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

It is currently 15 Dec 2018, 09:13

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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     December 15, 2018

     December 15, 2018

     10:00 PM PST

     11:00 PM PST

    Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

If n > 0, is (4^n + 1) divisible by 5? (1) n is the integral root of

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

Hide Tags

Manager
Manager
avatar
G
Joined: 28 Jun 2018
Posts: 147
Location: India
Concentration: Finance, Marketing
Schools: CUHK '21 (II)
GMAT 1: 650 Q49 V30
GPA: 4
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
If n > 0, is (4^n + 1) divisible by 5? (1) n is the integral root of  [#permalink]

Show Tags

New post 31 Jul 2018, 05:00
6
1
5
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (01:10) correct 40% (01:33) wrong based on 222 sessions

HideShow timer Statistics

If n > 0, is (\(4^{n}\) + 1) divisible by 5?

(1) n is the integral root of equation: \(\frac{n^{2}}{3}\) + n - 6 = 0
(2) n is an odd integer.

_________________

What to do if you are new to GMAT:
https://gmatclub.com/forum/what-to-do-if-you-are-new-272708.html#p2108758

GMAC official guides : https://gmatclub.com/forum/gmac-official-guides-the-master-directory-links-240610.html#p1854935

Give me kudos if you like it , it's totally harmless :)

Manager
Manager
User avatar
G
Status: Studying SC
Joined: 04 Sep 2017
Posts: 116
GPA: 3.6
WE: Sales (Computer Software)
If n > 0, is (4^n + 1) divisible by 5? (1) n is the integral root of  [#permalink]

Show Tags

New post Updated on: 02 Aug 2018, 04:15
1
kshitizbansal92 wrote:
If n > 0, is (4^n + 1) divisible by 5?

(1) n is the integral root of equation: \(n^2/3\) + n - 6 = 0
(2) n is an odd integer.


Statement (1)

Multiply by 3 to get rid of the fraction. \(n^2\) +3n -18 = 0... Factors to (n+6)(n-3). Roots are 3 and -6. It is given that n>0, so n must = 3.

Plug in n=3...... \(4^3\) + 1 = 65. Is 65 divisible by 5? YES.

Statement (2)

We know n has to be positive. so our possible values for n are 1,3,5,7,9 etc...

Make n=1 and we get \(4^1\) +1 =5. Divisible by 5? YES

Make n=3 and we get \(4^3\) + 1 = 65. Divisible by 5? YES

OR if you are sound in your number theory, you will know that 4 has a cyclicity of 2.
4^1=4
4^2=16
4^3=64
4^4=256

So for all odd integers it will end in units digit 4.
For all even integers it will end in units digit 6.

Answer: D
_________________

Would I rather be feared or loved? Easy. Both. I want people to be afraid of how much they love me.

How to sort questions by Topic, Difficulty, and Source:
https://gmatclub.com/forum/search.php?view=search_tags


Originally posted by MikeScarn on 31 Jul 2018, 05:15.
Last edited by MikeScarn on 02 Aug 2018, 04:15, edited 6 times in total.
Manager
Manager
User avatar
G
Status: Studying SC
Joined: 04 Sep 2017
Posts: 116
GPA: 3.6
WE: Sales (Computer Software)
Re: If n > 0, is (4^n + 1) divisible by 5? (1) n is the integral root of  [#permalink]

Show Tags

New post 31 Jul 2018, 05:58
2
For those thinking "What does 'integral root' mean?"

I just googled it. Actually "integral" means integer. So it’s just asking for the integer root.

Which can basically be used as a clue that n is an integer, but we still have to remember that n is positive.

When I first read the question, before looking at the statements, I thought "well if n is a decimal, zero, or a negative number, then the answer will be NO" So "integral" could be used as a quick clue that we will indeed be looking at integers. And n>0 shows us that we will be looking at positive numbers.
_________________

Would I rather be feared or loved? Easy. Both. I want people to be afraid of how much they love me.

How to sort questions by Topic, Difficulty, and Source:
https://gmatclub.com/forum/search.php?view=search_tags

Intern
Intern
avatar
B
Joined: 20 Jul 2018
Posts: 1
Re: If n > 0, is (4^n + 1) divisible by 5? (1) n is the integral root of  [#permalink]

Show Tags

New post 16 Sep 2018, 18:55
Answer option (D)
1)We get the roots of the equation as -6 and 3. We will only consider 3 and after substituting in the equation given in question , the answer comes as yes. Sufficient
2)Any Odd integer the digit at unit's place would be 4 , hence +1 would definitely be divisible by 5.
GMAT Club Bot
Re: If n > 0, is (4^n + 1) divisible by 5? (1) n is the integral root of &nbs [#permalink] 16 Sep 2018, 18:55
Display posts from previous: Sort by

If n > 0, is (4^n + 1) divisible by 5? (1) n is the integral root of

  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®.