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by mj41 » Mon Mar 29, 2010 8:23 am
Is the positive integer N a perfect square?

(1) The number of distinct factors of N is even.
(2) The sum of all distinct factors of N is even.


Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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by akahuja143 » Mon Mar 29, 2010 9:28 am
IMO D

Perfect square always has odd number of factors
for instance look at 4 = 1 ,2, 4 or say 36 1, 2, 3,4, 6, 9, 12,18, 36

And even the sum of factors would also be add try adding any of the above
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by gmatmachoman » Mon Mar 29, 2010 9:53 am
mj41 wrote:Is the positive integer N a perfect square?

(1) The number of distinct factors of N is even.
(2) The sum of all distinct factors of N is even.


Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
Good question .
Good wrk @akahuja!

Both sts gives a definite Answer that N is not a perfect Square!
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by mj41 » Mon Mar 29, 2010 11:30 am
Good Job OA is D
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by eaakbari » Mon Mar 29, 2010 11:10 pm
Statement 1
Every perfect square x^2 will have 2 factors x and then 1. Even if x is broken down further it will always be odd
Hence Suff


Statement 2
x^2 will have factors x and x and 1
which equals 2x+1 which will always be odd
Hence suff

Answer D
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by thephoenix » Tue Mar 30, 2010 2:48 am
mj41 wrote:Is the positive integer N a perfect square?

(1) The number of distinct factors of N is even.
(2) The sum of all distinct factors of N is even.
A perfect sqaure ALWAYS has an ODD number of factors, whose sum is ALWAYS ODD.

A perfect sqaure ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors.

Using the above facts, you can conclude that both statements are sufficient to answer the question.
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