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

 It is currently 16 Oct 2018, 03:10

### 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

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 05 Oct 2005
Posts: 474
If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

### Show Tags

Updated on: 20 Aug 2014, 03:19
3
2
00:00

Difficulty:

(N/A)

Question Stats:

75% (01:37) correct 25% (01:56) wrong based on 348 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
Joined: 22 Aug 2005
Posts: 1082
Location: CA
Re: If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

### Show Tags

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)
VP
Joined: 06 Jun 2004
Posts: 1012
Location: CA
Re: If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

### Show Tags

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.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8383
Location: Pune, India
Re: If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

### Show Tags

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.

_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Joined: 21 Mar 2014
Posts: 34
Re: If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

### Show Tags

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

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

Math Expert
Joined: 02 Sep 2009
Posts: 49892
Re: If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

### Show Tags

06 Dec 2015, 10:31
saroshgilani wrote:
Bunuel , what is x=0 ?

If x = 0, then the questions asks whether b = 2.

(1) gives $$2 = \sqrt{b+2}$$ --> b = 2. Sufficient.

Hope it's clear.
_________________
Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 384
If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

### Show Tags

16 Sep 2016, 16:33

(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
Joined: 09 Sep 2013
Posts: 8408
Re: If x is an integer, is 9^x + 9^(-x) = b ?  [#permalink]

### Show Tags

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.
_________________
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