It is currently 19 Mar 2018, 21:07

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# 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
Joined: 02 Sep 2009
Posts: 44322
If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

### Show Tags

28 Feb 2016, 09:37
Expert's post
3
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

82% (00:36) correct 18% (00:34) wrong based on 200 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
[Reveal] Spoiler: OA

_________________
Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1947
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

28 Feb 2016, 21:21
2
This post was
BOOKMARKED
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
+1 Kudos if you find this post helpful

Senior Manager
Joined: 20 Aug 2015
Posts: 394
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

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
Senior Manager
Joined: 15 Sep 2011
Posts: 357
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

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.

Senior Manager
Joined: 15 Jan 2017
Posts: 359
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

### Show Tags

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!
Director
Joined: 13 Mar 2017
Posts: 572
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

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

_________________

CAT 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
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
Joined: 15 Jan 2017
Posts: 359
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

### Show Tags

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

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
Joined: 13 Mar 2017
Posts: 572
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

05 Aug 2017, 06:50
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 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
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
Joined: 15 Jan 2017
Posts: 359
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

### Show Tags

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
Senior Manager
Joined: 06 Jul 2016
Posts: 436
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

05 Aug 2017, 08:52
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
Joined: 06 Jul 2016
Posts: 436
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

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.
_________________

Put in the work, and that dream score is yours!

Director
Joined: 13 Mar 2017
Posts: 572
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

05 Aug 2017, 14:08
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 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
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
Joined: 15 Jan 2017
Posts: 359
Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

### Show Tags

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   [#permalink] 06 Aug 2017, 06:54
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 Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.