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If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]
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28 Feb 2016, 09:37
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82% (00:36) correct 18% (00:34) wrong based on 200 sessions
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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]
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28 Feb 2016, 21:21
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Bunuel wrote: If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?
A. 1 B. 16 C. 81 D. 144 E. 256 f(x)=x^2 f(f(x)) = (x^2)^2 =x^4 A. 1 , x=1 B. 16 , x=2 C. 81 , x=3 D. 144 f(x)=12 Square root of 12 is not a positive integer . Hence 144 can not be the value of f(f(x)) . E. 256 , x=4 Answer D
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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]
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03 Mar 2016, 03:18
Bunuel wrote: If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?
A. 1 B. 16 C. 81 D. 144 E. 256 f(x)=x^2 f(f(x)) = (x^2)^2 = x^4 Therefore f(f(x)) will be numbers that are 4th power of other numbers. Checking the options: A. 1 = 1^$ B. 16 = 2^4 C. 81 = 3^4 D. 144. This cannot be written as the 4th power of any number E. 256 = 4^4 Correct Option: D



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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]
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03 Mar 2016, 17:23
If you memorized the first ten powers of two as well as the first five powers of three, then this question takes you less than thirty seconds.
Answer D.



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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]
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05 Aug 2017, 05:44
hello! So i got it till here: f(x)= x square so f(f(x)) = F(x square) = x^4 now, 16,81,256 are all fourth of 2^2, 3^4 and 4^4  how is it that 4^ 4 is the answer? Would appreciate some detail on the explanation, thank you!



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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]
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05 Aug 2017, 06:18
Bunuel wrote: If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?
A. 1 B. 16 C. 81 D. 144 E. 256 f(x) = x^2 f(f(x)) = (x^2)^2 = x^4 A. 1^4 B. 2^4 C. 3^4 D. 12^2 E. 4^4 Answer D
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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]
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05 Aug 2017, 06:32
shashankism wrote: Bunuel wrote: If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?
A. 1 B. 16 C. 81 D. 144 E. 256 f(x) = x^2 f(f(x)) = (x^2)^2 = x^4 A. 1^4 B. 2^4 C. 3^4 D. 12^2 E. 4^4 Answer DHi wanted to reiterate my query. I asked why is 4^4 the right answer, since 2,3 and 1 are all raised to power 4 in the options. So I am not able to understand why only 4^4 is the answer and not 1,2 or 3. Thank you



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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]
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05 Aug 2017, 06:50
Madhavi1990 wrote: shashankism wrote: Bunuel wrote: If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?
A. 1 B. 16 C. 81 D. 144 E. 256 f(x) = x^2 f(f(x)) = (x^2)^2 = x^4 A. 1^4 B. 2^4 C. 3^4 D. 12^2 E. 4^4 Answer DHi wanted to reiterate my query. I asked why is 4^4 the right answer, since 2,3 and 1 are all raised to power 4 in the options. So I am not able to understand why only 4^4 is the answer and not 1,2 or 3. Thank you Madhavi1990 12^2 is the answer and not 4^4 .. I have mentioned option D i.e. 12^2. Please look carefully into my solution .
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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]
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05 Aug 2017, 07:21
I did actually, but didnt understand why 144 is the answer if its 12^2 (f(x) = x^2 f(f(x)) = (x^2)^2 = x^4. Isn't it supposed to be a power of 4? How does 12 feature as a power of 4? Please do clarify



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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]
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05 Aug 2017, 08:52
Madhavi1990 wrote: I did actually, but didnt understand why 144 is the answer if its 12^2 (f(x) = x^2 f(f(x)) = (x^2)^2 = x^4. Isn't it supposed to be a power of 4? How does 12 feature as a power of 4? Please do clarify It says CANNOT be the value of f(f(x)). Only 144 is not the fourth power of any integer. Hope this helps. Sent from my iPhone using GMAT Club Forum mobile app
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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]
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05 Aug 2017, 09:10
Bunuel wrote: If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?
A. 1 B. 16 C. 81 D. 144 E. 256 x = 1 f(f(x)) = \(x^4\) = \(1^4\) = 1. x = 2 f(f(x)) = \(x^4\) = \(2^4\) = 16. x = 3 f(f(x)) = \(x^4\) = \(3^4\) = 81. x = 4 f(f(x)) = \(x^4\) = \(4^4\) = 256. Above are all values of f(f(x)) for all x = positive integer. 144 = \(12^2\) => It cannot be written in the form \(x^4\) as no integer to the power of 4 results in 144. And that is why D is the answer.
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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]
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05 Aug 2017, 14:08
Madhavi1990 wrote: I did actually, but didnt understand why 144 is the answer if its 12^2 (f(x) = x^2 f(f(x)) = (x^2)^2 = x^4. Isn't it supposed to be a power of 4? How does 12 feature as a power of 4? Please do clarify Madhavi1990The question is asking which option is not of the type x^4 Clearly 12^2 is not of the type x^4 .. Hope that helps..
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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]
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06 Aug 2017, 06:54
akshayk wrote: Bunuel wrote: If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?
A. 1 B. 16 C. 81 D. 144 E. 256 x = 1 f(f(x)) = \(x^4\) = \(1^4\) = 1. x = 2 f(f(x)) = \(x^4\) = \(2^4\) = 16. x = 3 f(f(x)) = \(x^4\) = \(3^4\) = 81. x = 4 f(f(x)) = \(x^4\) = \(4^4\) = 256. Above are all values of f(f(x)) for all x = positive integer. 144 = \(12^2\) => It cannot be written in the form \(x^4\) as no integer to the power of 4 results in 144. And that is why D is the answer. Thank you,this was insightful




Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT
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