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Is x the square of an integer? (1) x = 12k+6 , where k is a

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Manager
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Kudos [?]: 162 [0], given: 10

Is x the square of an integer? (1) x = 12k+6 , where k is a [#permalink]  24 Apr 2010, 22:25
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Is xthe square of an integer?

(1) x = 12k+6, where kis a positive integer

(2) x =3q+9, where q is a positive integer

this is one of manhattan archive questions.
i think there should be some better explanation.
looking for that explanation thanks
Manager
Joined: 27 Dec 2009
Posts: 178
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Kudos [?]: 10 [3] , given: 3

Re: Is x the square of an integer [#permalink]  25 Apr 2010, 00:30
3
KUDOS
From Stmt 1 ,
x= 6(2k+1) where k = positive integer.
2k + 1 is always odd.
To be a square of an integer, 2k+1 has to be a multiple of 6 and that is not possible.
So, x can't be square of an integer.

Stmt 1 sufficient.

From Stmt 2,
x= 3(q+3)
putting different values of q can have 2 different results.
Example put q=1, x =12 ... not a square of an integer
put q=24 , x = 81 ... square of an integer 9.

Stmt 2 ,Not sufficient.

Manager
Joined: 13 Dec 2009
Posts: 132
Followers: 5

Kudos [?]: 162 [0], given: 10

Re: Is x the square of an integer [#permalink]  25 Apr 2010, 01:01
msand wrote:
From Stmt 1 ,
x= 6(2k+1) where k = positive integer.
2k + 1 is always odd.
To be a square of an integer, 2k+1 has to be a multiple of 6 and that is not possible.
So, x can't be square of an integer.

Stmt 1 sufficient.

From Stmt 2,
x= 3(q+3)
putting different values of q can have 2 different results.
Example put q=1, x =12 ... not a square of an integer
put q=24 , x = 81 ... square of an integer 9.

Stmt 2 ,Not sufficient.

good explanation thanks you..OA
[Reveal] Spoiler:
A
Manager
Joined: 27 Dec 2009
Posts: 178
Followers: 2

Kudos [?]: 10 [0], given: 3

Re: Is x the square of an integer [#permalink]  25 Apr 2010, 01:15
einstein10 wrote:
msand wrote:
From Stmt 1 ,
x= 6(2k+1) where k = positive integer.
2k + 1 is always odd.
To be a square of an integer, 2k+1 has to be a multiple of 6 and that is not possible.
So, x can't be square of an integer.

Stmt 1 sufficient.

From Stmt 2,
x= 3(q+3)
putting different values of q can have 2 different results.
Example put q=1, x =12 ... not a square of an integer
put q=24 , x = 81 ... square of an integer 9.

Stmt 2 ,Not sufficient.

good explanation thanks you..OA
[Reveal] Spoiler:
A

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Re: Is x the square of an integer   [#permalink] 25 Apr 2010, 01:15
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