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# If x and y are positive integers, is xy a multiple of 8? (1)

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SVP
Joined: 21 Jul 2006
Posts: 1508
If x and y are positive integers, is xy a multiple of 8? (1) [#permalink]

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11 Dec 2007, 02:47
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If x and y are positive integers, is xy a multiple of 8?

(1) The greatest common divisor of x and y is 10

(2) The least common myltiple of x and y is 100

Director
Joined: 09 Aug 2006
Posts: 754
Re: DS: GCM & LCM [#permalink]

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11 Dec 2007, 02:59
tarek99 wrote:
If x and y are positive integers, is xy a multiple of 8?

(1) The greatest common divisor of x and y is 10

(2) The least common myltiple of x and y is 100

I think the answer is B.

Stat 1:
If x = 10 y = 10 then xy is not a multiple of 8
If x = 20 y = 30 then xy is a multiple of 8
Insuff.

Stat 2:
If LCM is 100 then the integers can be expressed as 100x and 100y. 100x * 100y is always divisible by 8. Sufficient.
Intern
Joined: 25 Nov 2007
Posts: 38
Re: DS: GCM & LCM [#permalink]

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11 Dec 2007, 09:35
GK_Gmat wrote:
tarek99 wrote:
If x and y are positive integers, is xy a multiple of 8?

(1) The greatest common divisor of x and y is 10

(2) The least common myltiple of x and y is 100

I think the answer is B.

Stat 1:
If x = 10 y = 10 then xy is not a multiple of 8
If x = 20 y = 30 then xy is a multiple of 8
Insuff.

Stat 2:
If LCM is 100 then the integers can be expressed as 100x and 100y. 100x * 100y is always divisible by 8. Sufficient.

(1) The greatest common divisor of x and y is 10

Meaning 10*a =x and 10*b=y . Meaning that xy = 100 ab , Neither a nor b can be even, because that will increase the GCD above 10. and multiplication of two odd numbers ab cannot be divisble by 8, 100ab is not divisible by 8 either ... Sufficient.

(2) The least common myltiple of x and y is 100 .
if x=5 and y =100 , XY is not mulitple of 8
if x=20 and y =100 XY is multiple of 8

Whats the OA
Manager
Joined: 29 Jul 2007
Posts: 181

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11 Dec 2007, 17:23
C.

If x, y >0; does XY/8 = int?

only if XY has 3 2's as 8 = 2^3

I. GCF is 10 or 2*5. GCF takes only factors that are common to both numbers. So all we know is that there are 2 2's for sure. There may be more, but we don't know.

II. LCD is 100 or 5^2*2^2. LCD takes the higher power of each factor. So all we know is that one of the two numbers has 2 2's in it. We are not sure if there is a 3rd 2 in the mix or not.

I and II taken together is sufficient. By I, we know that both numbers have a 2 in their factorization. By II, we know that one of the numbers (or both) have 2 2's (or 2^2) in their factorization. So taken together, we know for sure that there are at least 3 2's when X*Y.
Director
Joined: 03 Sep 2006
Posts: 859
Re: DS: GCM & LCM [#permalink]

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11 Dec 2007, 17:48
tarek99 wrote:
If x and y are positive integers, is xy a multiple of 8?

(1) The greatest common divisor of x and y is 10

(2) The least common myltiple of x and y is 100

From(i); GCD is 10, numbers can be any combination of multiples of 10, for example; 10&20, 10&30. One of the is multiple of 8 and other isn't.

From (ii); LCM is 100, again it can be any combination of numbers such as ;
5&100, 20&100. One of the is multiple of 8 and other isn't.

LCM*GCF=product of numbers

http://www.gmatclub.com/forum/t56958
Retired Moderator
Joined: 18 Jul 2008
Posts: 959
Re: DS: GCM & LCM [#permalink]

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19 Jan 2009, 14:31
LCM*GCF=product of numbers[/size]

Can someone explain the above?

LM wrote:
tarek99 wrote:
If x and y are positive integers, is xy a multiple of 8?

(1) The greatest common divisor of x and y is 10

(2) The least common myltiple of x and y is 100

From(i); GCD is 10, numbers can be any combination of multiples of 10, for example; 10&20, 10&30. One of the is multiple of 8 and other isn't.

From (ii); LCM is 100, again it can be any combination of numbers such as ;
5&100, 20&100. One of the is multiple of 8 and other isn't.

LCM*GCF=product of numbers

http://www.gmatclub.com/forum/t56958
Director
Joined: 29 Aug 2005
Posts: 854
Re: DS: GCM & LCM [#permalink]

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19 Jan 2009, 14:46
The simplest way is to test with actual numbers
LCM of 8 and 10 is 40
GCD is 2
8*10=2*40
Manager
Joined: 25 Aug 2007
Posts: 115
Location: NYC Baby!!!
Re: DS: GCM & LCM [#permalink]

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19 Jan 2009, 15:32
Wow it is C

yes LCF*GCD= product which you can then divide by 8

10*100= 1000/8 = 125
Intern
Joined: 19 Jan 2009
Posts: 17
Re: DS: GCM & LCM [#permalink]

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19 Jan 2009, 22:29
stmnt 1 : in sufficient
stmnt 2 : insufficient

combined :

lcm . gcd = x.y

1000 = xy

and 1000 is multiple of 8 .

Re: DS: GCM & LCM   [#permalink] 19 Jan 2009, 22:29
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