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If positive integer x is a multiple of 6 and positive

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Re: DS QUESTION [#permalink] New post 25 Oct 2010, 21:23
always making number properties look so simple Bunuel!
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xy multiple of 105 [#permalink] New post 04 Mar 2011, 23:57
82.) 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

Guys i tried this question twice my answer C but OA is different

as x is multiple of 6 x has minimum two factors 2,3 maximum can be any
as y is multiple of 14 y has minimum two factors 7,2 maximum can be any

Is xy multiple of 105 or is xy has minimum 5,3,7...

1) x is multiple of 9

so xy must have 2,3,3,3 ,7,2

but we need 5 also --------NS

2) y is multiple of 25
so xy must have 2,3,7,2,5,5
Sufficient

OK guys i got B. which is OA
Thanks


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Re: xy multiple of 105 [#permalink] New post 05 Mar 2011, 01:19
write this as follows:

x=6*a
y=14*b

where a, b integers

is xy is a multiple of 105? (or 35*3 or 3*7*5) ?

combine x*y=6*a*14*b= 2*3*2*7*a*b so to asnwer the question we must have at least a multiple of 3*5*7=105 out of which 3*7 exist . So the question reduces to whether either x or y have a 5 in itself or not.

1) not sufficient, we have been provided with data that x is a multipple of 9, but we do not have any additional information about y it may be or may not be a multiple of 5. we don't know exactly.

2) sufficient, becuase we are provided with the information that y is a multiple of 5 and we are provided with info that x and y are multiples of 6 and 14, it means that we have all sufficnet information to answer the question.

To check :
replace the y with any other number y=14*25*g , so g is any integer number becuase y is a multiple of both 14 and 25. and x is a multiple of 6 , so if combined you will have x*y=6*a*14*25*g=2100*a*g - this will produce a number which is a multiuple of 105. (2100 is divisible by 105).
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Re: DS QUESTION [#permalink] New post 06 Mar 2011, 19:37
x = 6k
y = 14l

xy = (kl) * 3 * 2 * 7 * 2

From 1, x = 18m

=> xy = (lm) 3^2 * 7 * 2 * 2, 5 is missing, so not sufficient

From 2, y = 25 * 14 n

=> xy = (kn) 5^2 * 2 * 7 * 3 * 2, which has 105 as a factor, so sufficient

Answer is B.
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Re: DS QUESTION   [#permalink] 06 Mar 2011, 19:37
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