Jun 2016, 05:46
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 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.

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Re: If a = -0.3, which of the following is true?   [#permalink] 11 Jun 2016, 05:46
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