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

It is currently 22 Sep 2018, 13:55

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

Is positive integer n divisible by 4?

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

Hide Tags

Senior Manager
Senior Manager
avatar
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 277
Is positive integer n divisible by 4?  [#permalink]

Show Tags

New post Updated on: 16 May 2017, 04:45
3
3
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (01:21) correct 40% (01:21) wrong based on 156 sessions

HideShow timer Statistics

Is positive integer n divisible by 4?

(1) \(n^2\) is divisible by 8

(2) \(\sqrt{n}\) is an even integer

_________________

I'm the Dumbest of All !!


Originally posted by shrive555 on 19 Oct 2010, 10:37.
Last edited by Bunuel on 16 May 2017, 04:45, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: Is positive integer n divisible by 4?  [#permalink]

Show Tags

New post 19 Oct 2010, 10:48
3
1
shrive555 wrote:
Is positive integer n is divisible by 4 ?

1) n^2 is divisible by 8
2) sqr/n is even integer.

any good explanation please :x


(1) n^2 is divisible by 8 --> \(n^2=8p=2^3*p\) --> in order n^2 to be a perfect square p must complete the power of 2 to even number (perfect square has even powers of its prime factors) --> \(n^2=8p=2^3*2q=2^4q\) --> \(n=\sqrt{2^4q}=4\sqrt{q}\). Sufficient.

(2) \(\sqrt{n}=2k\) --> \(n=4k^2\). Sufficient.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Current Student
User avatar
Joined: 15 Jul 2010
Posts: 211
GMAT 1: 750 Q49 V42
Re: Is positive integer n divisible by 4?  [#permalink]

Show Tags

New post 19 Oct 2010, 23:14
D

I solved it quite easily by putting in some numbers to find a pattern, but I love what Bunuel did!!!

Kudos for both Bunuel and the poster.
_________________

Consider KUDOS if my post was helpful. :-D

My Debrief: http://gmatclub.com/forum/750-q49v42-105591.html#p825487

Manager
Manager
avatar
Joined: 25 Aug 2010
Posts: 66
Re: Is positive integer n divisible by 4?  [#permalink]

Show Tags

New post 20 Oct 2010, 01:31
rather randomly picking numbers, follow Bunuel method... Cool stuff
Manager
Manager
avatar
Status: Keep fighting!
Affiliations: IIT Madras
Joined: 31 Jul 2010
Posts: 206
WE 1: 2+ years - Programming
WE 2: 3+ years - Product developement,
WE 3: 2+ years - Program management
Re: Is positive integer n divisible by 4?  [#permalink]

Show Tags

New post 20 Oct 2010, 05:45
thanks for the good question and a good explanation!
Senior Manager
Senior Manager
avatar
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 277
Re: Is positive integer n divisible by 4?  [#permalink]

Show Tags

New post 20 Oct 2010, 18:29
The Explanation i had was :

if n is divisible by 4 then n will have atleast two prime factors
n= 2x2x?x?x?

1- n^2 = n x n = ( 2x2 x ? x? ) ( 2x2 x? ? )

2= n = Sqr/n x Sqr/n
(2x?x?x? ..) x ( 2x?x?....)
(2x2.........)
Quote:
Bunel : perfect square has even powers of its prime factors

can you give example on this please
_________________

I'm the Dumbest of All !!

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: Is positive integer n divisible by 4?  [#permalink]

Show Tags

New post 21 Oct 2010, 18:36
1
shrive555 wrote:
The Explanation i had was :

if n is divisible by 4 then n will have atleast two prime factors
n= 2x2x?x?x?

1- n^2 = n x n = ( 2x2 x ? x? ) ( 2x2 x? ? )

2= n = Sqr/n x Sqr/n
(2x?x?x? ..) x ( 2x?x?....)
(2x2.........)
Quote:
Bunel : perfect square has even powers of its prime factors

can you give example on this please


\(x\) is a perfect square means that it's a square of some \(integer\) \(n\): \(x=n^2\), for example 4=2^2, 9=3^2, ... Now, as \(x=n^2\) then all powers of primes of x must be even (consider \(n=a^p*b^q*c^r\), where a, b and c are primes of n --> \(x=n^2=a^{2p}*b^{2q}*c^{2r}\)).

Check this for more:
perfect-square-101678.html?hilit=perfect%20square#p799742
a-perfect-square-79108.html?hilit=perfect%20square

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 27 Mar 2010
Posts: 98
Re: Is positive integer n divisible by 4?  [#permalink]

Show Tags

New post 21 Oct 2010, 19:18
Bunuel wrote:
shrive555 wrote:
Is positive integer n is divisible by 4 ?

1) n^2 is divisible by 8
2) sqr/n is even integer.

any good explanation please :x


(1) n^2 is divisible by 8 --> \(n^2=8p=2^3*p\) --> in order n^2 to be a perfect square p must complete the power of 2 to even number (perfect square has even powers of its prime factors) --> \(n^2=8p=2^3*2q=2^4q\) --> \(n=\sqrt{2^4q}=4\sqrt{q}\). Sufficient.

(2) \(\sqrt{n}=2k\) --> \(n=4k^2\). Sufficient.

Answer: D.



Bunuel, what made you think about :
in order n^2 to be a perfect square p must complete the power of 2 to even number (perfect square has even powers of its prime factors)

why n^2 be a perfect square???
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: Is positive integer n divisible by 4?  [#permalink]

Show Tags

New post 21 Oct 2010, 19:22
utin wrote:
Bunuel wrote:
shrive555 wrote:
Is positive integer n is divisible by 4 ?

1) n^2 is divisible by 8
2) sqr/n is even integer.

any good explanation please :x


(1) n^2 is divisible by 8 --> \(n^2=8p=2^3*p\) --> in order n^2 to be a perfect square p must complete the power of 2 to even number (perfect square has even powers of its prime factors) --> \(n^2=8p=2^3*2q=2^4q\) --> \(n=\sqrt{2^4q}=4\sqrt{q}\). Sufficient.

(2) \(\sqrt{n}=2k\) --> \(n=4k^2\). Sufficient.

Answer: D.



Bunuel, what made you think about :
in order n^2 to be a perfect square p must complete the power of 2 to even number (perfect square has even powers of its prime factors)

why n^2 be a perfect square???


Square of an integer is a perfect square --> n is an integer --> n^2 is a perfect square.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
G
Joined: 27 Dec 2016
Posts: 222
CAT Tests
Re: Is positive integer n divisible by 4?  [#permalink]

Show Tags

New post 04 May 2017, 18:26
Hi,

Can anyone please help me explain how S2 is sufficient? For example, if you pick 64 as n, you will get 8 and it is divisible by 4. But if you pick 100, you get 10 and it is not divisible by 4. Please help me as I am pretty confused here and not seeing how S2 is sufficient.

Thank You!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: Is positive integer n divisible by 4?  [#permalink]

Show Tags

New post 05 May 2017, 02:24
csaluja wrote:
Hi,

Can anyone please help me explain how S2 is sufficient? For example, if you pick 64 as n, you will get 8 and it is divisible by 4. But if you pick 100, you get 10 and it is not divisible by 4. Please help me as I am pretty confused here and not seeing how S2 is sufficient.

Thank You!


n in your examples is 64 or 100, not 8 or 10. Both 64 and 100 are divisible by 4. Check complete solution here: https://gmatclub.com/forum/is-positive- ... ml#p802917

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 08 May 2017
Posts: 1
Re: Is positive integer n divisible by 4?  [#permalink]

Show Tags

New post 24 Aug 2018, 00:20
In statement no. 2, why haven't we considered the possibility of n being zero?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: Is positive integer n divisible by 4?  [#permalink]

Show Tags

New post 24 Aug 2018, 00:27
1
usmanazeem wrote:
In statement no. 2, why haven't we considered the possibility of n being zero?



The question reads: Is positive integer n is divisible by 4 ? 0 is NOT a positive number.

But even for n = 0, the answer to the question whether n is divisible by 4, would be YES, because 0 is divisible by every integer (except 0 itself).

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 for more below threads:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Bot
Re: Is positive integer n divisible by 4? &nbs [#permalink] 24 Aug 2018, 00:27
Display posts from previous: Sort by

Is positive integer n divisible by 4?

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

Events & Promotions

PREV
NEXT


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®.