N-> perfect square??
A) Not square. (perfect square has odd number of distinct factors)
Sufficient
B) sum of all distinct=even.
3:1,3 (even)
36:1,2,3,6,12,18,36 (even) insufficient
IMO A
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cans
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Cans!!
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Cans!!
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3 is not a perfect square.
cans wrote:N-> perfect square??
A) Not square. (perfect square has odd number of distinct factors)
Sufficient
B) sum of all distinct=even.
3:1,3 (even)
36:1,2,3,6,12,18,36 (even) insufficient
IMO A
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CANS, I THINK THE ANSWER SHOULD BE Dcans wrote:N-> perfect square??
A) Not square. (perfect square has odd number of distinct factors)
Sufficient
B) sum of all distinct=even.
3:1,3 (even)
36:1,2,3,6,12,18,36 (even) insufficient
IMO A
IN YOUR OPTION B YOU FORGET TO COUNT NUMBER 4 AND 9. THEY ARE ALSO THE FACTORS OF 36. THE SUM OF 4+9 IS ODD. THUS AS PER YOUR EXPLANATION. THIS WILL BE THE SUM ODD
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saketk
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two basic things to remember --jogi1984 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.
1) the numbers of distinct factors of 'PERFECT SQUARES' are ALWAYS Odd..
consider this -- 4 -- 2^2 , number of factor = (2+1) = 3
36 = 2^2*3^2 , number of factors = (2+1) (2+1) =9
2) the sum of all distinct factors of a number is calculated this way
I always use my favorite number - 28 (this is the 2nd PERFECT NUMBER, first being 6)
28 = (2^2)(7^1)
sum of factors = (1 + 2 + 4)(1 + 7) = (7)(8) = 56 [EVEN]
So, using these 2 points you can solve this question. and yeah the answer should be D
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rohit_gmat
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