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

It is currently 26 Jun 2019, 11:26

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.

Close

Request Expert Reply

Confirm Cancel

If f(a*b) = f(a) + f(b), what is the value of f(1)?

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

Hide Tags

 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7501
GMAT 1: 760 Q51 V42
GPA: 3.82
If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

Show Tags

New post 07 Jan 2019, 00:55
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

43% (01:07) correct 57% (00:55) wrong based on 59 sessions

HideShow timer Statistics


[Math Revolution GMAT math practice question]

If \(f(a*b) = f(a) + f(b)\), what is the value of \(f(1)\)?

\(A. 1\)
\(B. -1\)
\(C. 0\)
\(D. 2\)
\(E. -2\)

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Director
Director
avatar
P
Joined: 31 Jul 2017
Posts: 516
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

Show Tags

New post 07 Jan 2019, 01:10
1
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(f(a*b) = f(a) + f(b)\), what is the value of \(f(1)\)?

\(A. 1\)
\(B. -1\)
\(C. 0\)
\(D. 2\)
\(E. -2\)


Let a = b= 1. We have -
f(1) = 2f(1)

f(1) = 0.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
Intern
Intern
avatar
B
Joined: 02 Dec 2017
Posts: 16
Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

Show Tags

New post 07 Jan 2019, 02:07
I got answer as 2, can anybody explain me how?
rahul16singh28 I didn't understand the logic of 2f(1)=0
Manager
Manager
User avatar
G
Joined: 11 Dec 2013
Posts: 119
Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
GMAT ToolKit User
Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

Show Tags

New post 07 Jan 2019, 02:47
fighterboy,

If f(1) is not equal to zero , then
f(1) = 2f(1) - Dividing both sides by f(1)
1=2 , which is not possible

Hence f(1) must be zero
_________________
KUDOS will increase your score
Intern
Intern
avatar
B
Joined: 02 Dec 2017
Posts: 16
Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

Show Tags

New post 07 Jan 2019, 03:17
Thanks a lot! I understood the logic.
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 936
Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

Show Tags

New post 07 Jan 2019, 04:29
fighterboy wrote:
Thanks a lot! I understood the logic.

Alternate explanation:

\(f\left( 1 \right) = 2 \cdot f\left( 1 \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,2 \cdot f\left( 1 \right) - f\left( 1 \right) = 0\,\,\,\,\, \Rightarrow \,\,\,\,f\left( 1 \right) = 0\)

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7501
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

Show Tags

New post 09 Jan 2019, 01:19
=>

Since \(1 = 1 * 1\), setting \(a = 1\) and \(b = 1\) yields \(f(1) = f(1*1) = f(1) + f(1)\) and \(f(1) = 2f(1),\) which is equivalent to \(f(1) = 0.\)

Therefore, the answer is C.
Answer: C
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Manager
avatar
B
Joined: 18 Oct 2018
Posts: 83
Location: India
Concentration: Finance, International Business
GPA: 4
WE: Business Development (Retail Banking)
Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

Show Tags

New post 09 Jan 2019, 11:33
Given f(a*b)=f(a)+f(b)
Let a = b= 1. We have -
f(1*1) = f(1)+f(1)
f(1)=2f(1)
2f(1)-f(1)=0
Hence, f(1)=0
GMAT Club Bot
Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?   [#permalink] 09 Jan 2019, 11:33
Display posts from previous: Sort by

If f(a*b) = f(a) + f(b), what is the value of f(1)?

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


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