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by buckeye10 » Sun Mar 22, 2009 5:31 pm
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...
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Re: sets

by KICKGMATASS123 » Sun Mar 22, 2009 5:42 pm
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
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Re: sets

by KICKGMATASS123 » Sun Mar 22, 2009 5:43 pm
What's the source and OA for this question? Can u confirm?
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Re: sets

by buckeye10 » Sun Mar 22, 2009 6:02 pm
KICKGMATASS123 wrote: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?
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by scoobydooby » Sun Mar 22, 2009 11:34 pm
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
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by buckeye10 » Tue Mar 24, 2009 6:31 am
scoobydooby wrote: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
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Re: sets

by Vemuri » Tue Mar 24, 2009 9:57 am
buckeye10 wrote: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.
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