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

 It is currently 24 May 2017, 03:40

### 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? 9 11 13 15

Author Message
Manager
Joined: 26 Dec 2007
Posts: 70
Followers: 1

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

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

### Show Tags

05 Jan 2008, 19:57
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

SVP
Joined: 28 Dec 2005
Posts: 1562
Followers: 3

Kudos [?]: 158 [0], given: 2

Re: Another exponent question from GMATprep Test 1 [#permalink]

### Show Tags

05 Jan 2008, 20:38
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
Joined: 12 Jul 2007
Posts: 861
Followers: 17

Kudos [?]: 307 [0], given: 0

Re: Another exponent question from GMATprep Test 1 [#permalink]

### Show Tags

05 Jan 2008, 20:51
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

Hope that helps! Let me know if my explanation leaves something to be desired
SVP
Joined: 04 May 2006
Posts: 1902
Schools: CBS, Kellogg
Followers: 23

Kudos [?]: 1122 [0], given: 1

Re: Another exponent question from GMATprep Test 1 [#permalink]

### Show Tags

05 Jan 2008, 21:12
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

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

how much time you need to solve this?
_________________
Director
Joined: 12 Jul 2007
Posts: 861
Followers: 17

Kudos [?]: 307 [0], given: 0

Re: Another exponent question from GMATprep Test 1 [#permalink]

### Show Tags

05 Jan 2008, 21:15
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, 21:15
Display posts from previous: Sort by