GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 16 Nov 2018, 12:42

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • GMATbuster's Weekly GMAT Quant Quiz # 9

     November 17, 2018

     November 17, 2018

     09:00 AM PST

     11:00 AM PST

    Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

If x=p*n^k+p where n and k are positive integers, is x divisible by 2?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
S
Joined: 26 Apr 2018
Posts: 39
If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

Show Tags

New post Updated on: 10 Sep 2018, 02:27
1
3
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

42% (01:49) correct 58% (02:08) wrong based on 66 sessions

HideShow timer Statistics

If \(x=p*n^k+p\) where n and k are positive integers, is x divisible by 2?

1) n+kn=915
2)p^35+35^p is even




Source: Exercise given by gmat tutors

Originally posted by bettatantalo on 09 Sep 2018, 01:56.
Last edited by chetan2u on 10 Sep 2018, 02:27, edited 2 times in total.
Formatted question
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7035
Re: If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

Show Tags

New post 09 Sep 2018, 03:17
2
bettatantalo wrote:
If x=p*n^k+p where n and k are positive integers, is x divisible by 2?

1) n+kn=915
2)p^35+35^p is even




Source: Exercise given by gmat tutors


\(x=p*n^k+p=p(n^k+1)\)
So for X to be divisible by 2, any one of the two - p and n^k+1- should be even
n^k+1 is even means n is odd.

Let us see the statements

1) n+kn=915
n(1+k)=915
Therefore n and k+1 are odd. So n is odd and k is even
Means n^k is odd^even=odd
Ans is YES
Sufficient

2) p^35+35^p is even
So p is odd..
But we don't know if n is odd or even
If n is odd, yes
If n is even, no
Insufficient

A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Manager
Manager
User avatar
S
Joined: 07 Aug 2018
Posts: 77
Location: Croatia (Hrvatska)
GMAT 1: 560 Q39 V28
CAT Tests
Re: If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

Show Tags

New post 10 Sep 2018, 02:22
Manager
Manager
User avatar
P
Joined: 18 Jun 2018
Posts: 232
Premium Member CAT Tests
If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

Show Tags

New post 11 Sep 2018, 08:20
bettatantalo wrote:
If \(x=p*n^k+p\) where n and k are positive integers, is x divisible by 2?

1) n+kn=915
2)p^35+35^p is even

Source: Exercise given by gmat tutors


OA: A

\(x=p*n^k+p=p*(n^k+1)\)

Given \(n\) and \(k\) are positive integers.

Term \(p*(n^k+1)\) will be divisible by \(2\) if either \(p\) or \((n^k+1)\) or both are divisible by \(2\).

if \(n\) is odd and \(k\) can be any positive integer,\((n^k+1)\) will be of form ODD+ODD= EVEN i.e Term \(p*(n^k+1)\) will be even.

if \(n\) is even and \(k\) can be any positive integer,\((n^k+1)\) will be of form EVEN+ODD= ODD i.e Term \(p*(n^k+1)\) will be odd.

Statement (1) : \(n+kn=915\)

\(n(1+k)=3*5*61\)

\(n\) can be \(3,5,61,15,183,305\)

this implies that \(n\) will be odd, leading to the term \(p*(n^k+1)\) being even.

So \(x\) will be divisible by \(2\)

Statement \(1\) alone is sufficient.

Statement (2) : \(p^{35}+35^p\) is even

\(p^{35}+35^p\) will be even if \(p^{35}\) is odd as \(35^p\) is odd.

So \(p\) is odd, but term \((n^k+1)\) can be even or odd.

\(x\) can be odd or even, depending upon value of \((n^k+1)\).

Statement \(2\) alone is not sufficient.
Intern
Intern
avatar
B
Joined: 04 Apr 2017
Posts: 19
Re: If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

Show Tags

New post 12 Sep 2018, 01:55
Hi chetan2u
How do you know that p is an integer from statement 1? I think we need statement 2 which confirms that p is an integer.
GMAT Club Bot
Re: If x=p*n^k+p where n and k are positive integers, is x divisible by 2? &nbs [#permalink] 12 Sep 2018, 01:55
Display posts from previous: Sort by

If x=p*n^k+p where n and k are positive integers, is x divisible by 2?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.