NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 06:13 It is currently 26 Apr 2024, 06:13
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

Perfect square

User avatar
xyz21
Intern
Intern
Joined: 26 Dec 2008
Posts: 29
Own Kudos [?]: 25 [0]
Given Kudos: 0
Concentration: General Mgmt, Strategy, Entrepreneurship
Schools:Booth (Admit R1), Sloan (Ding R1), Tuck (R1)
 Q48  V38
Send PM
Perfect square [#permalink] New post   05 Mar 2009, 23:50
a number is written with N 0s, N 1s and N 2s (e.g. two 0s, two 1s, and two 2s)

is the number perfect square?

1) N = 100
2) N = 20



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
mrsmarthi
Senior Manager
Senior Manager
Joined: 30 Nov 2008
Posts: 335
Own Kudos [?]: 1825 [0]
Given Kudos: 15
Concentration: Finance, General Management
Schools:Fuqua
 Q49  V29
Send PM
Re: Perfect square [#permalink] New post   06 Mar 2009, 08:15
With the count of each digits, we cannot ensure what the number is and hence there is no way we can say whether a number of Perfect square or not. (atleast that I am aware of).

So if I have to answer the question, I will pick E.

As a side note: - Here is one rule that we can make a note.

A number is said to be a perfect square, if the number when expressed as the product of the prime number, all the prime factors should have exponents which are even.
User avatar
GMAT TIGER
VP
VP
Joined: 29 Aug 2007
Posts: 1021
Own Kudos [?]: 1726 [0]
Given Kudos: 19
Send PM
Re: Perfect square [#permalink] New post   06 Mar 2009, 08:21
xyz21 wrote:
a number is written with N 0s, N 1s and N 2s (e.g. two 0s, two 1s, and two 2s)

is the number perfect square?

1) N = 100
2) N = 20


1: If N = 100, the number could be: 10,000, 10,011, 10,022, .......... 10,099.
10,000 is a perfect square but rest are not.

Not suff..

2: If N = 20, the number could be: 2,000, 2,011, 2,022, .......... 2,099.
In this case none is a perfect square.

So suff..

Hence B if I correctly understood the querstion..
User avatar
xyz21
Intern
Intern
Joined: 26 Dec 2008
Posts: 29
Own Kudos [?]: 25 [0]
Given Kudos: 0
Concentration: General Mgmt, Strategy, Entrepreneurship
Schools:Booth (Admit R1), Sloan (Ding R1), Tuck (R1)
 Q48  V38
Send PM
Re: Perfect square [#permalink] New post   06 Mar 2009, 09:37
GMAT TIGER wrote:
xyz21 wrote:
a number is written with N 0s, N 1s and N 2s (e.g. two 0s, two 1s, and two 2s)

is the number perfect square?

1) N = 100
2) N = 20


1: If N = 100, the number could be: 10,000, 10,011, 10,022, .......... 10,099.
10,000 is a perfect square but rest are not.

Not suff..

2: If N = 20, the number could be: 2,000, 2,011, 2,022, .......... 2,099.
In this case none is a perfect square.

So suff..

Hence B if I correctly understood the querstion..



N = 100 means that you would have a total of 300 digits (incld. 0s, 1s, 2s)
User avatar
xyz21
Intern
Intern
Joined: 26 Dec 2008
Posts: 29
Own Kudos [?]: 25 [0]
Given Kudos: 0
Concentration: General Mgmt, Strategy, Entrepreneurship
Schools:Booth (Admit R1), Sloan (Ding R1), Tuck (R1)
 Q48  V38
Send PM
Re: Perfect square [#permalink] New post   06 Mar 2009, 09:39
mrsmarthi wrote:
With the count of each digits, we cannot ensure what the number is and hence there is no way we can say whether a number of Perfect square or not. (atleast that I am aware of).

So if I have to answer the question, I will pick E.

As a side note: - Here is one rule that we can make a note.

A number is said to be a perfect square, if the number when expressed as the product of the prime number, all the prime factors should have exponents which are even.


hint: there is a way, the approach is very "aha!" type
User avatar
GMAT TIGER
VP
VP
Joined: 29 Aug 2007
Posts: 1021
Own Kudos [?]: 1726 [0]
Given Kudos: 19
Send PM
Re: Perfect square [#permalink] New post   06 Mar 2009, 11:12
xyz21 wrote:
GMAT TIGER wrote:
xyz21 wrote:
a number is written with N 0s, N 1s and N 2s (e.g. two 0s, two 1s, and two 2s)

is the number perfect square?

1) N = 100
2) N = 20


1: If N = 100, the number could be: 10,000, 10,011, 10,022, .......... 10,099.
10,000 is a perfect square but rest are not.

Not suff..

2: If N = 20, the number could be: 2,000, 2,011, 2,022, .......... 2,099.
In this case none is a perfect square.

So suff..

Hence B if I correctly understood the querstion..



N = 100 means that you would have a total of 300 digits (incld. 0s, 1s, 2s)


Thats not clear.
Can you again post it clearly?
User avatar
xyz21
Intern
Intern
Joined: 26 Dec 2008
Posts: 29
Own Kudos [?]: 25 [0]
Given Kudos: 0
Concentration: General Mgmt, Strategy, Entrepreneurship
Schools:Booth (Admit R1), Sloan (Ding R1), Tuck (R1)
 Q48  V38
Send PM
Re: Perfect square [#permalink] New post   06 Mar 2009, 11:15
GMAT TIGER wrote:

Thats not clear.
Can you again post it clearly?


To save typing really long numbers, let's say if N = 3 then the possible numbers are:

111000222, 210110220, 000221112 etc

Hope this helps
User avatar
neeshpal
Manager
Manager
Joined: 24 Feb 2007
Posts: 97
Own Kudos [?]: 1490 [1]
Given Kudos: 2
Location: nj
Send PM
Re: Perfect square [#permalink] New post   06 Mar 2009, 12:40
1
Kudos
xyz21 wrote:
a number is written with N 0s, N 1s and N 2s (e.g. two 0s, two 1s, and two 2s)

is the number perfect square?

1) N = 100
2) N = 20



IMO answer is D . i could be wrong here. heres my finding.

because if you add digits of any perfect square it comes up to either 1 or 4 or 9 or 7.

and here if we find the sum of these digits

1) 100*0 + 100*1 + 100*2 = 300 ---> 3 so , no
2) 20*0 + 20*1 + 20*2 = 60 ----> 6 so , no

with both choices we can tell that a number that is formed by any combination of digits in 1) and 2) will not be a perfect square.
User avatar
xyz21
Intern
Intern
Joined: 26 Dec 2008
Posts: 29
Own Kudos [?]: 25 [0]
Given Kudos: 0
Concentration: General Mgmt, Strategy, Entrepreneurship
Schools:Booth (Admit R1), Sloan (Ding R1), Tuck (R1)
 Q48  V38
Send PM
Re: Perfect square [#permalink] New post   06 Mar 2009, 14:02
neeshpal wrote:
xyz21 wrote:
a number is written with N 0s, N 1s and N 2s (e.g. two 0s, two 1s, and two 2s)

is the number perfect square?

1) N = 100
2) N = 20



IMO answer is D . i could be wrong here. heres my finding.

because if you add digits of any perfect square it comes up to either 1 or 4 or 9 or 7.

and here if we find the sum of these digits

1) 100*0 + 100*1 + 100*2 = 300 ---> 3 so , no
2) 20*0 + 20*1 + 20*2 = 60 ----> 6 so , no

with both choices we can tell that a number that is formed by any combination of digits in 1) and 2) will not be a perfect square.


Bravo! You nailed it!

1) sum of digits = 300 --> number is divisible by 3 but not by 3^2 --> not a perfect square
2) same

The answer is in fact D. I loves this problem because it looks so complicated on its face but requires a very fundamental principle.

+1 for you



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: Perfect square [#permalink]
06 Mar 2009, 14:02
Moderator:
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