Last visit was: 24 Apr 2026, 12:03 It is currently 24 Apr 2026, 12:03
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
Back to Forum
Create Topic
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,000
 [6]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,000
 [6]
When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? Updated on: 11 Aug 2025, 01:02
Originally posted by MathRevolution on 04 Feb 2016, 18:22.
Last edited by Bunuel on 11 Aug 2025, 01:02, edited 3 times in total.
1
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

70% (01:50) correct 30% (02:30) wrong based on 149 sessions

History

Date
Time
Result
Not Attempted Yet
If \(a=x+\frac{1}{x}\) and \(b=x-\frac{1}{x}\), then what is the value of \(\frac{2^{a^2}}{2^{b^2}}\)?

A. 2
B. 4
C. 8
D. 16
E. 32
ShowHide Answer
Official Answer
D
User avatar
Kurtosis
User avatar
Current Student
Joined: 13 Apr 2015
Last visit: 10 Nov 2021
Posts: 1,384
Own Kudos:
5,236
 [3]
Given Kudos: 1,228
Location: India
Products:
My Reviews
Posts: 1,384
Kudos: 5,236
 [3]
When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? 04 Feb 2016, 20:03
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
2^a = (2^x)*(2^(1/x))
2^b = (2^x)/(2^(1/x))

(2^a)^2 = 2^2a = (2^2x)*(2^2/x)
(2^b)^2 = 2^2b = (2^2x)/(2^2/x)

((2^a)^2)/(2^b)^2) = (2^2/x) * (2^2/x) = 2^4/x

If x = 1 then Answer = 16
If x = 2 then Answer = 4
If x = 4 then Answer = 1
If x = 4/3 then Answer = 8
If x = 4/5 then Answer = 32

Thus we can have multiple answers for this question since value of x is not specified. Please correct the question or let me know if I have made a mistake.
avatar
sharmilaz87
avatar
Joined: 04 May 2015
Last visit: 10 Jul 2016
Posts: 5
Own Kudos:
7
Given Kudos: 1
Posts: 5
Kudos: 7
When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? 04 Feb 2016, 20:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think you are correct Vyshak. I have also got the same ans.
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 24 Apr 2026
Posts: 11,229
Own Kudos:
45,008
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,008
When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? 04 Feb 2016, 21:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Vyshak
2^a = (2^x)*(2^(1/x))
2^b = (2^x)/(2^(1/x))

(2^a)^2 = 2^2a = (2^2x)*(2^2/x)
(2^b)^2 = 2^2b = (2^2x)/(2^2/x)

((2^a)^2)/(2^b)^2) = (2^2/x) * (2^2/x) = 2^4/x

If x = 1 then Answer = 16
If x = 2 then Answer = 4
If x = 4 then Answer = 1
If x = 4/3 then Answer = 8
If x = 4/5 then Answer = 32

Thus we can have multiple answers for this question since value of x is not specified. Please correct the question or let me know if I have made a mistake.
Show more

hi,
you are absolutely correct in your observation..
looking at the equation and the OA,
the equation could have been:-
(2^a)^(a+b)/(2^b)^(a+b)..
try out this Q ..

just a point, in these Q to save time, take the power to the numerator and then substitute for a and b..
example
2^a/2^b= 2^(a-b)= 2^(x + 1/x - x - (1/x))
= 2^(2/x)...
you should do this when you see a and b have common terms with change of sign..
Ofcourse, the way you have done is also absolutely correct..
avatar
Beixi88
avatar
Joined: 14 Jul 2015
Last visit: 07 Feb 2020
Posts: 18
Own Kudos:
32
Given Kudos: 83
GMAT 1: 680 Q44 V40
GMAT 2: 710 Q49 V37
GMAT 2: 710 Q49 V37
Posts: 18
Kudos: 32
When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? 04 Feb 2016, 22:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I have an itching feeling that my method is grasping at too many straws, but it gave me the correct answer. Can anyone give me some feedback on my method for solving the question?

Solve for a to get a = 2:

1. Given: \(a = x + \frac{1}{x}\)
2. \(ax = x^2 + \frac{x}{x}\) -> \(ax = x^2 + 1\)
3. \(0 = x^2 - ax + 1\)
4. \(x^2 - ax + 1 = (x-1)^2\). To complete the expression, a = 2

Solve for b to get b = 0:

1. Given: \(b = x - \frac{1}{x}\)
2. \(bx = x^2 - \frac{x}{x}\) -> \(bx = x^2 - 1\)
3. \(0 = x^2 - bx - 1\)
4. \(x^2 - bx - 1 = (x - 1)(x + 1)\). To complete the expression, b = 0

We plug in a = 2 and b = 0 into \(\frac{(2^a)^2}{(2^b)^2}=?\):
1. \(\frac{(2^a)^2}{(2^b)^2}=?\)
2. \(\frac{{2^{2a}}}{{2^{2b}}}=?\)
3. \(2^{2a} * 2^{-2b}\)
4. \(2^{2(a - b)}\)
5. \(2^{2(2 - 0)}\)
6. \(2^4 = 16\)

My answer is D, 16.

Please let me know if the method I used is incorrect or if you have any improvements on the method used.
User avatar
Kurtosis
User avatar
Current Student
Joined: 13 Apr 2015
Last visit: 10 Nov 2021
Posts: 1,384
Own Kudos:
5,236
 [1]
Given Kudos: 1,228
Location: India
Products:
My Reviews
Posts: 1,384
Kudos: 5,236
 [1]
When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? 04 Feb 2016, 22:31
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi @Beixi88,

Your solution focuses only on one of the solutions for 'a'. But a can also vary with the value of x.

According to your solution, we have one of the equations as x^2 - ax + 1 = 0. Here we have two unknowns x and a.. X and a can be plugged in many ways to solve the equation.
If x = 2, 5 - 2a = 0 --> a = 5/2. Thus we can have many values of a depending on the value of x.
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,000
 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,000
 [1]
When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? Updated on: 08 Feb 2016, 21:30
Originally posted by MathRevolution on 08 Feb 2016, 00:16.
Last edited by MathRevolution on 08 Feb 2016, 21:30, edited 1 time in total.
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
When a=x+(1/x) and b=x-(1/x), (2^a)^2/(2^b)^2=?

A. 2
B. 4
C. 8
D. 16
E. 32


--> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=2/x and a+b=2x, 2^(a-b)(a+b)=2^(2/x)(2x)=2^4=16.
Therefore, the answer is D.
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 24 Apr 2026
Posts: 11,229
Own Kudos:
45,008
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,008
When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? 08 Feb 2016, 00:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
When a=x+(1/x) and b=x-(1/x), (2^a)^2/(2^b)^2=?

A. 2
B. 4
C. 8
D. 16
E. 32


--> (2^a)^2/(2^b)^2 ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=2/x and a+b=2x, 2^(a-b)(a+b)=2^(2/x)(2x)=2^4=16.
Therefore, the answer is D.
Show more

HI,

I am sorry, your solution is wrong,...
(2^a)^2/(2^b)^2 = 2^(2a-2b) and not {(2)^(a^2-b^2)}

(2^a)^2=(2^a)*(2^a)=2^(a+a)= 2^2a..
REQUEST rectify the Question or the answer accordingly
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,000
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,000
When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? 08 Feb 2016, 21:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sorry for the confusion.

I have modified the question and the solution.

Thank you.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,975
Own Kudos:
1,117
Posts: 38,975
Kudos: 1,117
When a=x+(1/x) and b=x-(1/x), (2^a^2)/(2^b^2)=? 24 Feb 2023, 07:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109818 posts
Krunaal
Tuck School Moderator
853 posts