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
Rephrase - is xy/(2*2*2)... is this right?
Why is the answer (C)? If the LCM is 100, that means there are 2-2's and 2-5's in one prime box, and a 2 and a 5 in the other prime box.. right?
GMAT Forum
3 postsPage 1 of 1
- Guest
1) The greatest common divisor of x and y is 10
2*5
2) The least common multiple of x and y is 100
2*2*5*5
From (1), x and y each has 2 AND 5 as factors
From (2), x AND y have 2*2*5*5 as factors put together. Now, we know from (1) that 2*5 comes from common factors. So, that extra 2 has to come from either x OR y.
So, what do we have now? x has 2 and y has 2 as a factor. And either x or y has an extra 2.
xy is divisible by 8.
-givemeanid
2*5
2) The least common multiple of x and y is 100
2*2*5*5
From (1), x and y each has 2 AND 5 as factors
From (2), x AND y have 2*2*5*5 as factors put together. Now, we know from (1) that 2*5 comes from common factors. So, that extra 2 has to come from either x OR y.
So, what do we have now? x has 2 and y has 2 as a factor. And either x or y has an extra 2.
xy is divisible by 8.
-givemeanid
- StaceyKoprince
- ManhattanGMAT Staff
- Posts: 9360
- Joined: Wed Oct 19, 2005 9:05 am
- Location: Montreal
Your rephrase is good. Confusing one. This is a yes/no question, so a definitive yes or a definitive no will be sufficient.
As givemeanid said, statement 1 tells us that x and y each have a 2 and a 5 in their respective prime boxes. Don't have enough 2s. Insufficient.
Statement 2 tells us that there are a collective two 2s and two 5s, but we don't know which ones belong to x or y. Don't have enough 2s in any event. Insufficient.
(1) and (2) together. The factors of 100 are 2,2,5,5. From that, I can make 2, 4, 10, 20, 25, 50, and 100. Only 10, 20, 50, and 100 are divisible by 10, so ignore the others.
If I pick x=10, anything I pick for y would also have to be divisible by 10, so the LCM would be 10, not 100. So I can't pick 10 for one of the variables. The remaining possibilities: 20, 50, and 100.
20 = 2*2*5
50 = 2*5*5
100 = 2*2*5*5
I can't pick the same number for both x and y because then the GCD would no longer be 10. I have to pick two different numbers. And for the same reason, I can't pick 100. So x and y are 20 and 50 (in no particular order). That gives me the necessary three 2's to be divisible by 8.
As givemeanid said, statement 1 tells us that x and y each have a 2 and a 5 in their respective prime boxes. Don't have enough 2s. Insufficient.
Statement 2 tells us that there are a collective two 2s and two 5s, but we don't know which ones belong to x or y. Don't have enough 2s in any event. Insufficient.
(1) and (2) together. The factors of 100 are 2,2,5,5. From that, I can make 2, 4, 10, 20, 25, 50, and 100. Only 10, 20, 50, and 100 are divisible by 10, so ignore the others.
If I pick x=10, anything I pick for y would also have to be divisible by 10, so the LCM would be 10, not 100. So I can't pick 10 for one of the variables. The remaining possibilities: 20, 50, and 100.
20 = 2*2*5
50 = 2*5*5
100 = 2*2*5*5
I can't pick the same number for both x and y because then the GCD would no longer be 10. I have to pick two different numbers. And for the same reason, I can't pick 100. So x and y are 20 and 50 (in no particular order). That gives me the necessary three 2's to be divisible by 8.
Stacey Koprince
Instructor
Director, Content & Curriculum
ManhattanPrep
Instructor
Director, Content & Curriculum
ManhattanPrep
3 posts Page 1 of 1