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by TheCloakedMonk » Fri Sep 24, 2010 10:39 am
Anyone know how to do this problem:

(2^x) - (2^x-2) = 3(2^13), what is x?

a) 9
b) 11
c) 13
d) 15
e) 17

The answer is d) 15. I have no idea how to do this. Please help.

Thanks!
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by clock60 » Fri Sep 24, 2010 11:02 am
you may try to solve this way
2^x-(2^x/2^2)=3*2^13,
only for simplicity 2^x=k

k-k/4=3*2^13, here multiply on 4
4k-k=3*2^13*2^2
3k=3*2^15, here you can cancel 3, and left with
k=2^15, but our k=2^x
2^x=2^15, from here it is easy to notice that x=15
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by nasir » Fri Sep 24, 2010 11:12 am
you may try to solve this way
2^x-(2^x/2^2)=3*2^13,
only for simplicity 2^x=k

how did you get 2^2=4 ??
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by clock60 » Fri Sep 24, 2010 11:17 am
i very hope that (2^x-2) must be 2^(x-2)=2^x/2^2, if not i must think more...
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by diebeatsthegmat » Fri Sep 24, 2010 11:26 am
TheCloakedMonk wrote:Anyone know how to do this problem:

(2^x) - (2^x-2) = 3(2^13), what is x?

a) 9
b) 11
c) 13
d) 15
e) 17

The answer is d) 15. I have no idea how to do this. Please help.

Thanks!
2^x-2^(x-2)=32^13 <=> 2^x- (2^x/4)=32^13 <=> 4*2^x-2^x=3*4*2^13<=> 3*2^x=3*2^15
the answer is 15
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by TheCloakedMonk » Fri Sep 24, 2010 11:53 am
Thanks to both of you for your response. I can't thank you enough.

Best of luck.
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by TheCloakedMonk » Fri Sep 24, 2010 12:06 pm
Nasir,

Use the exponent division rule (X^a)/(X^b) = X^a-b

So 2^x-2 = (2^x)/(2^2)

Hope that clears it up.
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by nasir » Sun Sep 26, 2010 11:14 am
Yup !!! Got it... Thank you guys
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by GMATGuruNY » Sun Sep 26, 2010 11:48 am
TheCloakedMonk wrote:Anyone know how to do this problem:

(2^x) - (2^x-2) = 3(2^13), what is x?

a) 9
b) 11
c) 13
d) 15
e) 17

The answer is d) 15. I have no idea how to do this. Please help.

Thanks!
We could plug in the answer choices, which represent the value of x.

Answer choice C:
(2^13) - (2^13-2) = 3(2^13)
(2^13) - (2^11) = 3(2^13)
2^11(2^2 - 1) = 3(2^13)
2^11(3) = 3(2^13)

The left side is too small. The exponent needs to be increased by 2. Thus, the correct answer is D.
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by nasir » Sun Sep 26, 2010 11:51 am
i always forget about plugging in :(
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by narik11 » Sun Sep 26, 2010 7:46 pm
TheCloakedMonk wrote:Anyone know how to do this problem:

(2^x) - (2^x-2) = 3(2^13), what is x?

a) 9
b) 11
c) 13
d) 15
e) 17

The answer is d) 15. I have no idea how to do this. Please help.

Thanks!
2^X- (2^X * 2^-2)
= 2^X(1-1/4)
2^X(3/4)= 3(2^13)

=>2^X=4(2^13)
so X=15
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by quantskillsgmat » Mon Sep 27, 2010 2:32 am
2^x-2^x/2^2=2^x(1-1/4)=2^x(3/4)=3(2^13)
so 2^x=(2^13)x2^2=2^15
hence x=15
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by TheCloakedMonk » Wed Sep 29, 2010 1:00 pm
GMATGuruNY wrote:
TheCloakedMonk wrote:Anyone know how to do this problem:

(2^x) - (2^x-2) = 3(2^13), what is x?

a) 9
b) 11
c) 13
d) 15
e) 17

The answer is d) 15. I have no idea how to do this. Please help.

Thanks!
We could plug in the answer choices, which represent the value of x.

Answer choice C:
(2^13) - (2^13-2) = 3(2^13)
(2^13) - (2^11) = 3(2^13)
2^11(2^2 - 1) = 3(2^13)
2^11(3) = 3(2^13)

The left side is too small. The exponent needs to be increased by 2. Thus, the correct answer is D.

How do you get 15 (the correct answer) from 3(2^11) = 3(2^13). You say the exponent needs to be increased by 2 (11+2 = 13), but this does not give you 15.
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by GMATGuruNY » Wed Sep 29, 2010 1:41 pm
TheCloakedMonk wrote:
GMATGuruNY wrote:
TheCloakedMonk wrote:Anyone know how to do this problem:

(2^x) - (2^x-2) = 3(2^13), what is x?

a) 9
b) 11
c) 13
d) 15
e) 17

The answer is d) 15. I have no idea how to do this. Please help.

Thanks!
We could plug in the answer choices, which represent the value of x.

Answer choice C:
(2^13) - (2^13-2) = 3(2^13)
(2^13) - (2^11) = 3(2^13)
2^11(2^2 - 1) = 3(2^13)
2^11(3) = 3(2^13)

The left side is too small. The exponent needs to be increased by 2. Thus, the correct answer is D.

How do you get 15 (the correct answer) from 3(2^11) = 3(2^13). You say the exponent needs to be increased by 2 (11+2 = 13), but this does not give you 15.
The right side of the equation is 2^13(3).
When I plugged in x=13 (answer choice C), the left side of the equation became 2^11(3).
Since the resulting exponent on the left side of the equation needs to be increased by 2, the correct answer must be x=15.

Does this help?
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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by TheCloakedMonk » Thu Sep 30, 2010 11:22 am
GMATGuruNY wrote:
TheCloakedMonk wrote:
GMATGuruNY wrote:
TheCloakedMonk wrote:Anyone know how to do this problem:

(2^x) - (2^x-2) = 3(2^13), what is x?

a) 9
b) 11
c) 13
d) 15
e) 17

The answer is d) 15. I have no idea how to do this. Please help.

Thanks!
We could plug in the answer choices, which represent the value of x.

Answer choice C:
(2^13) - (2^13-2) = 3(2^13)
(2^13) - (2^11) = 3(2^13)
2^11(2^2 - 1) = 3(2^13)
2^11(3) = 3(2^13)

The left side is too small. The exponent needs to be increased by 2. Thus, the correct answer is D.

How do you get 15 (the correct answer) from 3(2^11) = 3(2^13). You say the exponent needs to be increased by 2 (11+2 = 13), but this does not give you 15.
The right side of the equation is 2^13(3).
When I plugged in x=13 (answer choice C), the left side of the equation became 2^11(3).
Since the resulting exponent on the left side of the equation needs to be increased by 2, the correct answer must be x=15.

Does this help?
Makes sense.

Thanks for the post.
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