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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