sets

[buckeye10]

Set X, Y, and Z consists positive multiples of 4, 5, and 6, respectively. If Set A is the intersection of X and Y, set B is the intersection of Y and Z, what is the least possible number of intersection of A and B?
A. 30
B. 60
C. 90
D. 120
E. 240

OA-B

Please help me solve this...

[KICKGMATASS123]

I think the Answer is C.

I didn't have a specific method to do this but i did i manually.

X = 4, 8, 12,16,....40,44, 60
Y= 5,10,15,20,25,...55,60
Z= 6,12, 18,24,30,...54, 60

As you can see 60 is incorporated in all the choices..
Therefore, the least possible # of integers of a and b is C

[KICKGMATASS123]

What's the source and OA for this question? Can u confirm?

[buckeye10]

What's the source and OA for this question? Can u confirm?

I am not sure about the source as I found this question in the material that was handed-off to me by a friend...

why do you say it is 90?

[scoobydooby]

B

Set A: intersection of X and Y=>elements of A must be multiples of both 4 and 5. the smallest number that is the multiple of both 4 and 5 is the lcm of 4 and 5, ie 20

Set B: intersection of Y and Z =>elements of B must be multiples of both 5 and 6. the smallest number that is the multiple of both 5 and 5 is the lcm of 4 and 6, ie 30

A intersection B: elements multiples of both 20 and 30, smallest multiple is lcm of 20 and 30 ie 60

in short A intersection B=> elements common to X, Y and Z.
so we need the smallest multiple of 4,5 and 6 or the lcm of 4,5 and 6 ie 60

[buckeye10]

B

Set A: intersection of X and Y=>elements of A must be multiples of both 4 and 5. the smallest number that is the multiple of both 4 and 5 is the lcm of 4 and 5, ie 20

Set B: intersection of Y and Z =>elements of B must be multiples of both 5 and 6. the smallest number that is the multiple of both 5 and 5 is the lcm of 4 and 6, ie 30

A intersection B: elements multiples of both 20 and 30, smallest multiple is lcm of 20 and 30 ie 60

in short A intersection B=> elements common to X, Y and Z.
so we need the smallest multiple of 4,5 and 6 or the lcm of 4,5 and 6 ie 60

Thanks ...makes sense

[Vemuri]

Set X, Y, and Z consists positive multiples of 4, 5, and 6, respectively. If Set A is the intersection of X and Y, set B is the intersection of Y and Z, what is the least possible number of intersection of A and B?
A. 30
B. 60
C. 90
D. 120
E. 240

OA-B

Please help me solve this...

The least common multiple of the 3 sets (4,5 &6) is 60. So, the answer should be B.