BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is the positive integer N a perfect square?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Sat Jul 10, 2010 1:44 am
Location: Kuwait
Thanked: 23 times
Followed by:1 members

Is the positive integer N a perfect square?

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
Without hard work, nothing grows but weeds.
Top
Source: — Data Sufficiency |
Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 am
Thanked: 230 times
Followed by:21 members

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
Top
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Sat Jul 10, 2010 1:44 am
Location: Kuwait
Thanked: 23 times
Followed by:1 members

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

Regards,
Without hard work, nothing grows but weeds.
Top
User avatar
Legendary Member
Posts: 540
Joined: Sat Dec 20, 2008 7:24 pm
Thanked: 37 times
Followed by:6 members

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
Top
Post new topic Post Reply
• Page 1 of 1