Last visit was: 17 Jun 2024, 00:52 It is currently 17 Jun 2024, 00:52
Close
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
Your Progress

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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Difficulty: 555-605 Level,    Inequalities,                      
Show Tags
Hide Tags
User avatar
Manager
Manager
Joined: 02 Dec 2012
Posts: 172
Own Kudos [?]: 24251 [178]
Given Kudos: 23
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 93696
Own Kudos [?]: 632380 [13]
Given Kudos: 82322
Send PM
avatar
Manager
Manager
Joined: 21 Oct 2013
Posts: 152
Own Kudos [?]: 216 [6]
Given Kudos: 19
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Send PM
General Discussion
Current Student
Joined: 10 Mar 2013
Posts: 360
Own Kudos [?]: 2722 [1]
Given Kudos: 200
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.7
WE:Marketing (Telecommunications)
Send PM
Re: If a = -0.3, which of the following is true? [#permalink]
1
Bookmarks
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)
avatar
Intern
Intern
Joined: 02 Jul 2015
Posts: 31
Own Kudos [?]: 5 [0]
Given Kudos: 1
WE:Investment Banking (Investment Banking)
Send PM
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 ?
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11723 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If a = -0.3, which of the following is true? [#permalink]
Expert Reply
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
avatar
Intern
Intern
Joined: 02 Jul 2015
Posts: 31
Own Kudos [?]: 5 [0]
Given Kudos: 1
WE:Investment Banking (Investment Banking)
Send PM
Re: If a = -0.3, which of the following is true? [#permalink]
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>
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11723 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If a = -0.3, which of the following is true? [#permalink]
Expert Reply
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
avatar
Intern
Intern
Joined: 02 Jul 2015
Posts: 31
Own Kudos [?]: 5 [0]
Given Kudos: 1
WE:Investment Banking (Investment Banking)
Send PM
Re: If a = -0.3, which of the following is true? [#permalink]
EMPOWERgmatRichC wrote:
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


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
Exponents.png [ 55.97 KiB | Viewed 46624 times ]
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11723 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If a = -0.3, which of the following is true? [#permalink]
Expert Reply
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
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3042
Own Kudos [?]: 6458 [4]
Given Kudos: 1646
Send PM
Re: If a = -0.3, which of the following is true? [#permalink]
4
Bookmarks
Expert Reply
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.
Manager
Manager
Joined: 03 Jan 2017
Posts: 86
Own Kudos [?]: 83 [1]
Given Kudos: 4
Send PM
Re: If a = -0.3, which of the following is true? [#permalink]
1
Bookmarks
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
Intern
Joined: 12 Mar 2017
Posts: 33
Own Kudos [?]: 29 [0]
Given Kudos: 22
Send PM
Re: If a = -0.3, which of the following is true? [#permalink]
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?
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11723 [1]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If a = -0.3, which of the following is true? [#permalink]
1
Kudos
Expert Reply
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
Senior SC Moderator
Joined: 22 May 2016
Posts: 5329
Own Kudos [?]: 35661 [0]
Given Kudos: 9464
Send PM
If a= -0.3, which of the following is true? [#permalink]
Expert Reply
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_____

____\(a\)______\(a^3\)____|____\(a^2\)____|_____

\(a < a^3 < a^2\)

Answer B
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19019
Own Kudos [?]: 22420 [0]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: If a= -0.3, which of the following is true? [#permalink]
Expert Reply
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

Answer: B
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [1]
Given Kudos: 799
Location: Canada
Send PM
If a = -0.3, which of the following is true? [#permalink]
1
Kudos
Expert Reply
Top Contributor
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


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

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.
Intern
Intern
Joined: 23 Nov 2018
Posts: 18
Own Kudos [?]: 13 [1]
Given Kudos: 104
Send PM
Re: If a = -0.3, which of the following is true? [#permalink]
1
Kudos
Can't believe i got this wrong. I chose E by completely forgetting that -.027 is less than -.3. Hate this aah :(
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) \(a^3 < a < a^2\)
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11723 [2]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If a = -0.3, which of the following is true? [#permalink]
1
Kudos
1
Bookmarks
Expert Reply
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
Intern
Joined: 23 Nov 2018
Posts: 18
Own Kudos [?]: 13 [2]
Given Kudos: 104
Send PM
Re: If a = -0.3, which of the following is true? [#permalink]
2
Kudos
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
GMAT Club Bot
Re: If a = -0.3, which of the following is true? [#permalink]
 1   2   
Moderator:
Math Expert
93696 posts