I got the answer right but I'm not how to solve this question (I guessed).
exponent questions like these give me a hard time since they contain a variable set that is + or - another variable set. I typically see problems where perhaps 2^x = 3(2^x) ,which is easier to solve but Im not sure how to get this one. Please help!
Help me solve this GMAT Quant Question (GMATPrep) #2
This topic has expert replies
- EricImasogie
- Newbie | Next Rank: 10 Posts
- Posts: 9
- Joined: Sat Aug 02, 2014 10:48 am
- Followed by:1 members
Last edited by EricImasogie on Fri Dec 12, 2014 5:52 pm, edited 1 time in total.
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
This requires some factoring.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
2^x - 2^(x-2) = 3(2^13)
2^(x-2)[2^2 - 1] = 3(2^13)
2^(x-2)[3] = 3(2^13)
Divide both sides by 3 to get: 2^(x-2)= 2^13
So, x-2 = 13
[spoiler]x = 15[/spoiler]
Cheers,
Brent
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi EricImasogie,
Factoring the equation (as Brent showed) is a useful approach here. You can actually take it a step further by TESTing THE ANSWERS (you might find it easier to manipulate numbers than to manipulate variables). One of those numbers IS the value of X, so you can plug them in, do the necessary math and find the one value that balances out the equation. Here's how to approach it:
Since the "right side" of the equation is greater than 2^14, X must be bigger than 14 (since the "left side" of the equation involves subtraction). So we can eliminate A, B and C.
Let's TEST answer D: 15
If X = 15, then...
2^15 - 2^13 can be factored into...
(2^13)(2^2 - 1) =
(2^13)(3)
This is EXACTLY what's on the "right side" of the equation, so X MUST be 15
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
Factoring the equation (as Brent showed) is a useful approach here. You can actually take it a step further by TESTing THE ANSWERS (you might find it easier to manipulate numbers than to manipulate variables). One of those numbers IS the value of X, so you can plug them in, do the necessary math and find the one value that balances out the equation. Here's how to approach it:
Since the "right side" of the equation is greater than 2^14, X must be bigger than 14 (since the "left side" of the equation involves subtraction). So we can eliminate A, B and C.
Let's TEST answer D: 15
If X = 15, then...
2^15 - 2^13 can be factored into...
(2^13)(2^2 - 1) =
(2^13)(3)
This is EXACTLY what's on the "right side" of the equation, so X MUST be 15
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
-
- Master | Next Rank: 500 Posts
- Posts: 447
- Joined: Fri Nov 08, 2013 7:25 am
- Thanked: 25 times
- Followed by:1 members
Alternatively, we can see that a SUBTRACTION is required, so we can use this clue to bring us closer to the answer on the right hand side of the equation:
3 x 2^13 = (4-1) x 2^13 = 4 x 2^13 - 2^13 = 2^15 - 2^13 = 2^n - 2^(n-2)
So n = 15
3 x 2^13 = (4-1) x 2^13 = 4 x 2^13 - 2^13 = 2^15 - 2^13 = 2^n - 2^(n-2)
So n = 15