NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 13:33 It is currently 26 Apr 2024, 13:33
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Which of the following is not a perfect square

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
virtualanimosity
Manager
Manager
Joined: 19 Aug 2009
Posts: 72
Own Kudos [?]: 961 [6]
Given Kudos: 46
Send PM
Which of the following is not a perfect square [#permalink] New post   04 Nov 2009, 00:22
1
Kudos
5
Bookmarks
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

33% (01:42) correct 67% (01:22) wrong based on 122 sessions
Hide Show timer Statistics
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
ShowHide Answer
Official Answer
D
User avatar
B
yangsta8
Senior Manager
Senior Manager
Joined: 31 Aug 2009
Posts: 290
Own Kudos [?]: 1041 [2]
Given Kudos: 20
Location: Sydney, Australia
 Q49  V41
Send PM
Re: Which of the following is not a perfect square [#permalink] New post   04 Nov 2009, 00:44
1
Kudos
1
Bookmarks
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 
User avatar
virtualanimosity
Manager
Manager
Joined: 19 Aug 2009
Posts: 72
Own Kudos [?]: 961 [0]
Given Kudos: 46
Send PM
Re: Which of the following is not a perfect square [#permalink] New post   04 Nov 2009, 00:52
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 
User avatar
B
yangsta8
Senior Manager
Senior Manager
Joined: 31 Aug 2009
Posts: 290
Own Kudos [?]: 1041 [0]
Given Kudos: 20
Location: Sydney, Australia
 Q49  V41
Send PM
Re: Which of the following is not a perfect square [#permalink] New post   04 Nov 2009, 01:31
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.
User avatar
shalva
Tuck School Moderator
Joined: 20 Aug 2009
Posts: 203
Own Kudos [?]: 330 [0]
Given Kudos: 69
Location: Tbilisi, Georgia
Schools:Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)
 Q50  V47
Send PM
Re: Which of the following is not a perfect square [#permalink] New post   04 Nov 2009, 01:32
Quote:
A perfect square will have exactly an even number of each of its factors.


A simple point, but worth remembering, Kudos!
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619229 [4]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: Which of the following is not a perfect square [#permalink] New post   04 Nov 2009, 23:57
1
Kudos
3
Bookmarks
Expert Reply
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.
User avatar
shalva
Tuck School Moderator
Joined: 20 Aug 2009
Posts: 203
Own Kudos [?]: 330 [0]
Given Kudos: 69
Location: Tbilisi, Georgia
Schools:Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)
 Q50  V47
Send PM
Re: Which of the following is not a perfect square [#permalink] New post   05 Nov 2009, 00:07
Quote:
A perfect square will have exactly an even number of each of its factors.


yeah, it holds only for prime factors
User avatar
shalva
Tuck School Moderator
Joined: 20 Aug 2009
Posts: 203
Own Kudos [?]: 330 [0]
Given Kudos: 69
Location: Tbilisi, Georgia
Schools:Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)
 Q50  V47
Send PM
Re: Which of the following is not a perfect square [#permalink] New post   05 Nov 2009, 00:15
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 . . .
User avatar
B
yangsta8
Senior Manager
Senior Manager
Joined: 31 Aug 2009
Posts: 290
Own Kudos [?]: 1041 [0]
Given Kudos: 20
Location: Sydney, Australia
 Q49  V41
Send PM
Re: Which of the following is not a perfect square [#permalink] New post   05 Nov 2009, 22:02
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 :)
User avatar
nonameee
Senior Manager
Senior Manager
Joined: 23 Apr 2010
Posts: 476
Own Kudos [?]: 353 [0]
Given Kudos: 7
Send PM
Re: Which of the following is not a perfect square [#permalink] New post   02 Jan 2011, 08:38
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.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619229 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: Which of the following is not a perfect square [#permalink] New post   02 Jan 2011, 08:47
Expert Reply
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.
User avatar
nonameee
Senior Manager
Senior Manager
Joined: 23 Apr 2010
Posts: 476
Own Kudos [?]: 353 [0]
Given Kudos: 7
Send PM
Re: Which of the following is not a perfect square [#permalink] New post   02 Jan 2011, 08:55
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?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619229 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: Which of the following is not a perfect square [#permalink] New post   02 Jan 2011, 09:04
Expert Reply
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.
User avatar
nonameee
Senior Manager
Senior Manager
Joined: 23 Apr 2010
Posts: 476
Own Kudos [?]: 353 [0]
Given Kudos: 7
Send PM
Re: Which of the following is not a perfect square [#permalink] New post   02 Jan 2011, 09:07
OK. Thanks. I guess I have to study it.
avatar
B
maxim7777
Intern
Intern
Joined: 24 Mar 2017
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 55
Send PM
Re: Which of the following is not a perfect square [#permalink] New post   09 Aug 2017, 12:21
Bunuel wrote:
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.


Could you please prove these rules?

I know only that the total number of factors (of a perfect square) is odd. Could you clarify the others?

Thanks in advance.
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6277 [0]
Given Kudos: 1646
Send PM
Re: Which of the following is not a perfect square [#permalink] New post   26 Jun 2018, 18:18
Expert Reply
virtualanimosity wrote:
Which of the following is not a perfect square

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


We know that a perfect square must end with 0, 1, 4, 5, 6, or 9, so we can see choice 2 is not a perfect square.

Now let’s check choice 1. Since 310^2 = 96,100 and 320^2 = 102,400, then, if 100,856 is a perfect square, it must be the square of either 314 or 316 since either one of these integers will produce a units digit of 6 when squared. However, since 314^2 = 98,596 and 316^2 = 99,856, we see that choice 1 is a not a perfect square, either.

Since both choices 1 and 2 are not perfect squares, we will conclude that the correct answer must be choice 4 (even though we have not verified that choice 3 is not a perfect square).

Answer: 4
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32689
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: Which of the following is not a perfect square [#permalink] New post   09 Sep 2023, 11:51
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: Which of the following is not a perfect square [#permalink]
09 Sep 2023, 11:51
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions