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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7361
GMAT 1: 760 Q51 V42 GPA: 3.82
If a and b are positive integers, is ab an even?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 63% (01:32) correct 37% (01:58) wrong based on 229 sessions

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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.

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

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1
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.

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

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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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7361
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If a and b are positive integers, is ab an even?  [#permalink]

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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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GRE 1: Q169 V154 Re: If a and b are positive integers, is ab an even?  [#permalink]

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

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---- 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
-- Sufficient to answer

-----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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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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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

you're getting answer as even
SUFFICIENT
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Re: If a and b are positive integers, is ab an even?  [#permalink]

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_________________ Re: If a and b are positive integers, is ab an even?   [#permalink] 04 Oct 2018, 08:39
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