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Math Expert V
Joined: 02 Sep 2009
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If A and B are positive integers, is A – B even?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 77% (00:57) correct 23% (00:53) wrong based on 30 sessions

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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

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Re: If A and B are positive integers, is A – B even?  [#permalink]

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A-B 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 A-B is Odd sufficient

GMAT Club Legend  V
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Re: If A and B are positive integers, is A – B even?  [#permalink]

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A-B ; 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 a-b 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
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Re: If A and B are positive integers, is A – B even?  [#permalink]

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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

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Re: If A and B are positive integers, is A – B even?  [#permalink]

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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

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Re: If A and B are positive integers, is A – B even?  [#permalink]

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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………………………………A-B = ?
even………odd………even*odd =even……..even-odd = 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………………………………A-B = ?
even………odd………even + odd =odd…….even-odd = odd
Odd………even……..odd + even = odd…….odd- even= odd

Therefore, statement (2) is sufficient.
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Re: If A and B are positive integers, is A – B even?  [#permalink]

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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

A-B=EVEN when a,b=odd,odd or even,even

(1) insufic
ab=even; a,b=e,e or e,o

(2) sufic
a+b=odd; a,b=o,e
a-b=odd

Ans (B)
Director  P
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Posts: 645
Re: If A and B are positive integers, is A – B even?  [#permalink]

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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

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