It is currently 22 Mar 2019, 14:58

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

Given 1/2f(x)=f(x/2),

Author Message
TAGS:
Intern
Joined: 17 Feb 2018
Posts: 2
Followers: 0

Kudos [?]: 1 [0], given: 0

Given 1/2f(x)=f(x/2), [#permalink]  17 Feb 2018, 12:03
00:00

Question Stats:

66% (00:34) correct 33% (01:11) wrong based on 9 sessions
Given $$\frac{1}{2} f(x)= f (\frac{1}{2} * x)$$, which of the following is true for all values of f(x)?

A.$$f(x)= 2x+2$$

B.$$f(x)=13x$$

C.$$f(x)=x^2$$

D.$$f(x)=x-10$$

E.$$f(x)=\sqrt{(x-4)}$$

I know the answer is B and I got it by trying each f(x) function. However the answer indicates, "the fastest method is to use logical: since the order of operations says that order does not matter with multiplication and division but does matter between multiplication and addition/subtraction, or multiplication and exponents, choose a function that has only multiplication and/or division."

Could anyone explain this logic? Thank you.
[Reveal] Spoiler: OA

Last edited by Carcass on 19 Feb 2018, 02:13, edited 2 times in total.
Edited by Carcass
Intern
Joined: 17 Feb 2018
Posts: 9
Followers: 0

Kudos [?]: 2 [0], given: 2

Re: A question on functions and formulas from Manhattan Prep 5lb [#permalink]  17 Feb 2018, 16:18
alihong2010 wrote:
Given 1/2f(x)=f(x/2), which of the following is true for all values of f(x)?

A.f(x)=2x+2
B.f(x)=13x
C.f(x)=x^2
D.f(x)=x-10
E.f(x)=sqrt(x-4)

I know the answer is B and I got it by trying each f(x) function. However the answer indicates, "the fastest method is to use logical: since the order of operations says that order does not matter with multiplication and division but does matter between multiplication and addition/subtraction, or multiplication and exponents, choose a function that has only multiplication and/or division."

Could anyone explain this logic? Thank you.

well, since the problem features transformations which feature multiplication (1/2*f(x)) and division (x/2), it's safe to say that the DM part of PEDMAS is used- I guess that leads to trying only equations with DM transformations? I'm not 100% sure either
Intern
Joined: 17 Feb 2018
Posts: 9
Followers: 0

Kudos [?]: 2 [0], given: 2

Re: A question on functions and formulas from Manhattan Prep 5lb [#permalink]  17 Feb 2018, 16:19
alihong2010 wrote:
Given 1/2f(x)=f(x/2), which of the following is true for all values of f(x)?

A.f(x)=2x+2
B.f(x)=13x
C.f(x)=x^2
D.f(x)=x-10
E.f(x)=sqrt(x-4)

I know the answer is B and I got it by trying each f(x) function. However the answer indicates, "the fastest method is to use logical: since the order of operations says that order does not matter with multiplication and division but does matter between multiplication and addition/subtraction, or multiplication and exponents, choose a function that has only multiplication and/or division."

Could anyone explain this logic? Thank you.

Moderator
Joined: 18 Apr 2015
Posts: 5862
Followers: 94

Kudos [?]: 1151 [0], given: 5465

Re: Given 1/2f(x)=f(x/2), [#permalink]  19 Feb 2018, 02:14
Expert's post
OE

Quote:
The fastest method is to use logic: since the order of operations says that order does not matter with multiplication and division but does matter between multiplication and addition/subtraction, or multiplication and exponents, choose a function that has only multiplication and/or division. Only answer choice (B) qualifies.

Hope this helps.
_________________
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1782 [1] , given: 397

Re: Given 1/2f(x)=f(x/2), [#permalink]  19 Feb 2018, 12:08
1
KUDOS
Expert's post
Plugging might be a safe option if you are not familiar with polynomials.

The logical way mentioned here is:

given $$f(cx)=cf(x)$$ where $$f(x)$$ is a polynomial say $$f(x)= a_nx^n + a_{n-1}x^{n-1}.....+ a_1x + a_0$$

So $$f(cx)=a_n(cx)^n + a_{n-1}(cx)^{n-1}.....+ a_1cx + a_0$$

Here $$f(cx)=cf(x)$$ if all coeffecients except $$a_1$$ is 0 i.e a linear function or all coeffecients excepts $$a_0$$ is 0 i.e. a constant function.

Since the options have only one linear function we can safely say that is the correct answer.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Re: Given 1/2f(x)=f(x/2),   [#permalink] 19 Feb 2018, 12:08
Display posts from previous: Sort by

Given 1/2f(x)=f(x/2),

 Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.