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

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

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New post 30 Aug 2016, 20:21
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A
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C
D
E

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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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New post 30 Aug 2016, 21:18
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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.


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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New post 30 Aug 2016, 22:40
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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Expert Post
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Re: If a and b are positive integers, is ab an even? [#permalink]

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New post 01 Sep 2016, 17:32
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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New post 01 Jan 2017, 10:03
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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If a and b are positive integers, is ab an even? [#permalink]

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New post 09 Mar 2017, 21:28
---- 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
-- 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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New post 10 Mar 2017, 02:51
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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New post 10 Mar 2017, 08:21
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

you're getting answer as even
SUFFICIENT
Re: If a and b are positive integers, is ab an even?   [#permalink] 10 Mar 2017, 08:21
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