December 14, 2018 December 14, 2018 09:00 AM PST 10:00 AM PST 10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners. December 14, 2018 December 14, 2018 10:00 PM PST 11:00 PM PST Carolyn and Brett  nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 268

Is positive integer n divisible by 4?
[#permalink]
Show Tags
Updated on: 16 May 2017, 03:45
Question Stats:
61% (01:34) correct 39% (01:39) wrong based on 166 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
I'm the Dumbest of All !!
Originally posted by shrive555 on 19 Oct 2010, 09:37.
Last edited by Bunuel on 16 May 2017, 03:45, edited 2 times in total.
Renamed the topic and edited the question.



Math Expert
Joined: 02 Sep 2009
Posts: 51214

Re: Is positive integer n divisible by 4?
[#permalink]
Show Tags
19 Oct 2010, 09:48



Current Student
Joined: 15 Jul 2010
Posts: 183

Re: Is positive integer n divisible by 4?
[#permalink]
Show Tags
19 Oct 2010, 22:14
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.
My Debrief: http://gmatclub.com/forum/750q49v42105591.html#p825487



Manager
Joined: 25 Aug 2010
Posts: 63

Re: Is positive integer n divisible by 4?
[#permalink]
Show Tags
20 Oct 2010, 00:31
rather randomly picking numbers, follow Bunuel method... Cool stuff



Manager
Status: Keep fighting!
Affiliations: IIT Madras
Joined: 31 Jul 2010
Posts: 196
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
20 Oct 2010, 04:45
thanks for the good question and a good explanation!



Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 268

Re: Is positive integer n divisible by 4?
[#permalink]
Show Tags
20 Oct 2010, 17:29
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
Joined: 02 Sep 2009
Posts: 51214

Re: Is positive integer n divisible by 4?
[#permalink]
Show Tags
21 Oct 2010, 17:36



Manager
Joined: 26 Mar 2010
Posts: 94

Re: Is positive integer n divisible by 4?
[#permalink]
Show Tags
21 Oct 2010, 18:18
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 (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
Joined: 02 Sep 2009
Posts: 51214

Re: Is positive integer n divisible by 4?
[#permalink]
Show Tags
21 Oct 2010, 18:22
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 (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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 27 Dec 2016
Posts: 258

Re: Is positive integer n divisible by 4?
[#permalink]
Show Tags
04 May 2017, 17:26
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
Joined: 02 Sep 2009
Posts: 51214

Re: Is positive integer n divisible by 4?
[#permalink]
Show Tags
05 May 2017, 01:24



Intern
Joined: 08 May 2017
Posts: 1

Re: Is positive integer n divisible by 4?
[#permalink]
Show Tags
23 Aug 2018, 23:20
In statement no. 2, why haven't we considered the possibility of n being zero?



Math Expert
Joined: 02 Sep 2009
Posts: 51214

Re: Is positive integer n divisible by 4?
[#permalink]
Show Tags
23 Aug 2018, 23:27




Re: Is positive integer n divisible by 4? &nbs
[#permalink]
23 Aug 2018, 23:27






