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

It is currently 16 Jan 2019, 00:15

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
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • The winning strategy for a high GRE score

     January 17, 2019

     January 17, 2019

     08:00 AM PST

     09:00 AM PST

    Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

If x and y are integers, is the sum of x and y even?

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52119
If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 11 Apr 2016, 03:07
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

69% (00:50) correct 31% (01:02) wrong based on 75 sessions

HideShow timer Statistics

Manager
Manager
avatar
B
Joined: 26 Dec 2012
Posts: 146
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)
CAT Tests
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 11 Apr 2016, 10:25
find out x+y= even or not.
1. x^2=y^2 , by rearranging, we can write this as (x+y)(x-y)=0; x+y=0 and 0 is even number so sufficient.
2. x^3-y^3 =0 by rearranging we do not about x+y so not sufficient.

Hence answer is A.
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1881
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post Updated on: 14 Apr 2016, 20:14
Bunuel wrote:
If x and y are integers, is the sum of x and y even?

(1) x^2 = y^2
(2) x^3 = y^3


x + y = even?

Statement 1: x^2 = y^2
Case 1:
Either x = y (x = 2 and y = 2)
or x = -y (x = 2 and y = -2)
Hence x + y = 2x or 0
Yes, the sum is even
Sufficient

Statement 2: x^3 = y^3
x = y (x = 2 and y = 2 OR x = -2 and y = -2)
Therefore x + y = 2x
Yes, the sum is even.
Sufficient

Option D

Originally posted by OptimusPrepJanielle on 14 Apr 2016, 01:09.
Last edited by OptimusPrepJanielle on 14 Apr 2016, 20:14, edited 1 time in total.
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1881
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 14 Apr 2016, 01:12
lipsi18 wrote:
find out x+y= even or not.
1. x^2=y^2 , by rearranging, we can write this as (x+y)(x-y)=0; x+y=0 and 0 is even number so sufficient.
2. x^3-y^3 =0 by rearranging we do not about x+y so not sufficient.

Hence answer is A.


Hi lipsi18,

In the statement 1, either of (x+y) or (x-y) can be zero.
Hence we cannot say that x + y = 0
Intern
Intern
avatar
Joined: 01 Jan 2015
Posts: 14
Location: India
Concentration: Technology, Marketing
WE: Information Technology (Computer Software)
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 14 Apr 2016, 08:06
Is it B ?
If so, will provide my line of reasoning.
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1881
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 14 Apr 2016, 20:13
subhamoycomputer wrote:
Is it B ?
If so, will provide my line of reasoning.


Hi subhamoycomputer,

The correct option here should be D.
However do post your reasoning as to why you thing option A is insufficient.
Manager
Manager
avatar
B
Joined: 29 Jul 2015
Posts: 63
Location: Australia
GMAT 1: 680 Q49 V33
GPA: 3.25
WE: Business Development (Energy and Utilities)
GMAT ToolKit User Premium Member
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 14 Apr 2016, 20:25
If x and y are integers, is the sum of x and y even?

(1) x^2 = y^2
(2) x^3 = y^3

x + y even?

Statement 1:

x^2 = y^2. This implies x = y or x =-y.

Either way x+y will be even (0 or 2x).

Statement 2:

X^3 = y^3.

Implies x = y.

So x + y is 2x, which is even.

So each statement is individually sufficient.

Answer D.
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2626
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User Premium Member
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 15 Apr 2016, 04:03
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6801
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 16 Apr 2016, 01:43
If x and y are integers, is the sum of x and y even?

(1) x^2 = y^2
(2) x^3 = y^3

There are 2 variables (x and y) in the original condition. In order to match the number of variables to the number of equations, we need 2 more equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer. Using both the condition 1) and the condition 2), we get 1)=2), from which we can obtain x=y=odd or x=y=even. The answer is always yes and the conditions are sufficient. Therefore, the correct answer is D.

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________

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 $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Current Student
User avatar
B
Status: It`s Just a pirates life !
Joined: 21 Mar 2014
Posts: 231
Location: India
Concentration: Strategy, Operations
GMAT 1: 690 Q48 V36
GPA: 4
WE: Consulting (Manufacturing)
Reviews Badge
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 18 Apr 2016, 02:31
Bunuel wrote:
If x and y are integers, is the sum of x and y even?

(1) x^2 = y^2
(2) x^3 = y^3


The Answer is D..Check for pairs (0,0) ...(1,1)....(-1,-1)
_________________

Aiming for a 3 digit number with 7 as hundredths Digit

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7199
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 18 Apr 2016, 02:44
1
Balajikarthick1990 wrote:
Bunuel wrote:
If x and y are integers, is the sum of x and y even?

(1) x^2 = y^2
(2) x^3 = y^3


The Answer is D..Check for pairs (0,0) ...(1,1)....(-1,-1)


You are correct...
But for (1), check for |x|=|y|.. May be important in some other Q
x=1, y=-1 ; x=-1, y=1; x=1,y=1; x=-1, y=-1
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Current Student
avatar
Joined: 02 Jun 2015
Posts: 81
Location: Brazil
Concentration: Entrepreneurship, General Management
GPA: 3.3
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 18 Apr 2016, 17:29
Let me understand, is 0 considered even?

Because if we use x = -y
Then the answer would be 0 for option A
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7199
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 18 Apr 2016, 19:07
douglasvg wrote:
Let me understand, is 0 considered even?

Because if we use x = -y
Then the answer would be 0 for option A



hi,
0 is EVEN but it is neither NEGATIVE nor POSITIVE...
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1299
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 20 Dec 2018, 06:59
Bunuel gmatbusters VeritasKarishma chetan2u

Could you share your approach?

Q is asking: Are both x and y even or odd?

For St 1, I took |x| = |y|
which is same as:
x = y and x = -y
or
x-y = 0
or
x + y = 0

Hence implying, both x and y have to be even/odd.

What is St 2 saying? How do I interpret odd powers of integer?
_________________

It's the journey that brings us happiness not the destination.

Intern
Intern
avatar
B
Joined: 08 Jul 2016
Posts: 17
Re: If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 20 Dec 2018, 07:20
1) x²=y²
So, x²-y²=0
So, (x+y)(x-y)=0
Either x+y=0 where 0 is even.
Or x-y=0 where 0 is even. If the difference of two integers is even, their sum is also even.

So statement (1) is sufficient.

(2) Cube of a number preserves the sign.
So x³=y³ means x=y, say x=y=a
So the sum will always be even =2a.

So statement (2) is sufficient.

Both are statements alone are sufficient so option D is the correct answer

Posted from my mobile device
Senior DS Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1195
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
If x and y are integers, is the sum of x and y even?  [#permalink]

Show Tags

New post 20 Dec 2018, 07:24
if \(x^ a = y ^a\), where a is an even integer
we get x = +/- y

But, if \(x^ b = y ^b\), where b is an odd integer
we get x = y


Good news, odd power are even easier to handle :cool:

Hence for Statement 2, sum of x and y = 2x or 2y = even


adkikani wrote:
Bunuel gmatbusters VeritasKarishma chetan2u

Could you share your approach?

Q is asking: Are both x and y even or odd?

For St 1, I took |x| = |y|
which is same as:
x = y and x = -y
or
x-y = 0
or
x + y = 0

Hence implying, both x and y have to be even/odd.

What is St 2 saying? How do I interpret odd powers of integer?

_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

GMAT Club Bot
If x and y are integers, is the sum of x and y even? &nbs [#permalink] 20 Dec 2018, 07:24
Display posts from previous: Sort by

If x and y are integers, is the sum of x and y even?

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


Copyright

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

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

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®.