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

It is currently 23 Jul 2018, 01:11

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

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

3 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 05 Oct 2005
Posts: 475
If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

Show Tags

New post Updated on: 20 Aug 2014, 03:19
3
2
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:14) correct 26% (01:25) wrong based on 345 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

Originally posted by yb on 27 Oct 2005, 17:59.
Last edited by Bunuel on 20 Aug 2014, 03:19, edited 1 time in total.
Edited the question and added the OA.
VP
VP
avatar
Joined: 22 Aug 2005
Posts: 1094
Location: CA
Re: If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

Show Tags

New post 27 Oct 2005, 18:11
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)
3 KUDOS received
VP
VP
avatar
Joined: 06 Jun 2004
Posts: 1030
Location: CA
Re: If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

Show Tags

New post 27 Oct 2005, 18:37
3
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
Expert Post
1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8132
Location: Pune, India
Re: If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

Show Tags

New post 19 Aug 2014, 22:35
1
2
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
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Intern
Intern
avatar
Joined: 21 Mar 2014
Posts: 35
Re: If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

Show Tags

New post 05 Dec 2015, 12:56
Bunuel , what is x=0 ?
_________________

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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47200
Re: If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

Show Tags

New post 06 Dec 2015, 10:31
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 398
If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

Show Tags

New post 16 Sep 2016, 16:33
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)
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7335
Premium Member
Re: If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

Show Tags

New post 05 Nov 2017, 06:25
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

Re: If x is an integer, is 9^x + 9^(-x) = b ? &nbs [#permalink] 05 Nov 2017, 06:25
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  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.