GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Dec 2019, 09:03 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If a = -0.3, which of the following is true?

Author Message
TAGS:

### Hide Tags

Manager  Joined: 02 Dec 2012
Posts: 173
If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

4
52 00:00

Difficulty:   45% (medium)

Question Stats: 59% (00:59) correct 41% (00:50) wrong based on 1898 sessions

### HideShow timer Statistics

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) $$a^3 < a < a^2$$
Math Expert V
Joined: 02 Sep 2009
Posts: 59730
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

3
3
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.

_________________
##### General Discussion
Manager  Joined: 21 Oct 2013
Posts: 177
Location: Germany
GMAT 1: 660 Q45 V36 GPA: 3.51
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

1
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
Manager  Joined: 07 Apr 2014
Posts: 98
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

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
Senior Manager  B
Joined: 10 Mar 2013
Posts: 461
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A\$)
GMAT 1: 580 Q46 V24 GPA: 3.88
WE: Information Technology (Consulting)
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

a^2 is the only positive number, so A,C and D are out. As a is a negative number a^3>a
Intern  Joined: 02 Jul 2015
Posts: 34
WE: Investment Banking (Investment Banking)
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

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 ?
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15736
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

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
_________________
Intern  Joined: 02 Jul 2015
Posts: 34
WE: Investment Banking (Investment Banking)
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

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>
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15736
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

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
_________________
Intern  Joined: 02 Jul 2015
Posts: 34
WE: Investment Banking (Investment Banking)
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

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 18629 times ]
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15736
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

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
_________________
Intern  Joined: 02 Jul 2015
Posts: 34
WE: Investment Banking (Investment Banking)
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

Understood. Thank you so much.
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

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.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

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  S
Joined: 03 Jan 2017
Posts: 134
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

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  B
Joined: 12 Mar 2017
Posts: 39
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

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?
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15736
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

1
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.

GMAT assassins aren't born, they're made,
Rich
_________________
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4157
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

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

RELATED VIDEO FROM OUR COURSE

_________________
Intern  B
Joined: 23 Nov 2018
Posts: 28
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

1
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) $$a^3 < a < a^2$$
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15736
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

1
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
_________________
Intern  B
Joined: 23 Nov 2018
Posts: 28
Re: If a = -0.3, which of the following is true?  [#permalink]

### Show Tags

2
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 Re: If a = -0.3, which of the following is true?   [#permalink] 22 Nov 2019, 21:44
Display posts from previous: Sort by

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