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

Click on the image below to understand what are the   Six Process Skills   that are important to master GMAT Quant

https://e-gmat.com/blogs/wp-content/uploads/2020/04/A1_main_QPS-e1586428062196.jpg

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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards