Author 
Message 
TAGS:

Hide Tags

Director
Joined: 21 Dec 2009
Posts: 578
Concentration: Entrepreneurship, Finance

Let the function g(a, b) = f(a) + f(b). [#permalink]
Show Tags
29 Nov 2012, 18:17
9
This post received KUDOS
46
This post was BOOKMARKED
Question Stats:
45% (02:20) correct 55% (01:41) wrong based on 505 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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.



VP
Joined: 02 Jul 2012
Posts: 1212
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: Let the function g(a, b) = f(a) + f(b). [#permalink]
Show Tags
29 Nov 2012, 21:55
11
This post received KUDOS
3
This post was BOOKMARKED
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



Math Expert
Joined: 02 Sep 2009
Posts: 43828

Re: Let the function g(a, b) = f(a) + f(b). [#permalink]
Show Tags
30 Nov 2012, 02:02
12
This post received KUDOS
Expert's post
21
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 plugin 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. forwhichofthefollowingfunctionsisfabfbfa124491.htmlforwhichofthefollowingfunctionsfisfxf1xfor85751.htmlfunctionsproblemneedhelp93184.htmlHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  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? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 21 Dec 2009
Posts: 578
Concentration: Entrepreneurship, Finance

Re: Let the function g(a, b) = f(a) + f(b). [#permalink]
Show Tags
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.



Current Student
Joined: 29 May 2013
Posts: 24
Concentration: Marketing, Entrepreneurship
GMAT Date: 08202014
GPA: 3.34

Re: Let the function g(a, b) = f(a) + f(b). [#permalink]
Show Tags
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 2a+b = 2a + 2b [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
Joined: 13 Dec 2013
Posts: 39

Re: Let the function g(a, b) = f(a) + f(b). [#permalink]
Show Tags
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.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7941
Location: Pune, India

Re: Let the function g(a, b) = f(a) + f(b). [#permalink]
Show Tags
04 Jun 2014, 20:19
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
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
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1839
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: Let the function g(a, b) = f(a) + f(b). [#permalink]
Show Tags
04 Jun 2014, 22:11
1
This post was BOOKMARKED
g(a + b, a + b) = g(a, a) + g(b, b) LHSg(a + b, a + b) = f(a+b) + f(a+b) = 2f(a+b) RHSg(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



Current Student
Joined: 14 May 2014
Posts: 45
GPA: 3.11

Re: Let the function g(a, b) = f(a) + f(b). [#permalink]
Show Tags
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 plugin 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. forwhichofthefollowingfunctionsisfabfbfa124491.htmlforwhichofthefollowingfunctionsfisfxf1xfor85751.htmlfunctionsproblemneedhelp93184.htmlHope 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..?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7941
Location: Pune, India

Re: Let the function g(a, b) = f(a) + f(b). [#permalink]
Show Tags
23 Jul 2015, 03:26
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



Intern
Joined: 04 Sep 2014
Posts: 4

Re: Let the function g(a, b) = f(a) + f(b). [#permalink]
Show Tags
03 Nov 2016, 22:54
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 plugin 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. forwhichofthefollowingfunctionsisfabfbfa124491.htmlforwhichofthefollowingfunctionsfisfxf1xfor85751.htmlfunctionsproblemneedhelp93184.htmlHope it helps. I was trying to solve the same problem with values a=2 and b=3, therefore then the question becomes: for which function f below will \(f(5)=f(2)+f(3)\). Based on this I observed that for option C:x, f(5)=5=5 and f(2)+f(3)=2+3=2+3=5 now I know the OA is E and the functions are equal for option E, but am I missing something in option C, it would be great if someone could shed some light on this.



Intern
Joined: 17 Sep 2017
Posts: 1
Location: United States (HI)
GPA: 3.06

Re: Let the function g(a, b) = f(a) + f(b). [#permalink]
Show Tags
11 Oct 2017, 00:09
Even I fully understand how to solve this problem, I don't think I can get the answer in 2 mins.... TOO MUCH CALCULATION



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7941
Location: Pune, India

Re: Let the function g(a, b) = f(a) + f(b). [#permalink]
Show Tags
11 Oct 2017, 02:43
patrickpeng wrote: Even I fully understand how to solve this problem, I don't think I can get the answer in 2 mins.... TOO MUCH CALCULATION A little bit of forethought will help you solve it quickly. You want: g(a + b, a + b) = g(a, a) + g(b, b) In the expression, you want that when you put a+b, it should be the same as when you put a and b individually. A: x +3 B: x^2 C: x D: 1/x E: x/4 Of the given options, x^2 may not be it since (a+b)^2 is not same as a^2 + b^2. Similarly, a+b is not the same as a + b In such questions, with x in the denominator, you certainly cannot split 1/(a+b) as 1/a + 1/b. I will try option (E) first since it has a multiplication (x * 1/4). We know that (a+b)*1/4 = a*(1/4) + b*(1/4)
_________________
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]
11 Oct 2017, 02:43






