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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

Please explain your answer

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.

Answer A

(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

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.

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

Please explain your answer

Answer should be "C".

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

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

Please explain your answer

Answer should be "C".

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