Find all School-related info fast with the new School-Specific MBA Forum

It is currently 20 Aug 2014, 07:01

Starting Soon:

Live Q&A Session with Cambridge Admissions Team   ||    Join Chat Room to Attend the Session


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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Numbers-Squares root

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 19 Aug 2009
Posts: 82
Followers: 1

Kudos [?]: 38 [0], given: 46

Numbers-Squares root [#permalink] New post 03 Nov 2009, 23:22
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

25% (01:40) correct 75% (03:45) wrong based on 5 sessions
Q.Which of the following is not a perfect square

1. 100856
2. 325137
3. 945729
4. All of these

Hint- value of perfect sq has to end in 1,4,5,6,9...so option 2 is definately not a perfect square

But how to find the rest...is ther any shortcut or will we have to find the prime factors of all n bring them to standard form
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 31 Aug 2009
Posts: 422
Location: Sydney, Australia
Followers: 6

Kudos [?]: 106 [1] , given: 20

GMAT Tests User
Re: Numbers-Squares root [#permalink] New post 03 Nov 2009, 23:44
1
This post received
KUDOS
A perfect square will have exactly an even number of each of its factors.
81 for example:
81 = 9x9 = 3x3x3x3 which is essentially 2 sets of 3x3
Or:
36 = 6x6 = 2x3x2x3 which is 2 sets of 2x3

1. 100856
2. 325137
3. 945729
4. All of these

You mention option 2 is not correct, so neither is option 4.
Statement 1: 100856
You can only factor it by 2 three times. This is not an even amount of 2s so it cannot be a perfect square.
Statement 3: 945729
You can factor 3 three times. This is not an even amount of 3s so it cannot be a perfect square

So if I’m not wrong then none of these are perfect square? Which seems odd as that’s not an answer option. Or I could be wrong 
Manager
Manager
avatar
Joined: 19 Aug 2009
Posts: 82
Followers: 1

Kudos [?]: 38 [0], given: 46

Re: Numbers-Squares root [#permalink] New post 03 Nov 2009, 23:52
Ans is
optn 4 as it says 'all of these' meaning all of these r not perfect squares


yangsta8 wrote:
A perfect square will have exactly an even number of each of its factors.
81 for example:
81 = 9x9 = 3x3x3x3 which is essentially 2 sets of 3x3
Or:
36 = 6x6 = 2x3x2x3 which is 2 sets of 2x3

1. 100856
2. 325137
3. 945729
4. All of these

You mention option 2 is not correct, so neither is option 4.
Statement 1: 100856
You can only factor it by 2 three times. This is not an even amount of 2s so it cannot be a perfect square.
Statement 3: 945729
You can factor 3 three times. This is not an even amount of 3s so it cannot be a perfect square

So if I’m not wrong then none of these are perfect square? Which seems odd as that’s not an answer option. Or I could be wrong 
Senior Manager
Senior Manager
avatar
Joined: 31 Aug 2009
Posts: 422
Location: Sydney, Australia
Followers: 6

Kudos [?]: 106 [0], given: 20

GMAT Tests User
Re: Numbers-Squares root [#permalink] New post 04 Nov 2009, 00:31
Ahh yes you are right I didn't read it properly. Also to answer your original question I guess there is no need to factor all prime factors, just factor a few until you find that there are not an even number.
Tuck Thread Master
User avatar
Joined: 20 Aug 2009
Posts: 312
Location: Tbilisi, Georgia
Schools: Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)
Followers: 12

Kudos [?]: 88 [0], given: 69

GMAT Tests User
Re: Numbers-Squares root [#permalink] New post 04 Nov 2009, 00:32
Quote:
A perfect square will have exactly an even number of each of its factors.


A simple point, but worth remembering, Kudos!
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19027
Followers: 3361

Kudos [?]: 24360 [1] , given: 2677

Re: Numbers-Squares root [#permalink] New post 04 Nov 2009, 22:57
1
This post received
KUDOS
Expert's post
yangsta8 wrote:
A perfect square will have exactly an even number of each of its factors.
81 for example:
81 = 9x9 = 3x3x3x3 which is essentially 2 sets of 3x3
Or:
36 = 6x6 = 2x3x2x3 which is 2 sets of 2x3


I think the red part needs some clarification:

A perfect square will have exactly an even number of each of its factors.

That's not true.

I think you meant that perfect square n^2, has even number of prime factors of n or in other words prime factors of n have even powers.

In your example: 81=3*3*3*3=3^4, but 81 has the factor 27, what about it? There are three 27 in 81.
Or 36=6*6=2^2*3^2 but what about 12 which is factor of 36? There are three 12 in 36.

There are some tips about the perfect square though:

1. The number of distinct factors of a perfect square is ALWAYS ODD.
2. The sum of distinct factors of a perfect square is ALWAYS ODD.
4. A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors.
5. Perfect square always has even number of powers of prime factors.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Tuck Thread Master
User avatar
Joined: 20 Aug 2009
Posts: 312
Location: Tbilisi, Georgia
Schools: Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)
Followers: 12

Kudos [?]: 88 [0], given: 69

GMAT Tests User
Re: Numbers-Squares root [#permalink] New post 04 Nov 2009, 23:07
Quote:
A perfect square will have exactly an even number of each of its factors.


yeah, it holds only for prime factors
Tuck Thread Master
User avatar
Joined: 20 Aug 2009
Posts: 312
Location: Tbilisi, Georgia
Schools: Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)
Followers: 12

Kudos [?]: 88 [0], given: 69

GMAT Tests User
Re: Numbers-Squares root [#permalink] New post 04 Nov 2009, 23:15
Man, there should be a way to add some posts to favorites, to "memories" or something like that. The only method available is to save permalinks . . .
Senior Manager
Senior Manager
avatar
Joined: 31 Aug 2009
Posts: 422
Location: Sydney, Australia
Followers: 6

Kudos [?]: 106 [0], given: 20

GMAT Tests User
Re: Numbers-Squares root [#permalink] New post 05 Nov 2009, 21:02
shalva wrote:
Quote:
A perfect square will have exactly an even number of each of its factors.


yeah, it holds only for prime factors


Yes you are right. Thanks for the clarification :)
Director
Director
avatar
Joined: 23 Apr 2010
Posts: 584
Followers: 2

Kudos [?]: 25 [0], given: 7

Re: Numbers-Squares root [#permalink] New post 02 Jan 2011, 07:38
Bunuel, is the concept of a perfect square tested on the GMAT? I have come across it several times on this forum, but I am not sure if it is tested on the GMAT. Thank you.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19027
Followers: 3361

Kudos [?]: 24360 [0], given: 2677

Re: Numbers-Squares root [#permalink] New post 02 Jan 2011, 07:47
Expert's post
nonameee wrote:
Bunuel, is the concept of a perfect square tested on the GMAT? I have come across it several times on this forum, but I am not sure if it is tested on the GMAT. Thank you.


What do you mean by "the concept of a perfect square"??? A perfect square, is just an integer that can be written as the square of some other integer, for example 16=4^2, is a perfect square.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
avatar
Joined: 23 Apr 2010
Posts: 584
Followers: 2

Kudos [?]: 25 [0], given: 7

Re: Numbers-Squares root [#permalink] New post 02 Jan 2011, 07:55
What I mean is that I've come across several questions here on the forum that have a phrase "perfect square", and I have never heard of it before. So the reason I'm asking is if I have to pay attention to these questions (and read about some useful properties of perfect squares) or not?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19027
Followers: 3361

Kudos [?]: 24360 [0], given: 2677

Re: Numbers-Squares root [#permalink] New post 02 Jan 2011, 08:04
Expert's post
nonameee wrote:
What I mean is that I've come across several questions here on the forum that have a phrase "perfect square", and I have never heard of it before. So the reason I'm asking is if I have to pay attention to these questions (and read about some useful properties of perfect squares) or not?


Again: a perfect square, is just an integer that can be written as the square of some other integer, for example 16=4^2, is a perfect square. So perfect square is just a name of such integers as 1, 4, 9, 16, ... There are several properties of a perfect square, which might be useful while solving specific GMAT questions. Now, it's up to you to decide whether to study these question and properties or not.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
avatar
Joined: 23 Apr 2010
Posts: 584
Followers: 2

Kudos [?]: 25 [0], given: 7

Re: Numbers-Squares root [#permalink] New post 02 Jan 2011, 08:07
OK. Thanks. I guess I have to study it.
Re: Numbers-Squares root   [#permalink] 02 Jan 2011, 08:07
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If the square root of t is a real number, is the square root Rock750 2 09 Apr 2013, 15:32
If the number of square units in the surface area of a arjtryarjtry 1 11 Sep 2008, 20:27
If the number of square units in the surface area of a giantSwan 5 15 May 2008, 15:45
The function F of a number is the square of that number nfa1rhp 2 29 Jul 2007, 10:41
The function F of a number is the square of that number mandy 4 24 Aug 2005, 04:07
Display posts from previous: Sort by

Numbers-Squares root

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.