If p and k are non-negative distinct integers, then is p^{18} . . . .

Question

If p and k are non-negative distinct integers, then is  p^{18} + 18^{pk}  odd?

(1)  p^k  is even
(2)  p^{k + 1}  is even

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ArunSharma12 · Accepted Answer

Given: p,k  \ge0

statement 1: p^k  is even
when p = 0 & k > 0 
 p^{18} + 18^{pk}  = even + 1 = odd
when p > 0 & even then k > 0
 p^{18} + 18^{pk}  = even + even = even 
not sufficient

statement 2: p^(k + 1)  is even
when p = 0 & k  \ge  0
 p^{18} + 18^{pk}  = even + 1 = odd
when p > 0 & even k = 0
 p^{18} + 18^{pk}  = even + 1 = odd
when p > 0, even & k > 0
 p^{18} + 18^{pk}  = even + even = even
not sufficient

combining both statements,
when p = 0 & k > 0 
 p^{18} + 18^{pk}  = even + 1 = odd
when p > 0, even & k > 0
 p^{18} + 18^{pk}  = even + even = even
not sufficient

Ans: E

minustark · Answer

If p and k are non-negative distinct integers, then is  p^{18} + 18^{pk}  odd?
 (1)  p^k  is even
(2)  p^(k + 1)  is even

1) p^k is even. So, we can assume that p is an even integer(including 0) and k >0. If p is 0, then p^18 +18^pk will be 0 + 1=1, odd. But if p is non-zero even, then p^18 +18^pk will be even. Not sufficient.
2) In this case also p can assume the value 0. not sufficient.
Together, p can be any even value including 0, which will make the sum 1. Other even values will add to an even integer. Not sufficient.
E is the answer.

stne · Answer

EgmatQuantExpert , 
Please check the OA 
Statement 1 : P=0 and k=1 ,  p^{18} + 18^{pk}  = 0+1 =1 Odd, so ans is yes 
  \hspace{8mm}   P=2  and\hspace{1mm} k=2 then  p^{18} + 18^{pk}  = even+even =even , so Ans is No.
INSUFF.

Hence A cannot be the answer.

In fact P=0 and K=1 and P=2 k=2 satisfy both statements , but give different Answers. In the current format ans. should be E.

KumarSam · Answer

Its simple. Answer is A
p and k are non-negative distinct integers
Given p>= 0 and k>=0
p^18= a 
18^(pk) = b

a+b = odd if ( a=odd, b = even ) and if ( a = even, b = odd )
a+b = even if ( a=even, b = even ) and if ( a = odd, b = odd )
b can be odd only if pk = 0 .

(1) p^k is even
This means that p = even, k not equal to 0 . ie k= 1,2,3,4,.....
p^18 is even
18^pk is even
Overall Even
SUFFICIENT

(2) p^(k+1) is even
This means that p is even, k = 0,1,2,3,4,...
p^18 is even
18^(pk) = 1 or even. Dont know
NOT SUFFICIENT

Hence Answer A

elPatron434 · Answer

I too feel that it is E. If it was mentioned in the stem that p was positive, then A would suffice.  Bunuel , is my understanding correct?

NischalP · Answer

How can 0 be considered as even number.

Answer is a clear A

According to the cyclic rule. 
None of the odd number power to any number --> leads to an even number.

stne · Answer

Dear NischalP , You should have googled it, before being so sure.According to my knowledge ZERO is in fact an EVEN number. https://www.britannica.com/story/is-zer ... odd-number Hope it's clear. OA is clearly wrong ! Hope Moderator looks into this.

NischalP · Answer

stne 
Dear friend,

I am not here to argue, But please check your fundamentals with your school teacher
before you check a random google site.

0 is neither even nor odd. (Atlease according to GMAT)
 GMATNinja  could clarify or any other moderator for instance.

stne · Answer

I suppose you still didn't do any research. Would you call this a random link also. https://gmatclub.com/forum/is-zero-even-84800.html Additionally instead of asking me to check with my school teacher, you should perhaps check your source, from where exactly did you come to know that 0 is not even. Please be a little respectful while replying, Thank you.

Bunuel · Answer

0 is an even number. There is not discussion about it. ZERO: 1. 0 is an integer. 2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even. 3. 0 is neither positive nor negative integer (the only one of this kind). 4. 0 is divisible by EVERY integer except 0 itself. Check more here: https://gmatclub.com/forum/number-proper ... 74996.html

stne · Answer

Dear Moderator,

Thank you for clearing this. 
Can you please look into the OA, unless many of us missed something , correct answer seems to be E. Thank you.

Bunuel · Answer

Yes, the answer to the question posted is E. There might be some formatting error or a typo in the text.

Kinshook · Answer

Asked: If p and k are non-negative distinct integers, then is  p^{18}+18^{pk}  odd?
p^{18} is even/odd if p is even/odd.
18^{pk} is odd if one of p/k is 0, otherwise is even.

Q. Is  p + 2^{pk}  odd?

If p and k are non-negative distinct integers; then both p & k are not 0, but one of them may be 0.

(1)  p^k  is even
If p is even ; p^k is even when  k 
eq 0  
But p may be 0
NOT SUFFICIENT

(2)  p^{k+1}  is even
If p is even ; p^k is even when  k+1 
eq 0  
k may be 0.
NOT SUFFICIENT

(1) + (2) 
(1)  p^k  is even
If p is even ; p^k is even when  k 
eq 0  
But p may be 0
(2)  p^{k + 1}  is even
If p is even ; p^k is even when  k+1 
eq 0  
k may be 0.
Either p or k may be 0
NOT SUFFICIENT

IMO E

desertEagle · Answer

What is 0 to the power 0??

Bunuel · Answer

0^0, in some sources equals to 1, some mathematicians say it's undefined. But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT.

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If p and k are non-negative distinct integers, then is p^{18} . . . .

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