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

 It is currently 15 Oct 2019, 02:04

### 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 − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58344
If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

### Show Tags

04 Dec 2014, 07:34
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:52) correct 24% (02:34) wrong based on 182 sessions

### HideShow timer Statistics

Tough and Tricky questions: Exponents.

If $$x - \frac{1}{2^6} - \frac{1}{2^7} - \frac{1}{2^8} = \frac{2}{2^9}$$, then x =

A) 1/2
B) 1/2^3
C) 1/2^4
D) 1/2^5
E) 1/2^9

Kudos for a correct solution.

Source: Chili Hot GMAT

_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1751
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

### Show Tags

04 Dec 2014, 19:39
8
$$x - \frac{1}{2^6} - \frac{1}{2^7} - \frac{1}{2^8} = \frac{2}{2^9}$$

$$x = \frac{1}{2^6} + \frac{1}{2^7} + \frac{1}{2^8} + \frac{2}{2^9}$$

$$x = \frac{1*2*2*2}{2^9} + \frac{1*2*2}{2^9} + \frac{1*2}{2^9} + \frac{2}{2^9}$$

$$x = \frac{8+4+2+2}{2^9} = \frac{16}{2^9} = \frac{1}{2^5}$$

_________________
Kindly press "+1 Kudos" to appreciate
##### General Discussion
Manager
Joined: 21 Sep 2012
Posts: 208
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

### Show Tags

04 Dec 2014, 07:44
1
1
x= 2/2^9+1/2^6+1/2^7+1/2^8
Take LCM i.e. 2^9

x=(2+2^3+2^2+2)/2^9
x=(2+8+4+2)/2^9
x=16/2^9
x=2^4/2^9
x=1/2^5

Ans - D
Math Expert
Joined: 02 Sep 2009
Posts: 58344
Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

### Show Tags

05 Dec 2014, 07:29
Bunuel wrote:

Tough and Tricky questions: Exponents.

If $$x - \frac{1}{2^6} - \frac{1}{2^7} - \frac{1}{2^8} = \frac{2}{2^9}$$, then x =

A) 1/2
B) 1/2^3
C) 1/2^4
D) 1/2^5
E) 1/2^9

Kudos for a correct solution.

Source: Chili Hot GMAT

_________________
Manager
Joined: 12 Sep 2014
Posts: 142
GMAT 1: 740 Q49 V41
GPA: 3.94
Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

### Show Tags

05 Dec 2014, 11:40
Choice D

When we start, notice that the RHS equals 2/2^9 = 1/2^8. Then add the factor of 1/2^8 to both sides yielding 2/2^8 on the RHS.
Keep doing this until you reach x-1/2^6 = 1/2^6, yielding x = 1/2^5.

D
Manager
Joined: 26 Feb 2015
Posts: 110
Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

### Show Tags

08 Mar 2015, 13:14
From this
$$x = \frac{1}{2^6} + \frac{1}{2^7} + \frac{1}{2^8} + \frac{2}{2^9}$$

To this
$$x = \frac{1*2*2*2}{2^9} + \frac{1*2*2}{2^9} + \frac{1*2}{2^9} + \frac{2}{2^9}$$

$$x = \frac{8+4+2+2}{2^9} = \frac{16}{2^9} = \frac{1}{2^5}$$

How?
Math Expert
Joined: 02 Sep 2009
Posts: 58344
Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

### Show Tags

08 Mar 2015, 13:39
erikvm wrote:
From this
$$x = \frac{1}{2^6} + \frac{1}{2^7} + \frac{1}{2^8} + \frac{2}{2^9}$$

To this
$$x = \frac{1*2*2*2}{2^9} + \frac{1*2*2}{2^9} + \frac{1*2}{2^9} + \frac{2}{2^9}$$

$$x = \frac{8+4+2+2}{2^9} = \frac{16}{2^9} = \frac{1}{2^5}$$

How?

This is also basic (finding the common denominator):

$$x = \frac{1}{2^6} + \frac{1}{2^7} + \frac{1}{2^8} + \frac{2}{2^9}=\frac{2^3}{2^9} + \frac{2^2}{2^9} + \frac{2}{2^9} + \frac{2}{2^9}=\frac{2^3+2^2+2+2}{2^9}$$.
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8043
Location: United States (CA)
Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

### Show Tags

08 Feb 2017, 19:49
Bunuel wrote:

Tough and Tricky questions: Exponents.

If $$x - \frac{1}{2^6} - \frac{1}{2^7} - \frac{1}{2^8} = \frac{2}{2^9}$$, then x =

A) 1/2
B) 1/2^3
C) 1/2^4
D) 1/2^5
E) 1/2^9

We can multiply the given equation by 2^9 and we have:

x(2^9) - 2^3 - 2^2 - 2^1 = 2

x(2^9) = 2 + 2^1 + 2^2 + 2^3

x(2^9) = 16

x = 16/2^9

x = 2^4/2^9

x = 1/2^5

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 30 May 2017
Posts: 18
Location: India
Concentration: Finance, Strategy
Schools: Wharton, IESE, ISB, NUS
GPA: 4
WE: Engineering (Consulting)
Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

### Show Tags

18 Aug 2019, 05:33
x= (2/2^9) +(1/2)^8 + (1/2)^7 + (1/2)^6
x =( 1/2^8) + ( 1/2^8)+ (1/2)^7 + (1/2)^6
x= (2/2^8) + (1/2)^7 + (1/2)^6
x = (1/2^7) +(1/2)^7 + (1/2)^6
x = (2/2^7) + (1/2)^6
x= (1/2)^6 + (1/2)^6
x = (2/2^6)
x = 1/2^5

_________________
You say this is a problem , I say this must be an opportunity
SVP
Joined: 03 Jun 2019
Posts: 1684
Location: India
If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

### Show Tags

18 Aug 2019, 07:23
Bunuel wrote:

Tough and Tricky questions: Exponents.

If $$x - \frac{1}{2^6} - \frac{1}{2^7} - \frac{1}{2^8} = \frac{2}{2^9}$$, then x =

A) 1/2
B) 1/2^3
C) 1/2^4
D) 1/2^5
E) 1/2^9

Kudos for a correct solution.

Source: Chili Hot GMAT

Given: $$x - \frac{1}{2^6} - \frac{1}{2^7} - \frac{1}{2^8} = \frac{2}{2^9}$$

$$x - \frac{1}{2^6} - \frac{1}{2^7} - \frac{1}{2^8} = \frac{2}{2^9}$$

$$x = \frac{1}{2^6} + \frac{1}{2^7} +\frac{1}{2^8} + \frac{2}{2^9}$$

$$x = \frac{(2-1)}{2^6} + \frac{(2-1)}{2^7} +\frac{(2-1)}{2^8} + \frac{1}{2^8}$$

$$x = \frac{1}{2^5}-\frac{1}{2^6} + \frac{1}{2^6}-\frac{1}{2^7} +\frac{1}{2^7}-\frac{1}{2^8} + \frac{1}{2^8}$$

$$x = \frac{1}{2^5}$$

IMO D
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =   [#permalink] 18 Aug 2019, 07:23
Display posts from previous: Sort by