Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Aug 2015, 02:36
GMAT Club Tests

Close

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
Your Progress

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Let the function g(a, b) = f(a) + f(b).

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
5 KUDOS received
Director
Director
avatar
Joined: 21 Dec 2009
Posts: 592
Concentration: Entrepreneurship, Finance
Followers: 16

Kudos [?]: 399 [5] , given: 20

Let the function g(a, b) = f(a) + f(b). [#permalink] New post 29 Nov 2012, 18:17
5
This post received
KUDOS
15
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

44% (03:31) correct 56% (01:45) wrong based on 262 sessions
Let the function g(a, b) = f(a) + f(b).

For which function f below will g(a + b, a + b) = g(a, a) + g(b, b)?

A: x +3
B: x^2
C: |x|
D: 1/x
E: x/4
[Reveal] Spoiler: OA

_________________

KUDOS me if you feel my contribution has helped you.


Last edited by Bunuel on 30 Nov 2012, 01:41, edited 1 time in total.
OA added.
7 KUDOS received
Moderator
Moderator
User avatar
Joined: 02 Jul 2012
Posts: 1228
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 89

Kudos [?]: 939 [7] , given: 116

Premium Member
Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 29 Nov 2012, 21:55
7
This post received
KUDOS
gmatbull wrote:
Let the function g(a, b) = f(a) + f(b).

For which function f below will g(a + b, a + b) = g(a, a) + g(b, b)?

A: x +3
B: x^2
C: |x|
D: 1/x
E: x/4

OA to be posted later.


The question is basically asking for which function f(a + b) = f(a) + f(b)

A)\(LHS = a + b + 3\)
\(RHS = a + 3 + b + 3 = a + b + 6.\)
Not equal

B)\(LHS = (a + b)^2\)
\(RHS = a^2 + b^2\)
Not equal

C)\(LHS = |a + b|\)
\(RHS = |a| + |b|\)
If a & b are of different polarity not equal.

D)\(LHS = \frac{1}{a + b}\)
\(RHS = \frac{1}{a} + \frac{1}{b}\)
Not equal

E)\(LHS = \frac{a + b}{4}\)
\(RHS = \frac{a}{4} + \frac{b}{4} = \frac{a + b}{4}\).
Equal.

Answer should be E
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Expert Post
6 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29110
Followers: 4726

Kudos [?]: 49771 [6] , given: 7403

Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 30 Nov 2012, 02:02
6
This post received
KUDOS
Expert's post
9
This post was
BOOKMARKED
Let the function g(a, b) = f(a) + f(b).

For which function f below will g(a + b, a + b) = g(a, a) + g(b, b)?


A: x +3
B: x^2
C: |x|
D: 1/x
E: x/4

We can use plug-in method to solve this question.

Since \(g(a, b) = f(a) + f(b)\), then:
\(g(a + b, a + b)=f(a+b)+f(a+b)=2f(a+b)\);
\(g(a, a) + g(b, b)=f(a)+f(a)+f(b)+f(b)=2f(a)+2f(b)\).

Thus the question asks: for which function f below will \(2f(a+b)=2f(a)+2f(b)\) --> \(f(a+b)=f(a)+f(b)\)?

Say a=-1 and b=1, then the question becomes: for which function f below will \(f(0)=f(-1)+f(1)\).

A: x +3
\(f(0)=0+3=3\)
\(f(-1)+f(1)=(-1+3)+(1+3)=6\)
No match.

B: x^2
\(f(0)=0^2=0\)
\(f(-1)+f(1)=(-1)^2+(1)^2=2\)
No match.

C: |x|
\(f(0)=|0|=0\)
\(f(-1)+f(1)=|-1|+|1|=2\)
No match.

D: 1/x
\(f(0)=\frac{1}{0}=undefined\)
\(f(-1)+f(1)=\frac{1}{-1}+\frac{1}{1}=0\)
No match.

E: x/4
\(f(0)=\frac{0}{4}=0\)
\(f(-1)+f(1)=\frac{-1}{4}+\frac{1}{4}=0\)
Match.

Answer: E.

Hope it's clear.

for-which-of-the-following-functions-is-f-a-b-f-b-f-a-124491.html
for-which-of-the-following-functions-f-is-f-x-f-1-x-for-85751.html
functions-problem-need-help-93184.html

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Director
Director
avatar
Joined: 21 Dec 2009
Posts: 592
Concentration: Entrepreneurship, Finance
Followers: 16

Kudos [?]: 399 [0], given: 20

Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 30 Nov 2012, 02:52
Bunuel and MacFauz,
your explanations make a lot of sense.
More so, Bunuel, you took time to explain the breakdown.

Thanks.
_________________

KUDOS me if you feel my contribution has helped you.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29110
Followers: 4726

Kudos [?]: 49771 [0], given: 7403

Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 23 Jul 2013, 01:15
Expert's post
Intern
Intern
avatar
Joined: 29 May 2013
Posts: 24
Concentration: Marketing, Entrepreneurship
Schools: Molson '17 (M)
GMAT Date: 08-20-2014
GPA: 3.34
Followers: 0

Kudos [?]: 10 [0], given: 8

Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 01 May 2014, 23:08
Bunuel wrote:
From 100 hardest questions.

Bumping for review and further discussion.




let a = 1 and b = 2, a+b = 3

A) x+3,
2(a+b+3) = 2(a+3) + 2(b+3)
2(a+b+3) = 2(a+b+3) + 6 [Can never be true]

B) x^2
2(a+b)^2 = 2(a^2)+2(b^2) [Can/Cannot be true]

C)|x|
2|a+b| = 2|a| + 2|b| [Can/Cannot be true]

D)1/x
2/(a+b) = (2/a)+(2/b) = 2(a+b)/ab [Can/Cannot be true]

E)x/4
2*(a+b)/4 = 2(a/4) + 2(b/4) = 2(a+b)/4 [Always true]

Ans 'E'
Intern
Intern
avatar
Joined: 13 Dec 2013
Posts: 40
Schools: Fuqua (I), AGSM '16
GMAT 1: 620 Q42 V33
Followers: 2

Kudos [?]: 10 [0], given: 10

GMAT ToolKit User
Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 04 Jun 2014, 03:18
g(a+b,a+b) = g(a,a)+g(b,b) = f(a) + f(a) + f(b) + f(b)= 2f(a) + 2f(b) = RHS
g(a+b,a+b) = f(a+b)+f(a+b) = 2f(a+b) = LHS

We divide by 2 both RHS and LHS and get

f(a+b)=f(a) + f(b)

I have an issue here: how do I know what to plug in from the answer choices? Since those are expressed in terms of X.

My approach was to take both a and b as the answer choice, but I don´t know if that is correct.

For d)

LHS: f(x/4 + x/4) = x/2
RHS: f(x/4) + f(x/4) = x/2

I'm sure i'm conceptually missing something.

Thanks.
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5853
Location: Pune, India
Followers: 1480

Kudos [?]: 7947 [0], given: 190

Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 04 Jun 2014, 20:19
Expert's post
Enael wrote:
g(a+b,a+b) = g(a,a)+g(b,b) = f(a) + f(a) + f(b) + f(b)= 2f(a) + 2f(b) = RHS
g(a+b,a+b) = f(a+b)+f(a+b) = 2f(a+b) = LHS

We divide by 2 both RHS and LHS and get

f(a+b)=f(a) + f(b)

I have an issue here: how do I know what to plug in from the answer choices? Since those are expressed in terms of X.

My approach was to take both a and b as the answer choice, but I don´t know if that is correct.



I am not sure what you mean by this last line but I can help you with the various variables.

The options (x+3), x^2 etc are the values of the function f(x)

Option (A) tells you that f(x) = x + 3
So if you want to find f(a) or f(b) or f(a+b), it is quite simple.
If f(x) = x+3, f(a) = a+3
If f(x) = x+3, f(a+b) = a+b+3
etc
Wherever you have x in the expression you put a or a+b or b as the case may be.

In this question, since options give the function f(x), you convert the entire g(x) into f(x).
You get that you need to find the function f(x) such that f(a+b) = f(a) + f(b)

The sum of individual functions of a and b and should be equal to the function of (a+b). We should look for an option where x is in the numerator and there is no addition/subtraction. So the first option I will try is (E)

If f(x) = x/4, f(a) = a/4, f(b) = b/4, f(a+b) = (a+b)/4

f(a) + f(b) = a/4 + b/4 = (a+b)/4

Hence, for option (E), f(a+b) = f(a) + f(b)

Answer (E)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1859
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 26

Kudos [?]: 1065 [0], given: 193

Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 04 Jun 2014, 22:11
g(a + b, a + b) = g(a, a) + g(b, b)

LHS

g(a + b, a + b)

= f(a+b) + f(a+b)

= 2f(a+b)

RHS

g(a, a) + g(b, b)

= f(a) + f(a) + f(b) + f(b)

= 2f(a) + 2f(b)

LHS = RHS

2f(a+b) = 2f(a) + 2f(b)

f(a+b) = f(a) + f(b)


\(\frac{a}{4} +\frac{b}{4} = \frac{a+b}{4}\)

Answer =E
_________________

Kindly press "+1 Kudos" to appreciate :)

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6109
Followers: 340

Kudos [?]: 69 [0], given: 0

Premium Member
Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 22 Jul 2015, 04:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
User avatar
Joined: 14 May 2014
Posts: 25
Followers: 0

Kudos [?]: 1 [0], given: 32

GMAT ToolKit User CAT Tests
Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 23 Jul 2015, 02:21
Bunuel wrote:
Let the function g(a, b) = f(a) + f(b).

For which function f below will g(a + b, a + b) = g(a, a) + g(b, b)?


A: x +3
B: x^2
C: |x|
D: 1/x
E: x/4

We can use plug-in method to solve this question.

Since \(g(a, b) = f(a) + f(b)\), then:
\(g(a + b, a + b)=f(a+b)+f(a+b)=2f(a+b)\);
\(g(a, a) + g(b, b)=f(a)+f(a)+f(b)+f(b)=2f(a)+2f(b)\).

Thus the question asks: for which function f below will \(2f(a+b)=2f(a)+2f(b)\) --> \(f(a+b)=f(a)+f(b)\)?

Say a=-1 and b=1, then the question becomes: for which function f below will \(f(0)=f(-1)+f(1)\).

A: x +3
\(f(0)=0+3=3\)
\(f(-1)+f(1)=(-1+3)+(1+3)=6\)
No match.

B: x^2
\(f(0)=0^2=0\)
\(f(-1)+f(1)=(-1)^2+(1)^2=2\)
No match.

C: |x|
\(f(0)=|0|=0\)
\(f(-1)+f(1)=|-1|+|1|=2\)
No match.

D: 1/x
\(f(0)=\frac{1}{0}=undefined\)
\(f(-1)+f(1)=\frac{1}{-1}+\frac{1}{1}=0\)
No match.

E: x/4
\(f(0)=\frac{0}{4}=0\)
\(f(-1)+f(1)=\frac{-1}{4}+\frac{1}{4}=0\)
Match.

Answer: E.

Hope it's clear.

for-which-of-the-following-functions-is-f-a-b-f-b-f-a-124491.html
for-which-of-the-following-functions-f-is-f-x-f-1-x-for-85751.html
functions-problem-need-help-93184.html

Hope it helps.


here i got confused because the given function "g" had 2 input variables whereas all option choices had single variable. it did not strike me that function g can be completely written in form of f. any tips on this..? how to avoid this or what shd be the line of thinking..?
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5853
Location: Pune, India
Followers: 1480

Kudos [?]: 7947 [1] , given: 190

Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 23 Jul 2015, 03:26
1
This post received
KUDOS
Expert's post
riyazgilani wrote:

here i got confused because the given function "g" had 2 input variables whereas all option choices had single variable. it did not strike me that function g can be completely written in form of f. any tips on this..? how to avoid this or what shd be the line of thinking..?



Yes, the tip is very simple: read the question very carefully.

Note that it says: For which function f below ...

So basically what you are given below (in options) is function f. So obviously it will have a single input.

Now you want certain condition in g to hold. Since you know the equivalency of f and g, convert g to f and you know which condition f should hold.

Hope it makes sense.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Re: Let the function g(a, b) = f(a) + f(b).   [#permalink] 23 Jul 2015, 03:26
    Similar topics Author Replies Last post
Similar
Topics:
4 Let Z be a function satisfying Z(ab) = Z(a)/bfor all positive real num manpreetsingh86 3 13 Jan 2015, 06:15
6 Experts publish their posts in the topic If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: Bunuel 4 05 Nov 2014, 07:38
2 Experts publish their posts in the topic Let the function p(n) represent the product of the first n p Vijayeta 4 28 Jul 2014, 02:57
3 Experts publish their posts in the topic Let g(x) = 4^x. If g(a) = 32. then a is equal to? suk1234 4 20 Oct 2013, 08:26
Two functions A(x) and B(x) are defined such that kingb 1 11 Nov 2012, 10:14
Display posts from previous: Sort by

Let the function g(a, b) = f(a) + f(b).

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.