Last visit was: 28 Apr 2026, 06:58 It is currently 28 Apr 2026, 06:58
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Events & Promotions
Back to Forum
Create Topic
   1   2 
555-605 (Medium)|   Algebra|   Exponents|                           
User avatar
avigutman
User avatar
Joined: 17 Jul 2019
Last visit: 30 Sep 2025
Posts: 1,285
Own Kudos:
1,908
 [3]
Given Kudos: 66
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert
Expert reply
Schools: NYU Stern (WA)
GMAT 3: 770 Q50 V45
Posts: 1,285
Kudos: 1,908
 [3]
If x is an integer, is 9^x + 9^(-x) = b ? (1) 3^x + 3^(-x) = (b + 2) 26 Oct 2022, 04:55
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
achloes
avigutman

I'd love to know if this question can be solved using a reasoning-based approach? It took me quite some time to arrive at the right answer even with plenty of rephrasing :(
Show more
Sure thing, achloes!
Given the symmetry of the expression 9^x + 9^(-x) with regards to the sign of x, statement (2) appears to be completely useless. This eliminates answer choices BCD.
Looking at statement (1) I’m going to make a (very) educated guess that it is sufficient to answer this yes/no question. Remember, I don’t have to find out the actual answer - I just need to believe that one could find it if one wanted to. The equation in statement (1) and the equation in the question stem are so similar that it’s highly likely to be (A).
This last part (deciding between A and E) isn’t a foolproof reasoning solution, but it has a high probability of success.

Posted from my mobile device
User avatar
johnnymbikes
User avatar
Joined: 28 Oct 2013
Last visit: 22 May 2024
Posts: 15
Own Kudos:
19
Given Kudos: 29
Location: United States (CA)
Schools: Oxford Said'25 (II)
Schools: Oxford Said'25 (II)
Posts: 15
Kudos: 19
If x is an integer, is 9^x + 9^(-x) = b ? (1) 3^x + 3^(-x) = (b + 2) 23 Nov 2023, 12:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Does the following logic work to push the Question stem to answer a Yes/No D/S Q?
Attachments

ds Q.JPG
ds Q.JPG [ 88.78 KiB | Viewed 941 times ]

User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 28 Apr 2026
Posts: 109,948
Own Kudos:
811,709
Given Kudos: 105,927
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,948
Kudos: 811,709
If x is an integer, is 9^x + 9^(-x) = b ? (1) 3^x + 3^(-x) = (b + 2) 23 Nov 2023, 12:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
johnnymbikes
Does the following logic work to push the Question stem to answer a Yes/No D/S Q?
Show more

Unfortunately nothing is correct there. For example, 9^x + 9^(-x) does not equal to 9^(x - x). If it were multiplication, then you'd be correct: 9^x*9^(-x) = 9^(x - x) because \(a^n*a^m=a^{n+m}\). However, generally \(a^n + a^m \neq a^{n+m}\).

I suggest to brush-up fundamentals on the exponents.

8. Exponents and Roots of Numbers




Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
User avatar
Serisha
User avatar
Joined: 17 Aug 2021
Last visit: 28 Aug 2025
Posts: 3
Given Kudos: 11
Location: South Africa
Posts: 3
Kudos: 0
If x is an integer, is 9^x + 9^(-x) = b ? (1) 3^x + 3^(-x) = (b + 2) 01 Jul 2025, 13:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Karishma, thank you for the below. Can you tell me where this part comes from in the first calculation? I'm struggling to understand the rule: +2∗3x∗3−
KarishmaB
yb
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)
Show more
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 28 Apr 2026
Posts: 109,948
Own Kudos:
811,709
Given Kudos: 105,927
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,948
Kudos: 811,709
If x is an integer, is 9^x + 9^(-x) = b ? (1) 3^x + 3^(-x) = (b + 2) 01 Jul 2025, 13:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Serisha
Hi Karishma, thank you for the below. Can you tell me where this part comes from in the first calculation? I'm struggling to understand the rule: +2∗3x∗3−
KarishmaB
yb
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)
Show more

The term \(2 * 3^x * 3^{-x}\) comes from squaring \((3^x + 3^{-x})\) using the identity \((a + b)^2 = a^2 + b^2 + 2ab\)

Here, \(a = 3^x\) and \(b = 3^{-x}\), so:

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

That’s where the \(2 * 3^x * 3^{-x}\) term comes from.
User avatar
RBgmatPre
User avatar
Joined: 14 Jun 2025
Last visit: 13 Nov 2025
Posts: 29
Own Kudos:
10
Given Kudos: 17
Posts: 29
Kudos: 10
If x is an integer, is 9^x + 9^(-x) = b ? (1) 3^x + 3^(-x) = (b + 2) 06 Jul 2025, 03:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
So, while solving this question, I misunderstood something

Should it be
\sqrt{} b + 2

(\sqrt{} b )+ 2

The answer remains A in both the cases, but I would like to be accurate in my learning.

Bunuel
SOLUTION

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

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

Square both sides: \(9^x+2*3^x*\frac{1}{3^x}+9^{-x}=b+2\);

\(9^x + 9^{-x} = b\).

So, the answer to the question is YES. Sufficient.


(2) x > 0. No sufficient.


Answer: A.
Show more
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 28 Apr 2026
Posts: 109,948
Own Kudos:
811,709
Given Kudos: 105,927
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,948
Kudos: 811,709
If x is an integer, is 9^x + 9^(-x) = b ? (1) 3^x + 3^(-x) = (b + 2) 06 Jul 2025, 08:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
RBgmatPre
So, while solving this question, I misunderstood something

Should it be
\sqrt{} b + 2

(\sqrt{} b )+ 2

The answer remains A in both the cases, but I would like to be accurate in my learning.

Bunuel
SOLUTION

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

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

Square both sides: \(9^x+2*3^x*\frac{1}{3^x}+9^{-x}=b+2\);

\(9^x + 9^{-x} = b\).

So, the answer to the question is YES. Sufficient.


(2) x > 0. No sufficient.


Answer: A.
Show more

It's the square root of (b + 2).
User avatar
totaltestprepNick
User avatar
Joined: 25 Aug 2014
Last visit: 27 Apr 2026
Posts: 469
Own Kudos:
4
Given Kudos: 2
GMAT 1: 750 Q49 V42
GMAT 1: 750 Q49 V42
Posts: 469
Kudos: 4
If x is an integer, is 9^x + 9^(-x) = b ? (1) 3^x + 3^(-x) = (b + 2) 01 Mar 2026, 14:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If x is an integer, is \(9^x + 9^{-x} = b\) ?


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

(2) x > 0
Show more

Show Spoiler
A




Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience

[email protected]
   1   2 
Moderators:
Bunuel
Math Expert
109948 posts
kingbucky
498 posts
Gmat860sanskar
212 posts