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

It is currently 31 Aug 2015, 01:44
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

IF 2^x 2^(x-2) = 3(2^13), what is the value of x? 9 11 13 15

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Manager
Manager
avatar
Joined: 26 Dec 2007
Posts: 70
Followers: 1

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

IF 2^x 2^(x-2) = 3(2^13), what is the value of x? 9 11 13 15 [#permalink] New post 05 Jan 2008, 18:57
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

IF 2^x – 2^(x-2) = 3(2^13), what is the value of x?

9
11
13
15
17

I guessed and got this one right, but have no idea how to solve. Please Help!
SVP
SVP
avatar
Joined: 28 Dec 2005
Posts: 1576
Followers: 2

Kudos [?]: 97 [0], given: 2

Re: Another exponent question from GMATprep Test 1 [#permalink] New post 05 Jan 2008, 19:38
i get x=15

i start off by factoring out 2^x from the right side, which leaves you with:

2^x(1-2^-2)
2^x(1-1/4)
2^x(3/4)

3/4 can be written as 3/2^2, and plugging in above you get:

2^x(3/2^2) --> (3)(2^x-2) = 3(2^13), which is given in the stem

2^x-2 = 2^13, i.e. x-2=13, x=15
Director
Director
User avatar
Joined: 12 Jul 2007
Posts: 862
Followers: 13

Kudos [?]: 228 [0], given: 0

Re: Another exponent question from GMATprep Test 1 [#permalink] New post 05 Jan 2008, 19:51
wow! what a question! I haven't seen this one before, but after a little playing around with it here's what I've come up with:

2^(x-2) will always be 1/4 of 2^x. This is because you're taking 2*2 (or 4) out of the equation (with the -2). The result will always be missing the 2*2 so it will be 1/4 of 2^x. Here are some examples to demonstrate:

2^3 = 2*2*2 = 8
2^1 = 2 = 2
8/2 = 4

2^5 = 2*2*2*2*2 = 32
2^3 = 2*2*2 = 8
32/8 = 4

2^8 = 2*2*2*2*2*2*2*2 = 256
2^6 = 2*2*2*2*2*2 = 64
256/64 = 4

so whatever number you get with 2^x, 2^(x-2) will always end up as 1/4 of that.

Now what does this mean for us? This means that

2^x - 2^(x-2) is equal to x - 1/4x or (3/4x) as a total
if 2^(x-2) is 1/4x and the total is 3/4x then you can say that 2^x-2^(x-2) = 3(2^x-2)

Now we have:

3(2^(x-2)) = 3(2^13)
x-2 = 13
x = 15

Answer D

Hope that helps! Let me know if my explanation leaves something to be desired :)
SVP
SVP
avatar
Joined: 04 May 2006
Posts: 1936
Schools: CBS, Kellogg
Followers: 19

Kudos [?]: 522 [0], given: 1

Premium Member
Re: Another exponent question from GMATprep Test 1 [#permalink] New post 05 Jan 2008, 20:12
eschn3am wrote:
wow! what a question! I haven't seen this one before, but after a little playing around with it here's what I've come up with:

2^(x-2) will always be 1/4 of 2^x. This is because you're taking 2*2 (or 4) out of the equation (with the -2). The result will always be missing the 2*2 so it will be 1/4 of 2^x. Here are some examples to demonstrate:

2^3 = 2*2*2 = 8
2^1 = 2 = 2
8/2 = 4

2^5 = 2*2*2*2*2 = 32
2^3 = 2*2*2 = 8
32/8 = 4

2^8 = 2*2*2*2*2*2*2*2 = 256
2^6 = 2*2*2*2*2*2 = 64
256/64 = 4

so whatever number you get with 2^x, 2^(x-2) will always end up as 1/4 of that.

Now what does this mean for us? This means that

2^x - 2^(x-2) is equal to x - 1/4x or (3/4x) as a total
if 2^(x-2) is 1/4x and the total is 3/4x then you can say that 2^x-2^(x-2) = 3(2^x-2)

Now we have:

3(2^(x-2)) = 3(2^13)
x-2 = 13
x = 15

Answer D

Hope that helps! Let me know if my explanation leaves something to be desired :)


how much time you need to solve this?
_________________

GMAT Club Premium Membership - big benefits and savings

Director
Director
User avatar
Joined: 12 Jul 2007
Posts: 862
Followers: 13

Kudos [?]: 228 [0], given: 0

Re: Another exponent question from GMATprep Test 1 [#permalink] New post 05 Jan 2008, 20:15
The hardest part is knowing what to look for. If you can catch the reasoning behind 2^x-2 being 1/4 of 2^x right off the bat the rest of it should fall into place in less than a minute.
Re: Another exponent question from GMATprep Test 1   [#permalink] 05 Jan 2008, 20:15
Display posts from previous: Sort by

IF 2^x 2^(x-2) = 3(2^13), what is the value of x? 9 11 13 15

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.