Data Sufficiency (DS) | Re: If A, B and n are positive integers, is (3A + B)^n even ?

If A, B and n are positive integers, is (3A+B)^n even

(3A+B)^n = ( OddXA+B)^n here we can omit the power n as (Odd)^n = Odd number and (Even)^n = Even number

Having said that,

(OddXA+B) may be solved in multiple cases

Case-1 A Odd B Odd
( OddXOdd+Odd)
(Odd+Odd)= even

Case-2 A Even B Odd
( OddXEven+Odd)
( Even+Odd)= Odd

Case-3 A Odd B Even
( OddXOdd+Even)
( Odd+Even)= Odd

Case-4 A Even B Even
( OddXEven+Even)
( Even+Even)= Even

Statement-1
A can be expressed in the form 8k+1, This means A is an Odd number but we do not know about B hence we cannot get an answer her eliminate A/D

Statement-2
7B is an Odd number, B is an odd number, but we cannot say anything about A, eliminate this answer.

Combining both statement we get A is odd and B is odd and this falls under case-1,

We can confidently say that answer is Yes (3A+b)^n is even

Answer C

Statistics : Posted by RohitKakkar • on 23 Jan 2023, 09:15 • Replies 2 • Views 81

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