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If positive integer x is a multiple of 6 and positive

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Manager
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If positive integer x is a multiple of 6 and positive [#permalink]

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New post 08 Jul 2009, 04:43
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If 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.

Any trick how to solve these kind of questions?

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Re: Divisible by 105? [#permalink]

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New post 08 Jul 2009, 05:08
Given x is a multiple of 6 and y is a multiple of 14
This means xy would be multiple of 42 (LCM of 6 and 14)

(1) x is a multiple of 9.
This means xy would be multiple of 126 (LCM of 6, 9, 14)
As 126 is not divisible by 105, we are not sure

(2) y is a multiple of 25.
This means xy would be multiple of 1050 (LCM of 6, 14, 25)
Hence xy divisible by 105

IMO B
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Manager
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Re: Divisible by 105? [#permalink]

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New post 08 Jul 2009, 05:18
ok thanks.
I dont know why I falter sometime on these type of questions.
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Re: Divisible by 105? [#permalink]

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New post 11 Jul 2009, 15:34
You don't need to think of LCM also,

Just consider the prime factors.

105 = 3*5*7

So if you know that xy has atleast 1 power each of 3,5, and 7, you can answer the ques

already x has 3 and y has 7 as factor, we only need to check for 5. Stmt 2 tells us that 5 will be there. so B
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Re: Divisible by 105? [#permalink]

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New post 12 Jul 2009, 08:29
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[quote="ankur55"]If 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.


x = 6m

y = 2*7*n

is 3*4*7*mn = 7*3*5z ie is 4mn = 5z , ie the question ask whether we can conclude if either of m or n has 5 as a factor??

from 1: m = 3b......insuff

from 2

n = 25k...............
answer is B
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Re: If positive integer x is a multiple of 6 and positive [#permalink]

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New post 16 Sep 2017, 01:16
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Re: If positive integer x is a multiple of 6 and positive   [#permalink] 16 Sep 2017, 01:16
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