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# Is positive integer x is a multiple of 6 and positive

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Manager
Joined: 28 Aug 2008
Posts: 98
Is positive integer x is a multiple of 6 and positive [#permalink]

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11 Sep 2008, 14:54
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Is positive integer x is a multiple of 6 and positive integer y is a multiple of 14. is xy a multiple of 105?

1) x is a multiple of 9

2) y is a multiple of 25
Director
Joined: 12 Jul 2008
Posts: 513
Schools: Wharton

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11 Sep 2008, 15:14
IgnitedMind wrote:
Is positive integer x is a multiple of 6 and positive integer y is a multiple of 14. is xy a multiple of 105?

1) x is a multiple of 9

2) y is a multiple of 25

Prime factorize 105
105 = 3*5*7

x = 2*3*m
y = 2*7*n
xy = 2*2*3*7*m*n

The questions asks if either x or y is also a multiple of 5.

(1) Insufficient

(2) Sufficient

Last edited by zonk on 11 Sep 2008, 22:15, edited 1 time in total.
Manager
Joined: 09 Jul 2007
Posts: 241

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11 Sep 2008, 17:16
IMO B.

105=3*5*7 => so we need a multiple of 5 to be sure..
Manager
Joined: 09 Jul 2007
Posts: 241

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11 Sep 2008, 18:12
1 says x is a multiple of 9=> it may or may not be a multiple of 5
VP
Joined: 17 Jun 2008
Posts: 1329

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11 Sep 2008, 18:42
IgnitedMind wrote:
Is positive integer x is a multiple of 6 and positive integer y is a multiple of 14. is xy a multiple of 105?

1) x is a multiple of 9

2) y is a multiple of 25

xy must have factors 7,5,3

(1)does not help INSUFFI since y can be multiple of 5 or not

(2)y is a multiple of 5 SUFFI 7,3 are already the factos of xy as per given condition

IMO B
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Re: DS - Multiples   [#permalink] 11 Sep 2008, 18:42
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