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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
Posts: 5575
GMAT 1: 800 Q59 V59
GPA: 3.82
If a and b are positive integers, is ab an even? [#permalink]

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30 Aug 2016, 20:21
00:00

Difficulty:

45% (medium)

Question Stats:

55% (01:24) correct 45% (01:21) wrong based on 172 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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 23 Apr 2015 Posts: 322 Location: United States Concentration: General Management, International Business WE: Engineering (Consulting) Re: If a and b are positive integers, is ab an even? [#permalink] ### Show Tags 30 Aug 2016, 21:18 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. Current Student Status: It`s Just a pirates life ! Joined: 21 Mar 2014 Posts: 235 Location: India Concentration: Strategy, Operations GMAT 1: 690 Q48 V36 GPA: 4 WE: Consulting (Manufacturing) Re: If a and b are positive integers, is ab an even? [#permalink] ### Show Tags 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 _________________ Aiming for a 3 digit number with 7 as hundredths Digit Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5575 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If a and b are positive integers, is ab an even? [#permalink] ### Show Tags 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154
Re: If a and b are positive integers, is ab an even? [#permalink]

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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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Intern
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, 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

-----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.
Senior Manager
Joined: 05 Jan 2017
Posts: 427
Location: India
Re: If a and b are positive integers, is ab an even? [#permalink]

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

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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

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