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xyz21
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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



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Perfect square 06 Mar 2009, 08:15
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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.
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Perfect square 06 Mar 2009, 08:21
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xyz21
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
Show more

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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Perfect square 06 Mar 2009, 09:37
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xyz21
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..
Show more


N = 100 means that you would have a total of 300 digits (incld. 0s, 1s, 2s)
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Perfect square 06 Mar 2009, 09:39
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mrsmarthi
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.
Show more

hint: there is a way, the approach is very "aha!" type
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Perfect square 06 Mar 2009, 11:12
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xyz21
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xyz21
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)
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Thats not clear.
Can you again post it clearly?
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Perfect square 06 Mar 2009, 11:15
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Thats not clear.
Can you again post it clearly?
Show more

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

111000222, 210110220, 000221112 etc

Hope this helps
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Perfect square 06 Mar 2009, 12:40
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xyz21
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
Show more


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.
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Perfect square 06 Mar 2009, 14:02
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neeshpal
xyz21
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.
Show more

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



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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
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Thank you for understanding, and happy exploring!