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jogi1984: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Wed Mar 30, 2011 7:36 am

by jogi1984 » Thu Sep 15, 2011 7:44 pm

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.

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Source: Beat The GMAT — Data Sufficiency | Thu Sep 15, 2011 7:44 pm

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Thu Sep 15, 2011 9:02 pm

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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jogi1984: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Wed Mar 30, 2011 7:36 am

by jogi1984 » Thu Sep 15, 2011 9:20 pm

The answer mentioned was D

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Fri Sep 16, 2011 9:10 am

36 1*36
2*18
3*12
4*9
6*6
The sum of distinct factors is odd, not even. D is correct

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Sep 16, 2011 9:32 am

I posted a solution here:

https://www.beatthegmat.com/mgmat-question-t81790.html

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HeintzC2: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Fri Jul 22, 2011 5:09 am; Thanked: 1 times

by HeintzC2 » Fri Sep 16, 2011 12:03 pm

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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[email protected]: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sun Jul 24, 2011 10:36 am

by [email protected] » Fri Sep 16, 2011 3:35 pm

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

CANS, I THINK THE ANSWER SHOULD BE D
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: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members; Thanked: 37 times

by saketk » Sun Sep 18, 2011 5:25 am

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.

two basic things to remember --

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: Master | Next Rank: 500 Posts; Posts: 158; Joined: Wed Jun 16, 2010 8:21 amFollowed by: 1 member; Thanked: 13 times

by rohit_gmat » Sun Sep 18, 2011 7:34 am

cans wrote:36:1,2,3,6,12,18,36 (even)

thts 7 numbers thr cans... thts odd

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