Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 Sep 2016, 15:59

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If 2^x - 2^(x-2) = 3*2^13, what is the value of x?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 11 Aug 2010
Posts: 10
Followers: 0

Kudos [?]: 2 [0], given: 0

If 2^x - 2^(x-2) = 3*2^13, what is the value of x? [#permalink]

### Show Tags

14 Nov 2010, 14:34
2
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

84% (01:48) correct 16% (01:24) wrong based on 190 sessions

### HideShow timer Statistics

If $$2^x - 2^{x-2} = 3(2^{13})$$, what value has x?

A. 9
B. 11
C. 13
D. 15
E. 17
[Reveal] Spoiler: OA
Veritas Prep GMAT Instructor
Joined: 26 Jul 2010
Posts: 237
Followers: 208

Kudos [?]: 444 [1] , given: 28

### Show Tags

15 Nov 2010, 15:18
1
KUDOS
1
This post was
BOOKMARKED
Hey guys,

This has always been a favorite problem of mine - the first time I saw it, an instructor had blanked on how to solve it and emailed me a photo from his phone asking for help. He had excused himself from a tutoring session and needed me to explain how to solve it (correctly, of course) within a few minutes, so the pressure was on!

Bunuel's explanation is perfect (as always), but when the pressure was on and I wasn't exactly thinking about factoring, I did this instead - I looked to see if there were a pattern in the subtraction at left (2 to an exponent minus 2 to another exponent, two less) that would always produce 3*something on the right. So I did:

x = 3 and x-2 = 1
2^3 - 2^1 = 8 - 2 = 6

And 6 = 3(2^1), so I had a start.

x = 4 and x-2 = 2
2^4 - 2^2 = 16 - 4 = 12

And 12 = 3(2^2), so the pattern held

x = 5 and x-2 = 3
2^5 - 2^3 = 32 - 8 = 24

And 24 = 3(2^3), and the pattern became clear...
The operation at left was always producing 3*2^(x-2) as its answer, so if x-2 = 13, then x = 15.

Strategically, using small numbers to establish patterns works pretty well when huge numbers (like 3(2^13)) are in play, and when exponents are involved (exponents are essentially just repetitive multiplication, so there are bound to be some repetitive patterns involved). If you can factor like Bunuel did, that's a great way to go...but I'd recommend having the "prove patterns w/ small numers" ideology in your arsenal!
_________________

Brian

Save \$100 on live Veritas Prep GMAT Courses and Admissions Consulting

Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Intern
Joined: 15 May 2012
Posts: 41
Followers: 0

Kudos [?]: 5 [1] , given: 94

Re: If 2^x - 2^(x-2) = 3*2^13, What is the value of x? [#permalink]

### Show Tags

08 Jun 2012, 21:04
1
KUDOS
2^x-2^x-2=3*2^13
2^x(1-2^-2)=2^13*3
2^x(1-1/2^2)=3*2^13
2^x(3/4)=3*2^13
2^x=3*2^13*4/3
2^x=2^13*4
2^x=2^13*2^2
2^x=2^15
Hence, x=15
Current Student
Joined: 08 Jan 2009
Posts: 326
GMAT 1: 770 Q50 V46
Followers: 25

Kudos [?]: 133 [1] , given: 7

Re: If 2^x - 2^(x-2) = 3*2^13, What is the value of x? [#permalink]

### Show Tags

09 Jun 2012, 00:44
1
KUDOS
This has the look of not factoring easily, so I applied some logic first.

We can rule out A,B and C (as the left hand side would all be 2^13 less a positive number (smaller than 2^13), so could never equal 3 * 2^13 (larger than 2^13)

Try D:
2^15 - 2^13 = 3*2^13

We can work with this easily:

Divide by 2^13
2^2 - 1 = 3
3 = 3

D
Math Expert
Joined: 02 Sep 2009
Posts: 34817
Followers: 6476

Kudos [?]: 82525 [0], given: 10107

### Show Tags

14 Nov 2010, 14:51
Pepe wrote:
Another question I have problem with:

If 2^x - 2^(x-2) = 3*2^13, What is the value of x?
A 9
B 11
C 13
D 15
E 17

$$2^x - 2^{x-2} = 3*2^{13}$$ --> factor out $$2^{x-2}$$ --> $$2^{x-2}*(2^2-1)=3*2^{13}$$ --> $$2^{x-2}*3=3*2^{13}$$ --> $$2^{x-2}=2^{13}$$ --> $$x-2=13$$ --> $$x=15$$.

_________________
Intern
Joined: 11 Aug 2010
Posts: 10
Followers: 0

Kudos [?]: 2 [0], given: 0

### Show Tags

14 Nov 2010, 14:56
Thank you Bunuel,

it's so simple if you see the solution
VP
Joined: 24 Jul 2011
Posts: 1064
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 112

Kudos [?]: 494 [0], given: 18

### Show Tags

06 Feb 2012, 01:21
2^x-2^(x-2)=3(2^13)
=> 2^(x-2) * [2^2 - 1] = 2^(15-2) * [2^2 - 1]
=> x = 15

Option (4)
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Intern
Joined: 10 May 2012
Posts: 1
Concentration: Accounting, Finance
GMAT Date: 06-04-2012
GPA: 3.98
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: If 2^x - 2^(x-2) = 3*2^13, What is the value of x? [#permalink]

### Show Tags

13 May 2012, 06:27
This is how I solved this problem.

2^x-2^x-2=3(2^13)
Factor 2^x 2^x(1-1)*2^-2=3(2^13)
x-2=13
x=15
Joined: 29 Mar 2012
Posts: 298
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 27

Kudos [?]: 362 [0], given: 23

Re: If 2^x - 2^(x-2) = 3*2^13, What is the value of x? [#permalink]

### Show Tags

09 Jun 2012, 02:39
Hi,

One can always try the options. Values less than 13 can be eliminated. Try others and whenever LHS = RHS, there you get the answer.

Regards,
Manager
Joined: 22 Jun 2012
Posts: 53
GMAT 1: 730 Q49 V40
Followers: 2

Kudos [?]: 18 [0], given: 6

### Show Tags

22 Jul 2012, 22:43
Hi,

Usually for problems where you have a number at different powers summed you can start by factoring by the smallest power of that number:

$$2^x-2^(x-2)=2^(x-2)*(2^2-1)=2^(x-2)*3$$

Hence

$$x-2=13$$
$$x=15$$

Not sure it is 700+ level
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11651
Followers: 527

Kudos [?]: 141 [0], given: 0

Re: If 2^x - 2^(x-2) = 3*2^13, what is the value of x? [#permalink]

### Show Tags

15 Jun 2014, 08:14
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.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 39

Kudos [?]: 1709 [0], given: 193

Re: If 2^x - 2^(x-2) = 3*2^13, what is the value of x? [#permalink]

### Show Tags

24 Jun 2014, 02:37
$$2^x - 2^{(x-2)} = 3*2^{13}$$

Working on LHS

$$2^x - 2^{(x-2)}$$

$$= 2^x - \frac{2^x}{4}$$

$$= 2^x (1 - \frac{1}{4})$$

$$= 2^x (\frac{3}{4})$$

Equating to RHS

$$2^x (\frac{3}{4}) = 3 * 2^{13}$$

$$2^x * 3 = 3 * 2^{15}$$

x = 15 = Answer = D
_________________

Kindly press "+1 Kudos" to appreciate

Re: If 2^x - 2^(x-2) = 3*2^13, what is the value of x?   [#permalink] 24 Jun 2014, 02:37
Similar topics Replies Last post
Similar
Topics:
4 If x<y, and y(y−2x)=2-x^2, what is the value of x−y? 3 07 Mar 2014, 02:28
3 If 2^x - 2^(x-2) = 3*2^(13), what is x? 10 03 Feb 2012, 08:27
10 If 2^x-2^(x-2)=3*2^13 what is the value of x? 6 15 Oct 2011, 12:26
If 2^x - 2^(x-2) = 3*2^13, what is the value of x? 2 03 Dec 2010, 09:37
4 If 2^x-2^(x-2)=3*2^13 what is the value of x? 8 13 Feb 2010, 11:00
Display posts from previous: Sort by