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integer properties

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Manager
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Affiliations: Beta Gamma Sigma
Joined: 14 Aug 2008
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Kudos [?]: 75 [0], given: 3

Schools: Harvard, Penn, Maryland
integer properties [#permalink]

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New post 24 May 2009, 21:02
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If n and y are positive integers, and 450y=n^3 , which of the following is an integer?

I. y / ( 3 * 2^2 * 5 )
II. y / ( 3^2 * 2 * 5 )
III. y / ( 3 * 2 * 5^2 )

A) None
B) I only
C) II only
D) III only
E) I,II, and III

Kudos [?]: 75 [0], given: 3

Senior Manager
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Joined: 08 Jan 2009
Posts: 325

Kudos [?]: 180 [0], given: 5

Re: integer properties [#permalink]

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New post 24 May 2009, 23:07
Soln:
( 2 * 3^2 * 5 ^2 ) * y = n^3

So y should be y = 2 ^2 * 5 * 3

So clearly see only 1 will satisfy

So B

Kudos [?]: 180 [0], given: 5

Manager
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Posts: 213

Kudos [?]: 30 [0], given: 17

Location: India
Re: integer properties [#permalink]

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New post 25 May 2009, 01:08
Only multiplying by (3 * 2^2 * 5) can make the expression in left hand side as cube, which would be equal to n^3. Hence the answer is B

Kudos [?]: 30 [0], given: 17

Manager
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Joined: 28 Jan 2004
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Kudos [?]: 29 [0], given: 4

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Re: integer properties [#permalink]

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New post 25 May 2009, 22:22
Am I missing something seriously !!!!!!

450 = 2*3*3*5*5

Optio 1 becomes
450/2*2*3*5 = (2*3*3*5*5)/(2*2*3*5) = 7.5 (so wrong)

Option 2 becomes
(2*3*3*5*5)/(2*3*3*5) = 10 (correct)

Option 3 becomes
(2*3*3*5*5)/(2*3*5*5) = 3 (correct)

Why the answer is b then ?

Kudos [?]: 29 [0], given: 4

Manager
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Joined: 28 Jan 2004
Posts: 202

Kudos [?]: 29 [0], given: 4

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Re: integer properties [#permalink]

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New post 25 May 2009, 22:25
I think i got what karthi4 is saying..........the ans. is b

Kudos [?]: 29 [0], given: 4

Manager
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Affiliations: Beta Gamma Sigma
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Posts: 209

Kudos [?]: 75 [0], given: 3

Schools: Harvard, Penn, Maryland
Re: integer properties [#permalink]

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New post 26 May 2009, 15:08
yeah I guess that is it, It was GMATPrep so I didn't get an explanation.

450 = 3^2 * 5^2 * 2

so the only value for y that results in a cube is 3 * 5 * 2^2,
because ( 3 * 3 * 5 * 5 * 2 ) * ( 3 * 5 * 2 * 2 ) = ( 3^3 * 5^3 * 2^3 ) or 15^3.
(450 being 15 squared)

so if y = 3 * 5 * 2^2

then

(3 * 5 * 2^2) / (2^2 * 3 * 5) = 1

1 is an integer, so b is the answer.

One of the harder PS questions I guess

Kudos [?]: 75 [0], given: 3

Re: integer properties   [#permalink] 26 May 2009, 15:08
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