If P and Q are integers and P0, then is Q divisible by 2?

Question

If  P   and  Q   are integers and  P>0 , then is  Q   divisible by  2 ?

(1)  (P+Q)(Q-P)  is Even
(2) P ^{Q}  + Q ^{P}  is Odd

chetan2u · Accepted Answer

Question is :  Is Q even?

(1) (P+Q)(Q-P) is Even
 Q^2-P^2  is even. 
Thus, either both P and Q are even or both are odd. 
Insufficient

(2) P^Q + Q^P is Odd
Thus, one of the two,  P^Q  or  Q^P  is even and other odd. 
Two cases-
a) when both have opposite property. 
Say one is 2 and other 3, so  2^3+3^2=17 
b) when both are even but one is 0, so  2^0+0^2=1+0=1 
Insufficient

Combined 
Both are even as per both statements and one of them is 0.
So Q is even. 
Sufficient

C

rajatchopra1994 · Answer

Dear  chetan2u  ,

2^0 and 0^2 will be 1 and 0
It should be 1+0 = 1 not 2+1=3.

I don't think, this will lead to any answer change.

Regards
Rajat

Posted from my mobile device

AnkithaSrinivas · Answer

from 1, we know nothing 
from 2, we know either one os even

together - we cant say which one is even

chetan2u · Answer

Thanks. 
Corrected the typo

MH321 · Answer

i. (P+Q)(Q-P)=Eeven
⇒Q²–P²
Simultaneously Odd or even.  INSUFFICIENT.

ii. P^Q+Q^P=Odd
Either of them interchangeably must be even while another must be odd to satisfy the equation.

Or both of them can be positive only if one of them is 0 and here it must be Q; 'cause P>0 given.  INSUFFICIENT.

But combinedly, the only value of Q that satisfies both of the equations in (i) and (ii) is 0 and any even value of P. 
i. 0²–2²=Even
i 2^0–0²=Odd

Hence, we wind up finding that Q is not divisible by 2. The answer comes with  NO. 
 Ans. C

If the question were   is Q even?   then our answer would come with  YES  as Q=0 which is an even number. 
However, in both cases, the answer is  C.

Posted from my mobile device

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If P and Q are integers and P>0, then is Q divisible by 2?

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