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

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

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

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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Re: If a = -0.3, which of the following is true? [#permalink]
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 46624 times ]
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Re: If a = -0.3, which of the following is true? [#permalink]

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

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

Aren't both of them same?
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Re: If a = -0.3, which of the following is true? [#permalink]
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nandetapuri wrote:
Bunuel 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

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.

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

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

Originally posted by BrentGMATPrepNow on 30 Aug 2017, 14:34.
Last edited by BrentGMATPrepNow on 28 May 2020, 09:23, edited 1 time in total.
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Re: If a = -0.3, which of the following is true? [#permalink]
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Can't believe i got this wrong. I chose E by completely forgetting that -.027 is less than -.3. Hate this aah
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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Hi legendinthewomb,

I think that you mean to say that -0.3 is less than - 0.027 (since -0.3 is further to the 'left' on a Number Line).

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Re: If a = -0.3, which of the following is true? [#permalink]
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yes lol. *facepalms
EMPOWERgmatRichC wrote:
Hi legendinthewomb,

I think that you mean to say that -0.3 is less than - 0.027 (since -0.3 is further to the 'left' on a Number Line).

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