2^(x-2) is a common factor for 2^x and 2^(x-2), so you get:
2^x - 2^(x-2) = 2^(x-2) * [2^2 - 1] = 2^(x - 2) * (4 - 1) = 2^(x - 2) * 3 = 3 * 2^13
This means that x - 2 = 13, so x = 15.
And yes, I do believe this question has been answered before...
what is x
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
-
dumb.doofus
- Master | Next Rank: 500 Posts
- Posts: 435
- Joined: Sat Sep 27, 2008 2:02 pm
- Location: San Jose, CA
- Thanked: 43 times
- Followed by:1 members
- GMAT Score:720
One love, one blood, one life. You got to do what you should.
https://dreambigdreamhigh.blocked/
https://gmattoughies.blocked/
https://dreambigdreamhigh.blocked/
https://gmattoughies.blocked/
-
kanha81
- Master | Next Rank: 500 Posts
- Posts: 431
- Joined: Sat Jan 10, 2009 9:32 am
- Thanked: 16 times
- Followed by:1 members
Deepoe,deepoe wrote:2^x – 2^x-2 = 3(2^13), what is x?
a. 9
b. 11
c. 13
d. 15
e. 17
Don't know if this question already have been asked, if so I'M SORRY
Please type your questions clearly!!!
A better way to write this out would be:
Notice the highlighted part!!!!
2^x - 2^(x-2) = 3 (2^13)
2^x * (1- (1/2^2) ) = 3 * (2^13)
2^x * (3/4) = 3 * (2^13)
2^x = (2^2) * (2^13)
2^x = 2^15
x = 15
[D]
Want to Beat GMAT.
Always do what you're afraid to do. Whoooop GMAT
Always do what you're afraid to do. Whoooop GMAT
Sorrykanha81 wrote:Deepoe,deepoe wrote:2^x – 2^x-2 = 3(2^13), what is x?
a. 9
b. 11
c. 13
d. 15
e. 17
Don't know if this question already have been asked, if so I'M SORRY
Please type your questions clearly!!!
A better way to write this out would be:
Notice the highlighted part!!!!
2^x - 2^(x-2) = 3 (2^13)
2^x * (1- (1/2^2) ) = 3 * (2^13)
2^x * (3/4) = 3 * (2^13)
2^x = (2^2) * (2^13)
2^x = 2^15
x = 15
[D]
Could you explain these steps:
2^x * (1- (1/2^2) ) = 3 * (2^13)
2^x * (3/4) = 3 * (2^13)
Thanks!
