If 2^x - 2^x-2 = 3*(2)^13, What is the value of x?

Question

If 2^x - 2^x-2 = 3*(2)^13, What is the value of x? A.12 B.14 C.15 D.17 E.19

ajith · Answer

bhumika.k.shah wrote:If 2^x - 2^x-2 = 3*(2)^13, What is the value of x? A.12 B.14 C.15 D.17 E.19 2^x - 2^x/4 = 2^x(1-1/4) = 2^x(3/4) = 3*2^(x-2) x-2 =13 x =15

thephoenix · Answer

2^x - 2^x-2 = 3*(2)^13 2^x - 2^x-2=2^x-2^x/2^2=2^x(1-1/4)=2^x*(3/4)=3*2^x-2--->x-2=13--->x=15

harshavardhanc · Answer

you can go through all the lengthy calculation and arrive at the answer. No one will get this question wrong. definitely! Everyone knows how to solve a linear equation and knows powers of 2.

But, I think this question can be a boon or a bane ? it totally depends on you.

You spend at 3 mins in making an equation and then solve it.

Or

you can see 3 as (2^2 - 1 ) and save at least 2 mins ! that's 2 extra minutes!

Now the R.H.S becomes 2^13 * ( 2^2 -1 ) = 2^15 - 2^13 ( looks like L.H.S ? )

Pick your X !

Regards,
Harsha

ajith · Answer

harshavardhanc wrote:you can go through all the lengthy calculation and arrive at the answer. No one will get this question wrong. definitely! Everyone knows how to solve a linear equation and knows powers of 2.

But, I think this question can be a boon or a bane ? it totally depends on you.

You spend at 3 mins in making an equation and then solve it.

Or

you can see 3 as (2^2 - 1 ) and save at least 2 mins ! that's 2 extra minutes!

Now the R.H.S becomes 2^13 * ( 2^2 -1 ) = 2^15 - 2^13 ( looks like L.H.S ? )

Pick your X !

Sources for the time statistics please! This problem can be done in less than 45 seconds in equation method

in this case at least the equation method is fool proof and better than non-scientific methods

harshavardhanc · Answer

Sources for the time statistics please!

--> oh, so you ARE practicing CR as well. Good! Keep it up !

This problem can be done in less than 45 seconds in equation method

-- > Sooooooper!!!

in this case at least the equation method is fool proof and better than non-scientific methods

--> non-scientific???? did you mean non-conventional ? Then yes, my method was non-conventional.

Scientific????? I still did not understand how a scientific formula is used in the a Math problem? was it used in the solve-by-equation method? I may have missed that ! sorry again!

No offenses dude! But, if you're hurt because I questioned you're method of solving, then please accept my apology!

But, GMAC knows that we have a habit of starting from the "given" or the "L.H.S", and use the info to arrive at the answer.

This question, I think, is the same trap, wanting us do what we normally do.

My point was, why not take a different path and start with the numbers here and make it look like the part which has variables?

You said that it will take 45 seconds to make an eq and solve it. You surely must have done it within that time, but slow-heads like me will take more than 45 secs to solve an eq. That's how we were made by the almighty!

Anyway, we now have two methods to solve this question. Fellow forum-mates can choose their pick .

Regards,
Harsha

ajith · Answer

I think problem was too straight forward to try anything unconventional. I have nothing against the unconventional methods and I am all for those.

Having said that, I do not want to get into arguments. There is nothing personal in here and I do not want to offend anybody

bhumika.k.shah · Answer

ajith,
i got it so far. kindly explain how u got the part in bold???

ajith wrote:
bhumika.k.shah wrote:If 2^x - 2^x-2 = 3*(2)^13, What is the value of x?

A.12
B.14
C.15
D.17
E.19
2^x - 2^x/4 = 2^x(1-1/4) = 2^x(3/4) = 3*2^(x-2)

x-2 =13

x =15

armaan700+ · Answer

bhumika.k.shah wrote:ajith,
i got it so far. kindly explain how u got the part in bold???

ajith wrote:
bhumika.k.shah wrote:If 2^x - 2^x-2 = 3*(2)^13, What is the value of x?

A.12
B.14
C.15
D.17
E.19
2^x - 2^x/4 = 2^x(1-1/4) = 2^x(3/4) = 3*2^(x-2)

x-2 =13

x =15

just compare RHS and LHS

3*2^15=3*2^(x-2)
property of exponents
if n^k*m^l=n^a*m^b
then k=a
and l=b
hence x-2=15

ajith · Answer

bhumika.k.shah wrote:ajith,
i got it so far. kindly explain how u got the part in bold???

ajith wrote:
bhumika.k.shah wrote:If 2^x - 2^x-2 = 3*(2)^13, What is the value of x?

A.12
B.14
C.15
D.17
E.19
2^x - 2^x/4 = 2^x(1-1/4) = 2^x(3/4) = 3*2^(x-2)

x-2 =13

x =15

just compare RHS and LHS

3*2^15=3*2^(x-2)
property of exponents
if n^k*m^l=n^a*m^b
then k=a
and l=b
hence x-2=15

thephoenix · Answer

armaan700+ wrote:bhumika.k.shah wrote:ajith, i got it so far. kindly explain how u got the part in bold??? ajith wrote:bhumika.k.shah wrote:If 2^x - 2^x-2 = 3*(2)^13, What is the value of x? A.12 B.14 C.15 D.17 E.19 2^x - 2^x/4 = 2^x(1-1/4) = 2^x(3/4) = 3*2^(x-2) x-2 =13 x =15 just compare RHS and LHS 3*2^15=3*2^(x-2) property of exponents if n^k*m^l=n^a*m^b then k=a and l=b hence x-2=15 in exponents a^x=b*y---->x=y

bhumika.k.shah · Answer

YES IT DID Any good link for exponents and roots ..??? ajith wrote: Hope that Helps

ajith · Answer

bhumika.k.shah wrote:YES IT DID Any good link for exponents and roots ..??? ajith wrote: Hope that Helps https://www.mathsisfun.com/algebra/expo ... s.html

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

If 2^x - 2^x-2 = 3*(2)^13, What is the value of x?

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER