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Is the positive integer N a perfect square?

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by saleem.kh » Mon Sep 12, 2011 1:17 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.

I am not able to interpret statement 2. Please help.

Answer: D
Source: MGMAT CAT
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Source: — Data Sufficiency |
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by shankar.ashwin » Mon Sep 12, 2011 1:47 am
Take any perfect square; say 4 or 9.

Factors of 4 are : 1,2 and 4.
Factors of 9: 1,3 and 9.

Notice than for all perfect squares; the distinct factors are odd (its true for all perfect squares).

Statement (2) says sum of distinct factor is even;
Try summing up factors of 4 and 9; we always get an odd number for perfect squares. (In this case 7 and 13)
Hence using any of the statements we can say the number is not a perfect square. Hence D
saleem.kh 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.

I am not able to interpret statement 2. Please help.

Answer: D
Source: MGMAT CAT
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by saleem.kh » Mon Sep 12, 2011 2:34 am
Thank you so much. Brief and easy to understand explanation.

Regards,
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by navami » Mon Sep 12, 2011 8:02 am
D

CONSIDER 15 - Factors 15, 5, 3, 1 = Sum EVEN
Number of FACTOR 4 ( EVEN)

CONSIDER 8 - FACTORS 8,4,2,1 = Sum EVEN
Number of FACTOR 4 ( EVEN)

Hence not conclusive
This time no looking back!!!
Navami
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