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

Question

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

Bunuel · Accepted Answer

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

Thus, a < a^3 < a^2.

Answer: B.

unceldolan · Answer

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

BrainLab · Answer

a^2 is the only positive number, so A,C and D are out. As a is a negative number a^3>a 
Answer (B)

torreadortorment · Answer

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 ?

EMPOWERgmatRichC · Answer

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

torreadortorment · Answer

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>

EMPOWERgmatRichC · Answer

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

torreadortorment · Answer

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. Exponents.png

EMPOWERgmatRichC · Answer

Hi torreadortorment,

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.

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

JeffTargetTestPrep · Answer

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.

SeregaP · Answer

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

nandetapuri · Answer

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?

EMPOWERgmatRichC · Answer

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

generis · Answer

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

Answer B

ScottTargetTestPrep · Answer

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

Answer: B

BrentGMATPrepNow · Answer

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
Answer:B

legendinthewomb · Answer

Can't believe i got this wrong. I chose E by completely forgetting that -.027 is less than -.3. Hate this aah

EMPOWERgmatRichC · Answer

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

legendinthewomb · Answer

yes lol. *facepalms

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

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

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