It is currently 28 Nov 2020, 08:41

### 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

# For all integers x, the function f is defined as follows

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 13916
GRE 1: Q160 V160
Followers: 315

Kudos [?]: 3682 [1] , given: 12939

For all integers x, the function f is defined as follows [#permalink]  02 Mar 2018, 16:18
1
KUDOS
Expert's post
00:00

Question Stats:

80% (01:06) correct 20% (00:56) wrong based on 20 sessions
For all integers $$x$$, the function $$f$$ is defined as follows

$$\mathcal{f} (x) =$$ $$\left\{ \begin{array}{rcl}{x - 1} & \mbox{if x is even}\\{x + 1} & \mbox{if x is odd}\end{array}\right$$

If $$a$$ and $$b$$ are integers and $$f (a) + f (b) = a + b$$, which of the following statements must be true?

A $$a = b$$

B $$a = -b$$

C $$a + b$$ is odd.

D Both a and b are even.

E Both a and b are odd.
[Reveal] Spoiler: OA

_________________

New to the GRE, and GRE CLUB Forum?
GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ
Posting Rules: QUANTITATIVE | VERBAL
FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)
Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests
GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides
3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection
Books: All GRE Best Books
Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)
How is the GRE Score Calculated -The Definitive Guide (2021)
Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)
Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3036 [3] , given: 394

Re: For all integers x, the function f is defined as follows [#permalink]  03 Mar 2018, 04:17
3
KUDOS
Expert's post
Now there are 4 case possible:

Case 1: a is even b is even
Case 2: a is even b is odd
Case 3: a is odd b is even
Case 4: a is odd b is odd

rewriting the f(a) and f(b) in each case:

Case 1: $$f(a)= a-1$$ and $$f(b)= b-1$$ so .... $$f(a)+f(b)= a+b-2$$
Case 2: $$f(a)= a-1$$ and $$f(b)= b+1$$ so .... $$f(a)+f(b)= a+b$$
Case 3: $$f(a)= a+1$$ and $$f(b)= b-1$$ so .... $$f(a)+f(b)= a+b$$
Case 4: $$f(a)= a+1$$ and $$f(b)= b+1$$ so .... $$f(a)+f(b)= a+b+2$$

$$f(a)+f(b)= a+b$$ holds only when either a is odd and b is even or vice versa.

Hence option C is correct!
_________________

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

Try our free Online GRE Test

Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 94 [1] , given: 99

Re: For all integers x, the function f is defined as follows [#permalink]  09 May 2018, 07:00
1
KUDOS
basically the question is testing us to check if we can see that function is converting an even number to odd and an odd number to even and then the summation of the function output.

which is odd + even = Odd hence the answer is C - a+b is odd.
Re: For all integers x, the function f is defined as follows   [#permalink] 09 May 2018, 07:00
Display posts from previous: Sort by

# For all integers x, the function f is defined as follows

 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®.