It is currently 16 Dec 2017, 18:36

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x is an integer, is 9^x + 9^(-x) = b ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 05 Oct 2005
Posts: 485

Kudos [?]: 8 [1], given: 0

If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

Show Tags

New post 27 Oct 2005, 16:59
1
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:15) correct 26% (01:27) wrong based on 330 sessions

HideShow timer Statistics

If x is an integer, is \(9^x + 9^{-x} = b\)?

(1) \(3^x + 3^{-x} = \sqrt{b + 2}\)

(2) x > 0
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Aug 2014, 02:19, edited 1 time in total.
Edited the question and added the OA.

Kudos [?]: 8 [1], given: 0

VP
VP
avatar
Joined: 22 Aug 2005
Posts: 1111

Kudos [?]: 128 [0], given: 0

Location: CA
Re: If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

Show Tags

New post 27 Oct 2005, 17:11
A.

3^x + 3^(-x) = sqrt(b+2)
squaring both sides

3^2x + 3^-2x + 2 * 3^0 = b+2

(3^2)^x + (3^2)^-x + 2 = b+2
9^x + 9^-x = b

wondering if any of the above steps require x to be > 0 (stmt 2)

Kudos [?]: 128 [0], given: 0

2 KUDOS received
VP
VP
avatar
Joined: 06 Jun 2004
Posts: 1050

Kudos [?]: 188 [2], given: 0

Location: CA
Re: If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

Show Tags

New post 27 Oct 2005, 17:37
2
This post received
KUDOS
1
This post was
BOOKMARKED
yb wrote:
If x is an integer, is 9^x + 9^(-x) = b ?

1) 3^x + 3^(-x) = sqrt(b+2)

2) x>0



(1) 3^x + 3^(-x) = sqrt(b+2) = [3^x + 3^(-x)]^2 = b+2
[3^x + 3^(-x)] [3^x + 3^(-x)] = [3^2x + 3^0 + 3^0 + 3^-2x]= b+2
3^2x + 1 + 1 + 3^-2x = b+2
9^x + 2 + 9^-x = b+2
9^x + 9^-x = b - Thus (1) is sufficient

(2) Reveals nothing about b. Insufficient.

A is the answer

Kudos [?]: 188 [2], given: 0

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7799

Kudos [?]: 18144 [1], given: 236

Location: Pune, India
Re: If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

Show Tags

New post 19 Aug 2014, 21:35
1
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
yb wrote:
If x is an integer, is 9^x + 9^(-x) = b ?

1) 3^x + 3^(-x) = sqrt(b+2)

2) x>0


Note that 9^x is the square of 3^x so we know that we should try to square stmnt 1.

1) \(3^x + 3^{-x} = \sqrt{(b+2)}\)
\(3^{2x} + 3^{-2x} + 2*3^x*3^{-x} = \sqrt{(b+2)}^2\)
\(9^x + 9^{-x} = b + 2 - 2 = b\)

We answer with 'Yes' and hence this statement alone is sufficient.

2) x > 0
Obviously not sufficient.

Answer (A)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 18144 [1], given: 236

Intern
Intern
avatar
Joined: 21 Mar 2014
Posts: 39

Kudos [?]: 6 [0], given: 13

Re: If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

Show Tags

New post 05 Dec 2015, 11:56
Bunuel , what is x=0 ?
_________________

kinaare paaon phailane lage hian,
nadi se roz mitti kat rahi hai....

Kudos [?]: 6 [0], given: 13

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135874 [0], given: 12715

Re: If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

Show Tags

New post 06 Dec 2015, 09:31

Kudos [?]: 135874 [0], given: 12715

Senior Manager
Senior Manager
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 408

Kudos [?]: 26 [0], given: 283

If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

Show Tags

New post 16 Sep 2016, 15:33
Correct answer is A

(1) 3^x + 3^(-x) = sqrt(b+2)
= [3^x + 3^(-x)]^2 = [sqrt(b+2)]^2 (square both sides)
= 3^(2x) + 3^(-2x) = b+2
= 9^x + 9^(-x) = b+2

SUFFICIENT

(2) x > 0

NOT SUFFICIENT (this statement doesn't provide any information we can use to verify the statement)

Kudos [?]: 26 [0], given: 283

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14813

Kudos [?]: 288 [0], given: 0

Premium Member
Re: If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

Show Tags

New post 05 Nov 2017, 05:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 288 [0], given: 0

Re: If x is an integer, is 9^x + 9^(-x) = b ?   [#permalink] 05 Nov 2017, 05:25
Display posts from previous: Sort by

If x is an integer, is 9^x + 9^(-x) = b ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.