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# Is X divisible by 15

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Manager
Joined: 02 Aug 2007
Posts: 222
Schools: Life
Is X divisible by 15 [#permalink]

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01 Feb 2009, 12:41
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Is X divisible by 15?

1. When X is divided by 10, the result is an integer
2. $$X^2$$ is a multiple of 30

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient
SVP
Joined: 07 Nov 2007
Posts: 1789
Location: New York
Re: Is X divisible by 15 [#permalink]

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01 Feb 2009, 13:05
x-ALI-x wrote:
Is X divisible by 15?

1. When X is divided by 10, the result is an integer
2. $$X^2$$ is a multiple of 30

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

1.

when X=10.. Is X divisible by 15? No
when X=30 .. is X divisible by 15? Yes
not sufficient

2. X^2 =30k

assume X = sqrt(30) (x can be fractional number) Is X divisible by 15? No
ASSUM X= 30 is X is divisble by 15? Yes
not sufficient

combined

combined
from statement1 it is clear that X must be integer.
X^2 =30k
For X to be integer K must be multiple of 30*l^2 (here l any integer number.1,2.. ..etc)

X --> multiple of 30

Is X divisible by 15> Yes.

sufficient

C
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Senior Manager
Joined: 26 May 2008
Posts: 426
Schools: Kellogg Class of 2012
Re: Is X divisible by 15 [#permalink]

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01 Feb 2009, 22:58
Agree with C

Cheers,
Unplugged
SVP
Joined: 04 May 2006
Posts: 1877
Schools: CBS, Kellogg
Re: Is X divisible by 15 [#permalink]

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01 Feb 2009, 23:27
x-ALI-x wrote:
Is X divisible by 15?

1. When X is divided by 10, the result is an integer
2. $$X^2$$ is a multiple of 30

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

B.

X^2 is a multiple of 30, X must be a multiple of 30 or X must contain 30, so X must be divisible by 15.
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Re: Is X divisible by 15 [#permalink]

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01 Feb 2009, 23:59
sondenso wrote:
x-ALI-x wrote:
Is X divisible by 15?

1. When X is divided by 10, the result is an integer
2. $$X^2$$ is a multiple of 30

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

B.

X^2 is a multiple of 30, X must be a multiple of 30 or X must contain 30, so X must be divisible by 15.

If x^2 is a multiple of 30, then x must contain at least a: 2, 3, 5 making B the correct choice. What's the OA?
SVP
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Posts: 1789
Location: New York
Re: Is X divisible by 15 [#permalink]

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02 Feb 2009, 00:02
chicagocubsrule wrote:
sondenso wrote:
x-ALI-x wrote:
Is X divisible by 15?

1. When X is divided by 10, the result is an integer
2. $$X^2$$ is a multiple of 30

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

B.

X^2 is a multiple of 30, X must be a multiple of 30 or X must contain 30, so X must be divisible by 15.

If x^2 is a multiple of 30, then x must contain at least a: 2, 3, 5 making B the correct choice. What's the OA?

X^2 =30k
assume X = sqrt(30) i.e X^2=30 (x can be fractional number) Is X divisible by 15? No
ASSUM X= 30 is X is divisble by 15? Yes
not sufficient
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Re: Is X divisible by 15 [#permalink]

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02 Feb 2009, 00:13
x2suresh wrote:
X^2 =30k
assume X = sqrt(30) i.e X^2=30 (x can be fractional number) Is X divisible by 15? No
ASSUM X= 30 is X is divisble by 15? Yes

Agree, X is NOT an integer!

silly mistake!
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Manager
Joined: 02 Aug 2007
Posts: 222
Schools: Life
Re: Is X divisible by 15 [#permalink]

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02 Feb 2009, 16:46
Great stuff, OA is C
Manager
Joined: 13 Jan 2009
Posts: 170
Re: Is X divisible by 15 [#permalink]

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02 Feb 2009, 20:44
Tricky question
Re: Is X divisible by 15   [#permalink] 02 Feb 2009, 20:44
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# Is X divisible by 15

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