GMAT Prep Arithmatic Question - Please Help with Good Explanation!

[bobbycronkey]

Hi,

I received the following question on the practice test, so I know the right answer, I just can't figure out the process of getting the answer. Could someone please explain step by step the method for solving this? I tried a post on ScoreTop, but I was unable to even understand the explanation. This one is driving me crazy, I must be missing something!!! Thank you!

Question:

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

Thanks again for the assistance!

[eltonr]

It is D = 15
2^x - 2^(x -2) = 3 (2^13)
(3 * 2^x)/4 = 3 (2^13)
3 * 2^x = 3(2^15)
Hence x = 15

Elton

[narda]

Elton,

In the second step, how did you get '3' on the left side of the equation?

Thanks,
Narda

[yowas]

In the second step, how did you get '3' on the left side of the equation?

2^(x-2) can be rewritten as 2^x/2^2 or 2^x/4

So now on the left side we have:
2^x - 2^x/4
To get a common denominator multiply the first term by 4/4
(4*2^x - 2^x)/4

This is where the 3 comes from: factor out 2^x
[2^x * (4 - 1)] / 4
(2^x * 3) / 4

Now we can finish

2^x * 3 = 4 * 3 * 2^13
2^x * 3 = 2^2 * 2^13 * 3
2^x * 3 = 2^15 * 3
x = 15

[kartikayeg]

Yep agree with D

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

takeing 2^x common
2^x ( 1 - 1/4) = 3(2^13)
2^x (3/4) = 3(2^13)

taking 3/4 to the other side
2^x = 3(2^13) (4/3) ----- the 3s cancel each other
2^x = (2^13) 2^2
2^x = 2^(13+2) = 2^15
x=15

[KillGmat]

ans is D.Its quite easy if you are good in exponents and know the concepts well.. Nice explanation by everyone.

[anandisonline]

D...simple prob...well elaborated

[abraxas]

Thanks guys!