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

Redeem

Perfect squares-No of factors.

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 1077
Joined: Mon Dec 13, 2010 1:44 am
Thanked: 118 times
Followed by:33 members
GMAT Score:710

Perfect squares-No of factors.

by bblast » Sun Jul 10, 2011 7:54 am
Cant recall a concept :

A perfect square has odd number of factors,

Is the opposite also true ? Any integer with odd number of factors is a perfect square ? I think yes.
Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

My gmat journey :
https://www.beatthegmat.com/710-bblast-s ... 90735.html
My take on the GMAT RC :
https://www.beatthegmat.com/ways-to-bbla ... 90808.html
How to prepare before your MBA:
https://www.youtube.com/watch?v=upz46D7 ... TWBZF14TKW_
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 905
Joined: Sun Sep 12, 2010 1:38 am
Thanked: 378 times
Followed by:123 members
GMAT Score:760

by Geva@EconomistGMAT » Sun Jul 10, 2011 8:28 am
bblast wrote:Cant recall a concept :

A perfect square has odd number of factors,

Is the opposite also true ? Any integer with odd number of factors is a perfect square ? I think yes.
This has the ring of truth (at least for positive integers). Generally speaking, factors come in "pairs" of two integers, the product of which reaches the original number.

For example,
6 can be split into two pairs of factors: 2 and 3, 1 and 6.
48 can be split into five pairs of factors: 1 and 48, 2 and 24, 3 and 16, 4 and 12, 6 and 8.

The only way an integer will have an odd number of factors is if one of the pairs is actually the same factor times itself: 36 splits into 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6. - which would make it a perfect square.
Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com
Top
User avatar
Legendary Member
Posts: 1077
Joined: Mon Dec 13, 2010 1:44 am
Thanked: 118 times
Followed by:33 members
GMAT Score:710

by bblast » Sun Jul 10, 2011 9:03 am
thank you Geva. You actually pointed the root of the theory behind odd no of factors.

So if i devise a DS question :

If x is a positive integer, is x a perfect square ?

1>x has odd no of factors.
2>no of factors of x = 3.


statement 1 is sufficient, as per discussion.
fancy statement 2 means x = square of a prime and hence, sufficient. sorry if the question is really lame. :)
Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

My gmat journey :
https://www.beatthegmat.com/710-bblast-s ... 90735.html
My take on the GMAT RC :
https://www.beatthegmat.com/ways-to-bbla ... 90808.html
How to prepare before your MBA:
https://www.youtube.com/watch?v=upz46D7 ... TWBZF14TKW_
Top
User avatar
GMAT Instructor
Posts: 905
Joined: Sun Sep 12, 2010 1:38 am
Thanked: 378 times
Followed by:123 members
GMAT Score:760

by Geva@EconomistGMAT » Mon Jul 11, 2011 12:43 am
bblast wrote:thank you Geva. You actually pointed the root of the theory behind odd no of factors.

So if i devise a DS question :

If x is a positive integer, is x a perfect square ?

1>x has odd no of factors.
2>no of factors of x = 3.


statement 1 is sufficient, as per discussion.
fancy statement 2 means x = square of a prime and hence, sufficient. sorry if the question is really lame. :)
Wouldn't dream of making fun even if I did think it was lame, but it's actually a good question testing a solid concept. Stat. (2) is a specific case of stat. (1) because 3 is odd; meaning that if we accept that (1) is sufficient, then (2) is also sufficient by default.
Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com
Top
User avatar
Legendary Member
Posts: 1077
Joined: Mon Dec 13, 2010 1:44 am
Thanked: 118 times
Followed by:33 members
GMAT Score:710

by bblast » Mon Jul 11, 2011 2:05 am
statement 2 would have been slightly better if it read

x is the square of a prime number. - in this way we are not directly stating an odd no of factors.

Anyways, the topic is clear. Thank you sir.
Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

My gmat journey :
https://www.beatthegmat.com/710-bblast-s ... 90735.html
My take on the GMAT RC :
https://www.beatthegmat.com/ways-to-bbla ... 90808.html
How to prepare before your MBA:
https://www.youtube.com/watch?v=upz46D7 ... TWBZF14TKW_
Top
Post new topic Post Reply
• Page 1 of 1