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# If a and b are positive integers, is ab an even?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If a and b are positive integers, is ab an even? [#permalink]

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30 Aug 2016, 19:21
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If a and b are positive integers, is ab an even?
1) (a+1)b=even
2) (a+1)^b=odd

*An answer will be posted in 2 days.
[Reveal] Spoiler: OA

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Re: If a and b are positive integers, is ab an even? [#permalink]

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30 Aug 2016, 20:18
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KUDOS
MathRevolution wrote:
If a and b are positive integers, is ab an even?
1) (a+1)b=even
2) (a+1)^b=odd

*An answer will be posted in 2 days.

is $$ab$$ an even ?
which mean only $$a$$ or only $$b$$ or both $$a$$ and $$b$$ are even.

1) $$(a+1)b$$ = even, which can mean, $$b$$ alone is even or $$a$$ alone is odd or both $$b$$ is even and $$a$$ is odd. Not sufficient. Eliminate A and D
2) $$(a+1)^b$$ = odd, which means no matter what $$b$$ is , $$a$$ has to be even. Sufficient.

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Re: If a and b are positive integers, is ab an even? [#permalink]

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30 Aug 2016, 21:40
MathRevolution wrote:
If a and b are positive integers, is ab an even?
1) (a+1)b=even
2) (a+1)^b=odd

*An answer will be posted in 2 days.

st1 : a=1,b=1 NO and a=1,b=2 YES ---INSUFF
st2: a has to be even for statement to be odd ----SUFF

B
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Re: If a and b are positive integers, is ab an even? [#permalink]

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01 Sep 2016, 16:32
Since there are 2 variables in the original condition, the answer is C. However, we have to apply common mistake type 4(A) because it is one of key questions. In case of con 2), from a+1=odd, a=even, the answer is always yes and the condition is sufficient. Hence, the correct answer is B.
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Re: If a and b are positive integers, is ab an even? [#permalink]

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01 Jan 2017, 09:03
Nice Question.
Here is my solution to this one ->

Given data ->
A and B are positive integers
We need to see if atleast one of them is even or not (so that A*B will be even)

Statement 1->
A=odd
B=odd
NO
A=even
B=even
YES
Hence not sufficient

Statement 2=>
Positive exponent do not effect the even odd nature of any number
Hence A+1 must be odd => A must be even => AB will be even

Hence sufficient

Hence B

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Joined: 09 Dec 2013
Posts: 4
If a and b are positive integers, is ab an even? [#permalink]

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09 Mar 2017, 20:28
---- Statement 1 = (a+1)b=even----

Lets try a=odd
(odd+1)b=even
even*b=even
b=even/even
b=even

Now lets try a=Even
(Even+1)b=even
odd*b=even
b=even/odd
b=even

When a=odd, b=even
When a=even, b=even

Odd x even = even
even x even = even

hence in either case a*b=even

-----Statement 2 (a+1)^b=odd -----

Positive exponent do not effect the even odd nature of any number
Hence A+1 must be odd => A must be even => AB will be even

Hence Answer should be D Each alone is sufficient.
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Re: If a and b are positive integers, is ab an even? [#permalink]

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10 Mar 2017, 01:51
St 1: (a+1)b is even that mean either of one is even or both are even. INSUFFICIENT
St 2: (a+1)^b is odd. thane means a+1 is odd, hence a is even.therefore ab will be even.ANSWER

Option B
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Re: If a and b are positive integers, is ab an even? [#permalink]

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10 Mar 2017, 07:21
I don't agree to reply above that says
St 1: (a+1)b is even that mean either of one is even or both are even. INSUFFICIENT

even if either one is even or both are even final question asks is ab even?

If you look at even odd multiplication as below
Odd x even = even
even x even = even

SUFFICIENT
Re: If a and b are positive integers, is ab an even?   [#permalink] 10 Mar 2017, 07:21
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