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

 It is currently 23 Sep 2018, 09:18

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 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ?

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49320
If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ?  [#permalink]

Show Tags

09 Sep 2017, 08:10
1
4
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:31) correct 24% (01:57) wrong based on 157 sessions

HideShow timer Statistics

If $$2^{(-2x)} + 2^{(-x)} - 6 = 0$$, $$x - \frac{1}{x} =$$ ?

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

_________________
Manager
Joined: 02 Nov 2015
Posts: 167
GMAT 1: 640 Q49 V29
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ?  [#permalink]

Show Tags

09 Sep 2017, 08:29
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
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 3136
Location: India
GPA: 3.12
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ?  [#permalink]

Show Tags

09 Sep 2017, 08:44
Since we have been asked to find the value of $$x - \frac{1}{x}$$, this can be rewritten as $$\frac{x^2 - 1}{x}$$

The equation $$2^{(-2x)} + 2^{(-x)} - 6 = 0$$ => $$\frac{1}{{2^{(x)^2}}} + \frac{1}{{2^{(x)}}} - 6 = 0$$

Substituting $$\frac{1}{2^x}$$ be b

Therefore, $$b^2 + b - 6 = 0$$
Solving for b, b=-3 or 2

If b=2 | $$\frac{1}{2^x} = 2^{-x} = 2$$ So, x = -1

The value for the expression $$\frac{x^2 - 1}{x} = \frac{0}{-1} = 0$$(Option C)
_________________

You've got what it takes, but it will take everything you've got

BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 3136
Location: India
GPA: 3.12
If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ?  [#permalink]

Show Tags

09 Sep 2017, 08:47
kumarparitosh123 wrote:
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 $$x-\frac{1}{x} = -1 -(\frac{1}{-1}) = -1 + 1 = 0$$
_________________

You've got what it takes, but it will take everything you've got

Manager
Joined: 02 Nov 2015
Posts: 167
GMAT 1: 640 Q49 V29
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ?  [#permalink]

Show Tags

09 Sep 2017, 08:49
pushpitkc wrote:
kumarparitosh123 wrote:
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
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ?  [#permalink]

Show Tags

09 Sep 2017, 08:51
Bunuel wrote:
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
Manager
Joined: 12 Feb 2015
Posts: 56
Location: India
GPA: 3.84
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ?  [#permalink]

Show Tags

09 Sep 2017, 12:55
Bunuel wrote:
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
Director
Joined: 13 Mar 2017
Posts: 619
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ?  [#permalink]

Show Tags

09 Sep 2017, 21:06
Bunuel wrote:
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

_________________

CAT 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Manager
Joined: 04 May 2014
Posts: 161
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ?  [#permalink]

Show Tags

24 Sep 2017, 21:39
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
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ?  [#permalink]

Show Tags

26 Sep 2017, 16:28
Bunuel wrote:
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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ? &nbs [#permalink] 26 Sep 2017, 16:28
Display posts from previous: Sort by

If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ?

Events & Promotions

 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®.