It is currently 15 Nov 2018, 06:24

### 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

# a < 0 < b

Author Message
TAGS:
Moderator
Joined: 18 Apr 2015
Posts: 4876
Followers: 74

Kudos [?]: 973 [1] , given: 4479

a < 0 < b [#permalink]  15 Feb 2017, 08:46
1
KUDOS
Expert's post
00:00

Question Stats:

76% (00:36) correct 23% (00:44) wrong based on 72 sessions

$$a < 0 < b$$

 Quantity A Quantity B $$a^{-10}$$ $$b^{-5}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [2] , given: 375

Re: a < 0 < b [#permalink]  21 Feb 2017, 16:32
2
KUDOS
Expert's post
Explanation

The best strategy to solve these problems is by plugging values

Put a = -1 and b = 1, then we have

Quantity A is $$-1^{10} = 1$$

Quantity B is $$1^5 =1$$

Clearly, the quantities are equal. Now put a = -2 and b = 1

Quantity A is $$-2^{10} = 1024$$

Quantity B is $$1^5 =1$$

Now Quantity A is greater. Clearly, both A and C cannot be right at the same time so option D is the correct choice!
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern
Joined: 10 Aug 2017
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: a < 0 < b [#permalink]  10 Aug 2017, 08:35
But the question states a^-10 power and b^-5... and a < 0 < b

-1^-10 = -1
1^-5 = 1

In what circumstance can A and B be equal if you raise them to a negative power?

Ok, I am an idiot - I was playing with the equation in my calculator, which is why it was driving me nuts... because I was almost positive it was wrong... I was inputting -1^-10, and not (-1)^-10... You are correct.
Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 77 [0], given: 99

Re: a < 0 < b [#permalink]  19 May 2018, 09:38
I think the entity A will be a faction with a negative sign and entity B will be postive ..becasue the entity A is negative in nature ?

GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [2] , given: 375

Re: a < 0 < b [#permalink]  19 May 2018, 16:36
2
KUDOS
Expert's post
IshanGre wrote:
I think the entity A will be a faction with a negative sign and entity B will be postive ..becasue the entity A is negative in nature ?

$$a$$ is a negative number may or maynot be a fraction. However it is raised to even power.
If $$a$$ is a fraction then $$a^{-10}$$ is a number greater than 1.
if $$|a| > 1$$ then $$a^{-10}$$ is a fraction.

However in both cases they are positive.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 77 [0], given: 99

Re: a < 0 < b [#permalink]  21 May 2018, 06:13
sandy wrote:
IshanGre wrote:
I think the entity A will be a faction with a negative sign and entity B will be postive ..becasue the entity A is negative in nature ?

$$a$$ is a negative number may or maynot be a fraction. However it is raised to even power.
If $$a$$ is a fraction then $$a^{-10}$$ is a number greater than 1.
if $$|a| > 1$$ then $$a^{-10}$$ is a fraction.

However in both cases they are positive.

I can see but the question stem says that the a is raised to the power of negative 10? pls elaborate
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [1] , given: 375

Re: a < 0 < b [#permalink]  21 May 2018, 12:19
1
KUDOS
Expert's post
Say a=$$\frac{-1}{2}$$ then $$a^{-10}=(\frac{-1}{2})^{-10}= 2^{10}$$.

Also a=$$-2$$ then $$a^{-10}=(-2)^{-10}= (\frac{-1}{2})^{10}=\frac{1}{2^{10}}$$.

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern
Joined: 09 Jul 2018
Posts: 10
Followers: 0

Kudos [?]: 7 [0], given: 0

Re: a < 0 < b [#permalink]  16 Jul 2018, 17:53
How is it not B?

When we set a = -1 and b = 1:
qty1) -1^-10) = -1/1^10 = -1
qty2) 1^5 = 1

Thus QTY 2 is bigger.

Lets make a=-2 and b=2:
qty1) -2^-10 = -1/2^10
qty2) 2^5 = 32

Clearly a negative fraction is smaller than 32 making qty 2 greater again.

This has to mean that B is the answer. Why would it be D?
Moderator
Joined: 18 Apr 2015
Posts: 4876
Followers: 74

Kudos [?]: 973 [0], given: 4479

Re: a < 0 < b [#permalink]  17 Jul 2018, 13:29
Expert's post

$$a^{-10} = \frac{1}{a^{10}}$$ and if $$a$$ is $$-1 = 1^{10} = 1$$. So a ends up being positive.
_________________
Re: a < 0 < b   [#permalink] 17 Jul 2018, 13:29
Display posts from previous: Sort by