Hi,
Can you help me see if my reasoning is correct?
If X and Y are positive integers, is XY a multiple of 8?
1. The GCF of x and y is 10
2. The LCM of X and Y is 100
I used the MGMAT Venn Diagram approach for divisibility problems, which basically means putting the GCF into the shared area and the LCM is like (Group 1's factors + group 2's factors-both's factor). So for this problem, statement 1 tells me that I should 2 and 5 as common factors into the common area for 2 circles (X and Y).
Statement 2 tells me that besides the 2 and 5 in the shared common circle, there is another 2 and 5 in either of the circle not shared by the common area. So there will be only two 2's in all three sections, which means XY is not a multiple of 8 (need at least three 2's). But C makes it sufficient.
If my reasoning sounds obscure, please show me how you would approach this problem.
Thanks!
Can you help me see if my reasoning is correct?
If X and Y are positive integers, is XY a multiple of 8?
1. The GCF of x and y is 10
2. The LCM of X and Y is 100
I used the MGMAT Venn Diagram approach for divisibility problems, which basically means putting the GCF into the shared area and the LCM is like (Group 1's factors + group 2's factors-both's factor). So for this problem, statement 1 tells me that I should 2 and 5 as common factors into the common area for 2 circles (X and Y).
Statement 2 tells me that besides the 2 and 5 in the shared common circle, there is another 2 and 5 in either of the circle not shared by the common area. So there will be only two 2's in all three sections, which means XY is not a multiple of 8 (need at least three 2's). But C makes it sufficient.
If my reasoning sounds obscure, please show me how you would approach this problem.
Thanks!
