NehaPathak wrote:If x and y are positive integer then xy is a multiple of 8?
A)Least common divisor is 10.
B)Greatest common multiple is 100.
Please help me i really got confused......
A few problems with the wording here. Least common divisor? Greatest common multiple?
I'm assuming that the question should read:
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 multiple of x and y is 100
Let's find contradictory values for x and y to show that each statement alone is not sufficient.
Statement 1:
Consider 2 different cases that satisfy the condition that the greatest common divisor of x and y is 10
case a: x=10 and y=10, in which case xy is
not a multiple of 8
case b: x=10 and y=100, in which case xy
is a multiple of 8
Statement 1 is not sufficient
Statement 2:
Consider 2 different cases that satisfy the condition that the least common multiple of x and y is 100
case a: x=4 and y=25, in which case xy is
not a multiple of 8
case b: x=10 and y=100, in which case xy
is a multiple of 8
Statement 2 is not sufficient
Statements 1 & 2:
We have a nice rule that says "
[GCD of x and y][LCM of x and y] = xy"
So, from statements 1 and 2, we know that "
[10][100] = xy"
So, xy = 1000 and 1000
is a multiple of 8
Since we can now answer the target question with certainty, we can see that the answer is
C.
Cheers,
Brent
