It is currently 18 Dec 2018, 15:54
My Tests

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.

x is a negative integer

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4756
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1667 [0], given: 396

CAT Tests
x is a negative integer [#permalink] New post 26 Jan 2016, 01:17
Expert's post
00:00

Question Stats:

66% (00:43) correct 33% (00:31) wrong based on 39 sessions
x is a negative integer.

Quantity A
Quantity B
\(2^x\)
\(3^{x+1}\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.




Practice Questions
Question: 5
Page: 466
Difficulty: medium
[Reveal] Spoiler: OA

_________________

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

Try our free Online GRE Test

1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4756
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1667 [1] , given: 396

CAT Tests
Re: x is a negative integer [#permalink] New post 26 Jan 2016, 01:59
1
This post received
KUDOS
Expert's post
Solution

Since both quantities are algebraic expressions, another way to approach the comparison is to set up a placeholder relationship, denoted by |?|, between the two quantities and then to simplify to see what conclusions you can draw. As you simplify and draw conclusions, keeping in mind that x is a negative integer.

\(2^x |?| 3^x^+^1\)

or \(2^x |?| 3* 3^x\)
or \(\frac{2^x}{3^x} |?| 3\)

Let n = -x and since x is negative integer n is a positive integer.

or \((\frac{2}{3})^{-n} |?| 3\)

or \((\frac{3}{2})^n |?| 3\)

Now clearly for some values of n Quantity A is bigger (for example n = 1) and other values Quantity B is greater (for example n=3). Hence a relation ship between the two cannot be determined. Option D is correct.
_________________

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

Try our free Online GRE Test

2 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1253
Followers: 47

Kudos [?]: 1160 [2] , given: 7

Re: x is a negative integer [#permalink] New post 26 Jan 2016, 14:05
2
This post received
KUDOS
Expert's post
sandy wrote:
x is a negative integer.

Quantity A
Quantity B
\(2^x\)
\(3^x^+^1\)



Let's test some values of x.

x = -1
Quantity A = 2^(-1) = 1/2
Quantity B = 3^(-1 + 1) = 3^0 = 1
In this case, quantity B is greater

x = -3
Quantity A = 2^(-3) = 1/8
Quantity B = 3^(-3 + 1) = 3^(-2) = 1/9
In this case, quantity A is greater

Answer: D

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

2 KUDOS received
Intern
Intern
Joined: 23 Mar 2017
Posts: 9
Followers: 0

Kudos [?]: 13 [2] , given: 1

Re: x is a negative integer [#permalink] New post 09 Jun 2017, 14:36
2
This post received
KUDOS
Not edited properly mate.

It should be \(3^{x+1}\) not \(3^x\) + 1

Made me choose the wrong option.

1 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1253
Followers: 47

Kudos [?]: 1160 [1] , given: 7

Re: x is a negative integer [#permalink] New post 11 Jun 2017, 09:53
1
This post received
KUDOS
Expert's post
sandy wrote:
x is a negative integer.

Quantity A
Quantity B
\(2^x\)
\(3^x^+^1\)




Let's plug in some values for x and see what happens

x = -1
We get:
Quantity A: 2^(-1) = 1/2
Quantity B: 3^(-1 + 1) = 3^0 = 1
Quantity B is greater

x = -3
We get:
Quantity A: 2^(-3) = 1/8
Quantity B: 3^(-3 + 1) = 3^(-2) = 1/9
Quantity A is greater

Answer:
[Reveal] Spoiler:
D


RELATED VIDEO

_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

Intern
Intern
Joined: 19 Nov 2018
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 12

Re: x is a negative integer [#permalink] New post 29 Nov 2018, 15:02
Can someone please tell me why 3^x+1 is the same as 3∗3^x?

Or can just tell me the name of the rule?

I'm sure I should know it, but I don't.

Thanks for your help.
1 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1253
Followers: 47

Kudos [?]: 1160 [1] , given: 7

Re: x is a negative integer [#permalink] New post 29 Nov 2018, 17:14
1
This post received
KUDOS
Expert's post
arc601 wrote:
Can someone please tell me why 3^x+1 is the same as 3∗3^x?

Or can just tell me the name of the rule?

I'm sure I should know it, but I don't.

Thanks for your help.


It's called the Product Law, which says (b^x)(b^y) = b^(x + y)
For example, (2^5)(2^3) = 2^(5 + 3) = 2^8

So, (3)(3^x) = (3^1)(3^x)
= 3^(1 + x)
= 3^(x + 1)

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

Re: x is a negative integer   [#permalink] 29 Nov 2018, 17:14
Display posts from previous: Sort by

x is a negative integer

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.