GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 03 Apr 2020, 01:31

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 a and b are integers, is a^2 − b^2 even?

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62471
If a and b are integers, is a^2 − b^2 even?  [#permalink]

Show Tags

New post 24 Nov 2019, 23:37
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

67% (01:19) correct 33% (01:46) wrong based on 65 sessions

HideShow timer Statistics

SVP
SVP
avatar
V
Joined: 20 Jul 2017
Posts: 1501
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If a and b are integers, is a^2 − b^2 even?  [#permalink]

Show Tags

New post 25 Nov 2019, 00:51
2
(1) \(a^2+2ab+b^2\) is odd.
--> \((a + b)^2\) is odd
--> \(a + b\) is odd

Two cases are possible
Case 1: a = even & b = odd
--> \(a^2 - b^2\) = \(even^2 - odd^2\) = \(even - odd = odd\) --> A definite NO

Case 2: a = odd & b = even
--> \(a^2 - b^2 = odd^2 - even^2 = odd - even = odd\) --> A definite NO
--> Sufficient

(2) \(a\) is odd.
Nothing can be said about b --> Insufficient

IMO Option A
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 6049
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Re: If a and b are integers, is a^2 − b^2 even?  [#permalink]

Show Tags

New post 25 Nov 2019, 01:06
1
#1
(a+b)^2 is odd
so either of a or b is odd and even
in that case a^2-b^2 will not be even sufficient
#2
a is odd , value of b not know
insufficient
IMO A

If a and b are integers, is a^2−b^2 even?

(1) a2+2ab+b2 is odd.
(2) a is odd.
Director
Director
User avatar
D
Joined: 07 Mar 2019
Posts: 910
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: If a and b are integers, is a^2 − b^2 even?  [#permalink]

Show Tags

New post 25 Nov 2019, 02:40
1
If a and b are integers, is a^2−b^2 even?
\(a^2−b^2\) = even if
o - o = e (both a and b are odd)
e - e = e (both a and b are even)

(1) \(a^2+2ab+b^2\) is odd.
o + e + e = o (a - odd and b - even). Thus \(a^2−b^2\) = o - e = o NO
e + e + o = o (a - even and b - odd). Thus \(a^2−b^2\) = e - o = o NO

SUFFICIENT.

(2) a is odd.
nothing about b is given.

INSUFFICIENT.

Answer A.
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
VP
VP
avatar
P
Joined: 24 Nov 2016
Posts: 1359
Location: United States
Re: If a and b are integers, is a^2 − b^2 even?  [#permalink]

Show Tags

New post 25 Nov 2019, 03:48
1
Quote:
If a and b are integers, is a^2−b^2 even?

(1) a^2+2ab+b^2 is odd
(2) a is odd.


\((a,b)=integers\)
\(a^2−b^2=(a+b)(a-b)\)
\(e+-e=even…o+-o=even…e+-o=odd\)
\(ee=even…eo=even…oo=odd\)

(1) \(a^2+2ab+b^2\) is odd sufic

\(a^2+2ab+b^2=(a+b)^2=odd…a+b=odd\)
\((a,b)=(e,o):(a+b)(a-b)=o*o=odd\)

(2) a is odd. insufic

\((a,b)=(o,e):(a+b)(a-b)=o*o=odd\)
\((a,b)=(o,o):(a+b)(a-b)=e*e=even\)

Ans (A)
Senior Manager
Senior Manager
avatar
P
Joined: 01 Mar 2019
Posts: 485
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GMAT 1: 580 Q48 V21
GPA: 4
Reviews Badge
Re: If a and b are integers, is a^2 − b^2 even?  [#permalink]

Show Tags

New post 25 Nov 2019, 04:18
1
for a2−b2 to be even......both a,b should be either odd or even

(1) a2+2ab+b2 is odd......................this is possible when one is odd and other is even.....from this we can say that a2−b2 cannot be even......SUFFICIENT

(2) a is odd......Clearly INSUFFICIENT

OA:A
Manager
Manager
avatar
S
Joined: 30 Nov 2017
Posts: 67
GMAT 1: 690 Q49 V35
Re: If a and b are integers, is a^2 − b^2 even?  [#permalink]

Show Tags

New post 25 Nov 2019, 08:39
1
Q: a2-b2 is even?

The above expression will be even only when a & b are either odd or even as "even-even" or "odd-odd" is only even.

1) (a+b)2 is odd.
Therefore a+b is odd, which is only possible when a & b are of different types i.e. odd and even. No. Sufficient
2) No info about b. insufficient. IMO A
CR Forum Moderator
avatar
P
Joined: 18 May 2019
Posts: 800
GMAT ToolKit User Premium Member
Re: If a and b are integers, is a^2 − b^2 even?  [#permalink]

Show Tags

New post 25 Nov 2019, 12:00
1
We are to determine if a^2 - b^2 is even.
Now, a^2 - b^2 = (a+b)(a-b)
For this to be true, then either (a+b) must be even or (a-b) must be even. Better still, both a and b must be even or both a and b must be odd.

Statement 1: a^2 + 2ab + b^2 is odd.
The only condition whereby statement 1 can be satisfied is either when a is odd and b is even or when a is even and b is odd.
When a is odd and b is even, then a^2 - b^2 is odd and not even.
Similarly, when a is even and b is odd, then a^2 - b^2 is odd and not even.
Statement 1 is therefore sufficient on its own.

Statement 2: a is odd.
This is insufficient. This is because when a is odd and b is odd as well, we have a^2 - b^2 is even. However, if a is odd and b is even, then a^2 - b^2 is odd. Since there is a possibility of a^2 - b^2 to be either odd and even based on whether b is odd or even, statement 2 is not sufficient.

The answer is therefore A.
Director
Director
avatar
P
Joined: 25 Jul 2018
Posts: 642
Re: If a and b are integers, is a^2 − b^2 even?  [#permalink]

Show Tags

New post 25 Nov 2019, 14:28
1
a, b —integers,
—> Is \(a^{2} —b^{2}=( a—b)(a+b)\) even??

(Statement1): \((a+b)^{2}\) — odd
—>( a+b) is odd
In order (a+b) to be odd, one of either a or b must be odd integer.
—> so, (a—b) — (even+odd= odd) or (odd+even= odd)
—> Odd* Odd = Odd (always NO)
Sufficient

(Statement2): a is odd.
No info about what b is.
b could be odd or even integer.
—> Clearly insufficient

The answer is A.

Posted from my mobile device
Manager
Manager
avatar
P
Status: Student
Joined: 14 Jul 2019
Posts: 244
Location: United States
Concentration: Accounting, Finance
GPA: 3.9
WE: Education (Accounting)
CAT Tests
Re: If a and b are integers, is a^2 − b^2 even?  [#permalink]

Show Tags

New post 25 Nov 2019, 20:35
1
If a and b are integers, is \(a^2−b^2\) even?

(1\() a^2+2ab+b^2\) is odd.
(2) a is odd

\(a^2 - b^2 \)will be even if both a & b are even or odd.
(1) \((a+b)^2\) is odd. a+b is odd. so one of a & b is even and the other is odd. so\( a^2 -b^2\) is odd. sufficient.
(2) a is odd. no info about b. not sufficient.
A is the answer.
GMAT Club Bot
Re: If a and b are integers, is a^2 − b^2 even?   [#permalink] 25 Nov 2019, 20:35
Display posts from previous: Sort by

If a and b are integers, is a^2 − b^2 even?

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





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