Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62286

If A and B are positive integers, is A – B even?
[#permalink]
Show Tags
20 Feb 2020, 00:24
Question Stats:
77% (00:57) correct 23% (00:53) wrong based on 30 sessions
HideShow timer Statistics
Competition Mode Question If A and B are positive integers, is A – B even? (1) The product of A and B is even (2) A + B is odd
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Intern
Joined: 16 Dec 2019
Posts: 33
Location: Bulgaria
WE: Project Management (Manufacturing)

Re: If A and B are positive integers, is A – B even?
[#permalink]
Show Tags
20 Feb 2020, 00:47
AB is even when A and B are both Even or Odd
(1) A*B Even when bot even or both are different (2) A+B Odd when both are different in which case AB is Odd sufficient
Answer B



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 6057
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: If A and B are positive integers, is A – B even?
[#permalink]
Show Tags
20 Feb 2020, 01:13
AB ; even possible when both a& b are either even or odd #1 The product of A and B is even possible either both a & b are even or either of a & b is even and other is odd ; insufficient #2 A + B is odd possible when either of a & b is even and other is odd ; so therefore ab is not even; sufficient IMO B
If A and B are positive integers, is A – B even?
(1) The product of A and B is even (2) A + B is odd



HEC & IMD School Moderator
Status: Preparing for GMAT
Joined: 16 Dec 2018
Posts: 828
Location: Italy
Concentration: Leadership, Operations
WE: Engineering (Manufacturing)

Re: If A and B are positive integers, is A – B even?
[#permalink]
Show Tags
20 Feb 2020, 01:36
If A and B are positive integers, is A – B even? A and B could be even/odd(1) The product of A and B is even The product of two integers is even in 2 cases: Case A: Even X Even = Even, so, A  B = Even always Case B: Odd X Even = Even, so A  B = Odd always
Two different possibilities, Insufficient ... A D / B C E (2) A + B is odd It means Odd + Even = Odd Hence, A  B = Odd always Sufficient
'B' is the winner
_________________
JaSsFollow the founder BB and look at Study Plan , Retake Strategy Rules for Posting  Posting Rules , Verbal Posting RulesExperts  Bunuel , GMATNinja , SajjadAhmad , gmatbustersUseful forums All you need for Quant , Quant Megathread SC , CR , RC , SC Megathread , CR Megathread , RC Megathread



Director
Joined: 30 Sep 2017
Posts: 800
GMAT 1: 720 Q49 V40
GPA: 3.8

Re: If A and B are positive integers, is A – B even?
[#permalink]
Show Tags
20 Feb 2020, 02:26
Q. is A – B even?
(1) A*B = even If A=5 and B=2, then A–B= odd. If A=6 and B=2, then A–B= even. NOT SUFFICIENT (2) A + B is odd If A=5 and B=2, then A–B= odd. SUFFICIENT
FINAL ANSWER IS (B)
Posted from my mobile device



Manager
Joined: 14 Sep 2019
Posts: 220

Re: If A and B are positive integers, is A – B even?
[#permalink]
Show Tags
20 Feb 2020, 09:19
If A and B are positive integers, is A – B even?
(1) The product of A and B is even (2) A + B is odd
Solution: From statement (1), the product of A and B is even. So Either A or B is even or both A and B are even. This has been shown below: A……………..B………………AB………………………………AB = ? even………odd………even*odd =even……..evenodd = odd Odd………even……..odd*even = even…….odd even= odd even………even…….even*even = even….even even= even Therefore, not sufficient.
From statement (2), A + B is odd. So Either A or B is even This has been shown below: A……………..B………………A+B………………………………AB = ? even………odd………even + odd =odd…….evenodd = odd Odd………even……..odd + even = odd…….odd even= odd
Therefore, statement (2) is sufficient. Answer: B



VP
Joined: 24 Nov 2016
Posts: 1342
Location: United States

Re: If A and B are positive integers, is A – B even?
[#permalink]
Show Tags
20 Feb 2020, 16:59
Quote: If A and B are positive integers, is A – B even?
(1) The product of A and B is even (2) A + B is odd AB=EVEN when a,b=odd,odd or even,even (1) insuficab=even; a,b=e,e or e,o (2) sufica+b=odd; a,b=o,e ab=odd Ans (B)



Director
Joined: 25 Jul 2018
Posts: 645

Re: If A and B are positive integers, is A – B even?
[#permalink]
Show Tags
20 Feb 2020, 23:52
If A and B are positive integers, is A – B even?
(Statement1): A*B= even Even* Odd = Even —> Even— Odd = Odd ( No)
Even* Even= Even —> Even —Even = Even ( Yes) Insufficient
(Statement2): A + B is odd In order A+B to be odd, one of the integer A and integer B must be Odd —> Odd —Even = Odd ( Yes) —> Even — Odd= Odd (Yes)
Sufficient The answer is B
Posted from my mobile device




Re: If A and B are positive integers, is A – B even?
[#permalink]
20 Feb 2020, 23:52






