Last visit was: 16 Jul 2025, 01:19 It is currently 16 Jul 2025, 01:19
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 16 July 2025
Posts: 102,591
Own Kudos:
Given Kudos: 98,202
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,591
Kudos: 741,773
 [19]
3
Kudos
Add Kudos
16
Bookmarks
Bookmark this Post
User avatar
kumarparitosh123
Joined: 02 Nov 2015
Last visit: 19 Dec 2018
Posts: 131
Own Kudos:
65
 [1]
Given Kudos: 121
GMAT 1: 640 Q49 V29
GMAT 1: 640 Q49 V29
Posts: 131
Kudos: 65
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
User avatar
pushpitkc
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,819
Own Kudos:
5,871
 [1]
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,819
Kudos: 5,871
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
pushpitkc
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,819
Own Kudos:
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,819
Kudos: 5,871
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kumarparitosh123
It's an E.
The question breaks down to
1/(4^x)+1/(2^x)-6=0.

Let 1/2^x=a.
Then it becomes a^2+a-6=0.
On solving we get a=2 and -3.
Thus 1/(2^x)=2
Which gives x=-1.
So x-1/x equals 1+1=2.

My formatting may not be very good but have tried to keep it lucid.

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app

It must be C, kumarparitosh123

As x=-1, and we need to find the value of x-1/x

The expression \(x-\frac{1}{x} = -1 -(\frac{1}{-1}) = -1 + 1 = 0\)
User avatar
kumarparitosh123
Joined: 02 Nov 2015
Last visit: 19 Dec 2018
Posts: 131
Own Kudos:
Given Kudos: 121
GMAT 1: 640 Q49 V29
GMAT 1: 640 Q49 V29
Posts: 131
Kudos: 65
Kudos
Add Kudos
Bookmarks
Bookmark this Post
pushpitkc
kumarparitosh123
It's an E.
The question breaks down to
1/(4^x)+1/(2^x)-6=0.

Let 1/2^x=a.
Then it becomes a^2+a-6=0.
On solving we get a=2 and -3.
Thus 1/(2^x)=2
Which gives x=-1.
So x-1/x equals 1+1=2.

My formatting may not be very good but have tried to keep it lucid.

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app

It must be C, kumarparitosh123

As x=-1, and we need to find the value of x-1/x

The expression \(x-\frac{1}{x} = -1 -(\frac{1}{-1}) = -1 + 1 = 0\)
Yes Pushpitkc
My Bad. I don't know in which state of mind did I solve..

Thanks for pointing it out.
A lesson for me not to rush much..?

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
User avatar
niks18
User avatar
Retired Moderator
Joined: 25 Feb 2013
Last visit: 30 Jun 2021
Posts: 872
Own Kudos:
1,710
 [3]
Given Kudos: 54
Location: India
GPA: 3.82
Products:
Posts: 872
Kudos: 1,710
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(2^{(-2x)} + 2^{(-x)} - 6 = 0\), \(x - \frac{1}{x} =\) ?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

let \(2^{-x} = a\)
so the question becomes \(a^2 + a - 6 = 0\). Solving this we get
\((a-2)(a+3) = 0\). Therefore \(a = 2\) or \(a =-3\). But as "\(a\)" is a positive number (\(2\) raised to some power will always be positive), hence \(a = -3\) is not possible
So we get \(2^{-x} = 2\) or \(x = -1\)

therefore \(x- \frac{1}{x} = -1 +1 = 0\)

Option C
User avatar
himanshukamra2711
Joined: 12 Feb 2015
Last visit: 05 Feb 2020
Posts: 54
Own Kudos:
Given Kudos: 262
Location: India
GPA: 3.84
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(2^{(-2x)} + 2^{(-x)} - 6 = 0\), \(x - \frac{1}{x} =\) ?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2



2^-x=a

equation becomes a^2+a-6=0...comes out to be a=-3(not possible,since 2^-x is not equal to -3).Thus a=-2,
2^-x=-2
x=-1
and finally the answer comes out to be 0
User avatar
shashankism
Joined: 13 Mar 2017
Last visit: 23 Dec 2024
Posts: 611
Own Kudos:
Given Kudos: 88
Affiliations: IIT Dhanbad
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy)
Posts: 611
Kudos: 670
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(2^{(-2x)} + 2^{(-x)} - 6 = 0\), \(x - \frac{1}{x} =\) ?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
\(2^{(-2x)} + 2^{(-x)} - 6 = 0\)
=> \(1/2^{(2x)} + 1/2^{(x)} - 6 = 0\)

Let 2^x = y
=> \(1/y^2 + 1/y - 6 = 0\)
=> 6y^2 - 6y -1 = 0
=> 6y^2 - 3y + 2y -1 = 0
=> 3y (2y-1) + 2y-1 = 0
=> (3y +1) (2y-1) = 0
=> y = -1/3, 1/2

y = 2^-1
x = -1

x-1/x = -1 - (1/-1) = -1 +1 = 0

Answer C
User avatar
gps5441
Joined: 04 May 2014
Last visit: 03 Feb 2018
Posts: 109
Own Kudos:
Given Kudos: 126
Location: India
WE:Sales (Mutual Funds and Brokerage)
Posts: 109
Kudos: 77
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Plugin values of X
2ˆ(-2x)+2ˆ(-x)−6=0
We need a value of x which results the LHS of the equation to be zero.
Trial and error we can take x=(-1) I checked from given answer choices.
2ˆ(-2*-1)+2(-*-1)-6=0
2ˆ2+2-6
4+2-6=0
x-1/X=-1-1/(-1)=-1+1=0 Answer c
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,996
Own Kudos:
7,937
 [1]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,996
Kudos: 7,937
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
If \(2^{(-2x)} + 2^{(-x)} - 6 = 0\), \(x - \frac{1}{x} =\) ?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

We can let y = 2^(-x) and rewrite the equation as:

(2^(-x))^2 + 2^(-x) - 6 = 0

y^2 + y - 6 = 0

(y + 3)(y - 2) = 0

y = -3 or y = 2

Since y = 2^(-x), we can say 2^(-x) = -3 or 2^(-x) = 2. However, since 2 is positive, 2^(-x) will be positive regardless of the value of x. So, 2^(-x) can’t be -3, and thus it must be 2. Let’s solve the equation 2^(-x) = 2:

2^(-x) = 2^1

-x = 1

x = -1

Thus, x - 1/x = -1 - 1/(-1) = -1 + 1 = 0.

Answer: C
User avatar
jfranciscocuencag
Joined: 12 Sep 2017
Last visit: 17 Aug 2024
Posts: 229
Own Kudos:
Given Kudos: 132
Posts: 229
Kudos: 136
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shashankism
Bunuel
If \(2^{(-2x)} + 2^{(-x)} - 6 = 0\), \(x - \frac{1}{x} =\) ?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
\(2^{(-2x)} + 2^{(-x)} - 6 = 0\)
=> \(1/2^{(2x)} + 1/2^{(x)} - 6 = 0\)

Let 2^x = y
=> \(1/y^2 + 1/y - 6 = 0\)
=> 6y^2 - 6y -1 = 0

=> 6y^2 - 3y + 2y -1 = 0
=> 3y (2y-1) + 2y-1 = 0
=> (3y +1) (2y-1) = 0
=> y = -1/3, 1/2

y = 2^-1
x = -1

x-1/x = -1 - (1/-1) = -1 +1 = 0

Answer C

Hello shashankism !

Could you please explain to me how did you solve "the above in red"?

Thank you so much in advance!
User avatar
TryingToAceVerbal
Joined: 18 Nov 2021
Last visit: 07 Aug 2022
Posts: 13
Own Kudos:
Given Kudos: 285
Location: Germany
Concentration: Finance, Strategy
GMAT 1: 620 Q50 V25
GMAT 2: 700 Q50 V36
GMAT 2: 700 Q50 V36
Posts: 13
Kudos: 20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(2^{(-2x)} + 2^{(-x)} - 6 = 0\), \(x - \frac{1}{x} =\) ?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

substitute y = -x
=> \(2^{2y} + 2^{y} - 6 = 0\), \(\frac{1}{y} - y =\)?

\(2^{2y} + 2^{y} - 6 = 0\)
<=> \(2^{y} * (2^{y} + 1) - 2 * 3 = 0\)
<=> \(2^{y} * (2^{y} + 1) - 2^{1} * (2^{1} + 1) = 0\)
=> y = 1

\(\frac{1}{y} - y =\)?
=> \(\frac{1}{1} - 1 = 0\)
=> C
User avatar
bv8562
Joined: 01 Dec 2020
Last visit: 15 Jul 2025
Posts: 437
Own Kudos:
Given Kudos: 359
GMAT 1: 680 Q48 V35
GMAT 1: 680 Q48 V35
Posts: 437
Kudos: 464
Kudos
Add Kudos
Bookmarks
Bookmark this Post
2^(−2x)+2^(−x)−6=0

1/2x^2+1/2^x-6=0

To satisfy the given equation 1/2^2x+1/2^x must be equal to 6

To achieve this 'x' must be NEGATIVE, it can't be +ve, because if it's +ve then we will end up in two decimal values whose sum will never be 6 in this case

∴ x<0 and x=-1, we get

1/2^-2+1/2^-1 = 2^2+2 = 6

so, x-1/x = -1+1 = 0(C)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,413
Own Kudos:
Posts: 37,413
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Math Expert
102591 posts
PS Forum Moderator
695 posts