If 2^x - 2^x-2 = 3(2^13), what is the value of x?
*9 *11 *13 *15 *17
GMAT QUESTION(Can someone explain)
This topic has expert replies
-
- Junior | Next Rank: 30 Posts
- Posts: 10
- Joined: Thu Sep 25, 2008 9:15 am
- Location: new york
- GMAT Score:600
is the OA = 15?
I'm assuming the question is
2^x - 2^(x-2) = 3(2^13) ?
then take out 2^x
2^x * (1 - 2^-2) = 3(2^13)
equals => 2^x * (3/4) = 3(2^13)
then that also equals 2^x * (3/ 2^2) = 3(2^13)
2^x / 2^2 = 2^13
15-2 = 13
so x = 15?
I'm assuming the question is
2^x - 2^(x-2) = 3(2^13) ?
then take out 2^x
2^x * (1 - 2^-2) = 3(2^13)
equals => 2^x * (3/4) = 3(2^13)
then that also equals 2^x * (3/ 2^2) = 3(2^13)
2^x / 2^2 = 2^13
15-2 = 13
so x = 15?
-
- Master | Next Rank: 500 Posts
- Posts: 154
- Joined: Tue Aug 26, 2008 12:59 pm
- Location: Canada
- Thanked: 4 times
I worked it out and 15 is right.
Btw, you will want to put brackets on your exponent (x-2) for next time.
Btw, you will want to put brackets on your exponent (x-2) for next time.
- dmateer25
- Community Manager
- Posts: 1049
- Joined: Sun Apr 06, 2008 5:15 pm
- Location: Pittsburgh, PA
- Thanked: 113 times
- Followed by:27 members
- GMAT Score:710
I took 2 approaches with this.
1 similar to hwiya320.
The second I plugged in the numbers. This exponent problem was actually friendly for plugging in.
Starting with choice E
2^17 - 2^(17-2) = 3(2^13)
2^17 - 2^15 =
2^15(2^2-1) =
2^15(3)
No this isn't right
Next D
2^15 - 2^(15-2) = 3(2^13)
2^15 - 2^13 =
2^13 (2^2 - 1) =
2^13(3)
Bingo, 15 it is
1 similar to hwiya320.
The second I plugged in the numbers. This exponent problem was actually friendly for plugging in.
Starting with choice E
2^17 - 2^(17-2) = 3(2^13)
2^17 - 2^15 =
2^15(2^2-1) =
2^15(3)
No this isn't right
Next D
2^15 - 2^(15-2) = 3(2^13)
2^15 - 2^13 =
2^13 (2^2 - 1) =
2^13(3)
Bingo, 15 it is
-
- Senior | Next Rank: 100 Posts
- Posts: 45
- Joined: Mon Dec 08, 2008 9:55 pm
- Thanked: 4 times
you could also divide the first expression by 2^13. This gives you:
2^(x-13) - 2^(x-15)=3
Should be easier to plug in answers this way w/o doing additional work.
2^(x-13) - 2^(x-15)=3
Should be easier to plug in answers this way w/o doing additional work.