Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 May 2017, 08:52

# Live Now:

### 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 x?

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 266
Location: Kuwait
Schools: Columbia university
Followers: 5

Kudos [?]: 307 [1] , given: 52

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

### Show Tags

03 Feb 2012, 08:27
1
KUDOS
00:00

Difficulty:

5% (low)

Question Stats:

84% (02:02) correct 16% (02:48) wrong based on 158 sessions

### HideShow timer Statistics

If 2^x - 2^(x-2) = 3*2^(13), what is x?

A. 9
B. 11
C. 13
D. 15
E. 17
[Reveal] Spoiler: OA

_________________

Sky is the limit

Last edited by Bunuel on 25 Jun 2013, 05:17, edited 2 times in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 38856
Followers: 7723

Kudos [?]: 105994 [1] , given: 11602

### Show Tags

03 Feb 2012, 08:44
1
KUDOS
Expert's post
manalq8 wrote:
2^x _ 2^x-2=(3)(2^13). what is X?

the way I did this q is

x-x-2=13

but the X's are cancelled so how are we going to get the X?

If 2^x - 2^(x-2) = 3*2^(13), what is x?
A. 9
B. 11
C. 13
D. 15
E. 17

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

Hope it's clear.
_________________
Manager
Joined: 30 May 2013
Posts: 188
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
Followers: 0

Kudos [?]: 72 [0], given: 72

2^x – 2^(x-2) = 3(2^13), what is x? [#permalink]

### Show Tags

27 Aug 2013, 23:35
2^x – 2^(x-2) = 3(2^13), what is x?
a. 9
b. 11
c. 13
d. 15
e. 17
Math Expert
Joined: 02 Sep 2009
Posts: 38856
Followers: 7723

Kudos [?]: 105994 [0], given: 11602

Re: 2^x – 2^(x-2) = 3(2^13), what is x? [#permalink]

### Show Tags

28 Aug 2013, 01:31
rrsnathan wrote:
2^x – 2^(x-2) = 3(2^13), what is x?
a. 9
b. 11
c. 13
d. 15
e. 17

Merging similar topics.
_________________
Intern
Joined: 01 Jun 2010
Posts: 42
Followers: 0

Kudos [?]: 17 [1] , given: 3

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

### Show Tags

28 Aug 2013, 14:27
1
KUDOS
I did it a bit differently, but I arrived at the right answer. Here is the way I did it:
$$2^x - 2^{x-2} = 3* 2^{13}$$
Factor out a $$2^x$$ which gives:
$$2^x(1 - \frac{1}{4}) = 3* 2^{13}$$
Clean up:
$$2^x(\frac{3}{4}) = 3* 2^{13}$$
At this point I realized that the 4 in the denominator could be factored out so that's what I did:
$$2^{x-2}(3) = 3* 2^{13}$$
From here you have $$2^{x-2} = 2^{13}$$ so $$x = 15$$

I hope that helps.
_________________

Please don't forget to give kudos if you found someone's post helpful. Everyone likes kudos!

Manager
Joined: 13 Jul 2013
Posts: 73
GMAT 1: 570 Q46 V24
Followers: 0

Kudos [?]: 10 [0], given: 21

### Show Tags

06 Sep 2013, 11:14
Bunuel wrote:
manalq8 wrote:
2^x _ 2^x-2=(3)(2^13). what is X?

the way I did this q is

x-x-2=13

but the X's are cancelled so how are we going to get the X?

If 2^x - 2^(x-2) = 3*2^(13), what is x?
A. 9
B. 11
C. 13
D. 15
E. 17

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

Hope it's clear.

Can you please explain the red highlighted part? I read other explanations but it wasn't clear. I am unable to understand how did you factor out 2^(x-2)?
Intern
Joined: 01 Jun 2010
Posts: 42
Followers: 0

Kudos [?]: 17 [0], given: 3

### Show Tags

06 Sep 2013, 13:59
theGame001 wrote:
Bunuel wrote:
manalq8 wrote:
2^x _ 2^x-2=(3)(2^13). what is X?

the way I did this q is

x-x-2=13

but the X's are cancelled so how are we going to get the X?

If 2^x - 2^(x-2) = 3*2^(13), what is x?
A. 9
B. 11
C. 13
D. 15
E. 17

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

Hope it's clear.

Can you please explain the red highlighted part? I read other explanations but it wasn't clear. I am unable to understand how did you factor out 2^(x-2)?

Sure! First notice that $$2^{x-2} * 2^{2} = 2^{x}$$ So, we know that $$2^{x-2}$$ is a factor of $$2^{x}$$. I am using the product rule for exponents: $$x^{a}*x^{b}=x^{a+b}$$ It helps to think of this rule in reverse (going from right -> left). What I mean by that is we can also write it as $$x^{a+b}=x^{a}*x^{b}$$ When I factor out the $$2^{x-2}$$ I am really separating $$2^{x}$$ into $$2^{x-2} * 2^{2}$$. So,
$$2^x - 2^{x-2} = 3*2^{13}$$ which becomes $$2^{x-2}(2^2-1)= 3*2^{13}$$ after we factor out the $$2^{x}$$.

Does that help?
_________________

Please don't forget to give kudos if you found someone's post helpful. Everyone likes kudos!

Director
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 512
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Followers: 26

Kudos [?]: 828 [0], given: 630

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

### Show Tags

09 Sep 2013, 09:30
Quote:
Clean up:
2^x(\frac{3}{4}) = 3* 2^{13}
At this point I realized that the 4 in the denominator could be factored out so that's what I did:
2^{x-2}(3) = 3* 2^{13}
From here you have 2^{x-2} = 2^{13} so x = 15

It seems that in the bolded step above you could have multiplied both sides by 4/3 thus canceling the 3 from the other side out. You would then be left with 4 or (2*2) or 2^2 in addition to the 2^13 leaving you with the 2^15. Just thought that might be a little quicker.
Manager
Joined: 29 Sep 2013
Posts: 53
Followers: 0

Kudos [?]: 36 [0], given: 48

### Show Tags

21 Oct 2013, 07:15
Bunuel wrote:
manalq8 wrote:
2^x _ 2^x-2=(3)(2^13). what is X?

the way I did this q is

x-x-2=13

but the X's are cancelled so how are we going to get the X?

If 2^x - 2^(x-2) = 3*2^(13), what is x?
A. 9
B. 11
C. 13
D. 15
E. 17

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

Hope it's clear.

Now it's a pretty simple point, but it got silly old me baffled, so i searched up the net and came up with the following explanation.
$$2^{x-2}(2^2-1)= 3*2^{13}$$

If from $$N^x - N^{x-a}, N^{x-a}$$ is factored out we will have:
$$N^{x-a} (N^b - 1)$$
Where $$b = x - a$$
Example 1
$$5^8 - 5^5 = 5^5 (5^3 - 1) = 5^5 (125 - 1) = 5^5*124$$
Example 2
$$2^x - 2^{x-2} = 2^x (2^2 - 1) = 2^x (4 - 1) = 2^x . 3$$

Now in Example $$2$$ we don't know the value of the $$x$$ but we know the difference between$$x$$ and$$x-2$$ is $$2$$ therefore,$$b = 2$$.
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 51

Kudos [?]: 2166 [0], given: 193

### Show Tags

26 Feb 2014, 03:09
suk1234 wrote:
Bunuel wrote:
manalq8 wrote:
2^x _ 2^x-2=(3)(2^13). what is X?

the way I did this q is

x-x-2=13

but the X's are cancelled so how are we going to get the X?

If 2^x - 2^(x-2) = 3*2^(13), what is x?
A. 9
B. 11
C. 13
D. 15
E. 17

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

Hope it's clear.

Now it's a pretty simple point, but it got silly old me baffled, so i searched up the net and came up with the following explanation.
$$2^{x-2}(2^2-1)= 3*2^{13}$$

If from $$N^x - N^{x-a}, N^{x-a}$$ is factored out we will have:
$$N^{x-a} (N^b - 1)$$
Where $$b = x - a$$
Example 1
$$5^8 - 5^5 = 5^5 (5^3 - 1) = 5^5 (125 - 1) = 5^5*124$$
[color=#ff0000]Example 2
[b]$$2^x - 2^{x-2} = 2^x (2^2 - 1) = 2^x (4 - 1) = 2^x . 3$$
[/color][/b]

Now in Example $$2$$ we don't know the value of the $$x$$ but we know the difference between$$x$$ and$$x-2$$ is $$2$$ therefore,$$b = 2$$.

The highlighted Example 2 is wrong

2^x - 2^{x-2} =

2^x (1 - 1/4 ) =

2^x . 3/4 =

2^(x-2) . 3 Hope this helps

_________________

Kindly press "+1 Kudos" to appreciate

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15421
Followers: 649

Kudos [?]: 207 [0], given: 0

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

### Show Tags

29 May 2016, 00:47
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.
_________________
Re: If 2^x - 2^(x-2) = 3*2^(13), what is x?   [#permalink] 29 May 2016, 00:47
Similar topics Replies Last post
Similar
Topics:
If x is a positive integer, what is (2^x/2^(–x))^x ? 3 18 May 2017, 11:53
9 If x<y, and y(y−2x)=2-x^2, what is the value of x−y? 3 09 Jun 2016, 01:36
4 If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n? 8 20 May 2017, 16:11
If 2^x - 2^(x-2) = 3*2^13, what is the value of x? 2 03 Dec 2010, 11:18
6 If 2^x - 2^(x-2) = 3*2^13, what is the value of x? 12 22 Feb 2017, 13:08
Display posts from previous: Sort by