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# Perfect square

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Manager
Joined: 26 Dec 2008
Posts: 57
Schools: Booth (Admit R1), Sloan (Ding R1), Tuck (R1)

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05 Mar 2009, 22:50
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
Senior Manager
Joined: 30 Nov 2008
Posts: 483
Schools: Fuqua

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06 Mar 2009, 07:15
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.
SVP
Joined: 29 Aug 2007
Posts: 2467

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06 Mar 2009, 07:21
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..
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Manager
Joined: 26 Dec 2008
Posts: 57
Schools: Booth (Admit R1), Sloan (Ding R1), Tuck (R1)

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06 Mar 2009, 08:37
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)
Manager
Joined: 26 Dec 2008
Posts: 57
Schools: Booth (Admit R1), Sloan (Ding R1), Tuck (R1)

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06 Mar 2009, 08:39
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
SVP
Joined: 29 Aug 2007
Posts: 2467

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06 Mar 2009, 10:12
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?
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Manager
Joined: 26 Dec 2008
Posts: 57
Schools: Booth (Admit R1), Sloan (Ding R1), Tuck (R1)

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06 Mar 2009, 10:15
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
Senior Manager
Joined: 24 Feb 2007
Posts: 262
Location: nj

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06 Mar 2009, 11:40
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.
Manager
Joined: 26 Dec 2008
Posts: 57
Schools: Booth (Admit R1), Sloan (Ding R1), Tuck (R1)

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06 Mar 2009, 13:02
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
Re: Perfect square   [#permalink] 06 Mar 2009, 13:02
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# Perfect square

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