Zuleron 700+ Level Set #10

Question

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!

clock60 · Answer

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

nasir · Answer

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 ??

clock60 · Answer

i very hope that (2^x-2) must be 2^(x-2)=2^x/2^2, if not i must think more...

diebeatsthegmat · Answer

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

TheCloakedMonk · Answer

Thanks to both of you for your response. I can't thank you enough. Best of luck.

TheCloakedMonk · Answer

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.

nasir · Answer

Yup !!! Got it... Thank you guys

GMATGuruNY · Answer

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.

nasir · Answer

i always forget about plugging in

narik11 · Answer

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

quantskillsgmat · Answer

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

TheCloakedMonk · Answer

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.

GMATGuruNY · Answer

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?

TheCloakedMonk · Answer

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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