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Q26: If positive integer x is a multiple of 6 and positive

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Q26: If positive integer x is a multiple of 6 and positive [#permalink] New post 01 Oct 2007, 06:01
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Q26:
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.
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Re: DS [#permalink] New post 01 Oct 2007, 06:47
Balvinder wrote:
Q26:
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.

I've got C.
St1: Insuf.
St.2: Insuf.
Together: Suffic. b/c Greatest Common Factor is 2x3^2x5^2x7=3150.
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Re: DS [#permalink] New post 01 Oct 2007, 06:51
Balvinder wrote:
Q26: 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.



B is suff. y is a multiple of 350. xy is a multiple of 1050. so enough..
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Re: DS [#permalink] New post 01 Oct 2007, 11:06
Balvinder wrote:
Q26:
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.


B.

Stat 1 tells us that x is a multiple of 18.

xy/105 = (18 * y)/105; since 105 is not a multiple of 18, answer depends on the value of y as well; insuff.

Stat 2 tells us that y is a multiple of 350.

xy/105 = (x * 350)/105 = (10 * x)/3; since x is a multiple of 6, it has to be divisible by 3. Therefore the whole expression is an integer. Suff.
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Re: DS [#permalink] New post 01 Oct 2007, 11:44
Balvinder wrote:
Q26:
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.



I guess it is D. yes or no questions are far too tricky. there are so many possibilities. even my posts made me doubt my answer.

x is multiple of 6 ---> 6, 12, 18, 24, 36...90...
y is multiple of 14---> 14, 28, ...70...14*25....14*75

so we need to find if x*y is multiple of 105=3*5*7

1. x is multiple of 9 so it can be 90 and is divisible by 6
then 90=2*3*3*5
so 90*14/105=(2*3*3*5)(2*7)/(3*5*7)
suff.

2. y is divisible by 25 and we know that it is also divisible by 14 so
14*75/105=(2*7)(3*5*5)/(3*5*7)
so suff.

am i nuts :)
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 [#permalink] New post 01 Oct 2007, 11:53
It is B. realised I got it wrong on the first statement, Yes or No quesiton are so tricky for me. does anyone have anything that has DS explanations in details. aproach and others. i had almost all my tests in YES or NO question wrong so far.

appreaciate the reply
  [#permalink] 01 Oct 2007, 11:53
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