GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Oct 2019, 00:05 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If f(x)=x^2 and x is a positive integer, which of the following CANNOT

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58430
If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags 00:00

Difficulty:   5% (low)

Question Stats: 79% (01:06) correct 21% (01:02) wrong based on 161 sessions

HideShow timer Statistics

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

_________________
Verbal Forum Moderator V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2401
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags

2
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

_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Senior Manager  Joined: 20 Aug 2015
Posts: 386
Location: India
GMAT 1: 760 Q50 V44 Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags

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
Senior Manager  Joined: 15 Sep 2011
Posts: 309
Location: United States
WE: Corporate Finance (Manufacturing)
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags

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.

Senior Manager  S
Joined: 15 Jan 2017
Posts: 341
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags

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!
Director  D
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags

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

_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Senior Manager  S
Joined: 15 Jan 2017
Posts: 341
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags

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

Hi wanted to re-iterate 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 Director  D
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags

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

Hi wanted to re-iterate 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 .
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Senior Manager  S
Joined: 15 Jan 2017
Posts: 341
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags

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 Senior Manager  G
Joined: 06 Jul 2016
Posts: 358
Location: Singapore
Concentration: Strategy, Finance
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags

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
_________________
Put in the work, and that dream score is yours!
Senior Manager  G
Joined: 06 Jul 2016
Posts: 358
Location: Singapore
Concentration: Strategy, Finance
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags

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.
_________________
Put in the work, and that dream score is yours!
Director  D
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags

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 The 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..
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Senior Manager  S
Joined: 15 Jan 2017
Posts: 341
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags

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 Manager  B
Joined: 16 May 2018
Posts: 84
Location: Hungary
Schools: Queen's MBA'20
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT  [#permalink]

Show Tags

Can someone pls explain me how does :
f(x) = x^2 becomes:
f(f(x)) = (x^2)^2 = x^4 ? Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT   [#permalink] 02 Mar 2019, 06:29
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  