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

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

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12 Dec 2012, 09:05
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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) $$a^3 < a < a^2$$
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Re: If a = -0.3, which of the following is true?  [#permalink]

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12 Dec 2012, 09:07
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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, 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
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Re: If a = -0.3, which of the following is true?  [#permalink]

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11 Sep 2014, 13:22
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, 03:15
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, 05:41
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, 18:37
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 Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Intern Joined: 02 Jul 2015 Posts: 35 WE: Investment Banking (Investment Banking) Re: If a = -0.3, which of the following is true? [#permalink] ### Show Tags 24 Dec 2015, 23:12 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: 14351 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If a = -0.3, which of the following is true? [#permalink] ### Show Tags 25 Dec 2015, 11:49 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 _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If a = -0.3, which of the following is true?  [#permalink]

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25 Dec 2015, 12:14
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.

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.

Attachment:

Exponents.png [ 55.97 KiB | Viewed 15538 times ]
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Re: If a = -0.3, which of the following is true?  [#permalink]

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25 Dec 2015, 12:32

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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# Rich Cohen

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Intern Joined: 02 Jul 2015 Posts: 35 WE: Investment Banking (Investment Banking) Re: If a = -0.3, which of the following is true? [#permalink] ### Show Tags 25 Dec 2015, 23:43 Understood. Thank you so much. Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2823 Re: If a = -0.3, which of the following is true? [#permalink] ### Show Tags 11 Jun 2016, 06:46 Walkabout 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 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. _________________ # Jeffrey Miller Head of GMAT Instruction Jeff@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Manager Joined: 03 Jan 2017 Posts: 139 Re: If a = -0.3, which of the following is true? [#permalink] ### Show Tags 25 Mar 2017, 11:52 it's very tricky! I got into the E trap :D if we calculate it first: -0,3, -0,27, 0,09 we can figure out that B is the answer Intern Joined: 12 Mar 2017 Posts: 39 Re: If a = -0.3, which of the following is true? [#permalink] ### Show Tags 13 Jul 2017, 19:42 Bunuel wrote: Walkabout 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 a=-0.3; a^2=0.09; a^3=-0.027; Thus, a < a^3 < a^2. Answer: B. 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? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14351 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If a = -0.3, which of the following is true? [#permalink] ### Show Tags 13 Jul 2017, 20:38 1 nandetapuri wrote: Bunuel wrote: Walkabout 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 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. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If a = -0.3, which of the following is true?  [#permalink]

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30 Aug 2017, 14:34
Top Contributor
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

If a = -0.3, then:
a = -0.3
a² = (-0.3)(-0.3) = 0.09
a³ = (-0.3)(-0.3)(-0.3) = -0.027

If we order these values, we get: -0.3 < -0.027 < 0.09
In other words, a < a³ < a²

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

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