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# a is divisible by 60 . b is not divisible by 21. Is a*b

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a is divisible by 60 . b is not divisible by 21. Is a*b [#permalink]  19 Sep 2003, 04:34
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a is divisible by 60 . b is not divisible by 21. Is a*b divisible by
48?
a. a*b is divisible by 540
b. a^2 * b is divisible by 36

after you get your answer, check my work and tell me whether i am right?

1. a*b is divisible by 540

a*b = 540 s

540 not a mutliple of 48 and so a*b not divisible by 48...
sufficient

2. a^2 * b is divisible by 36

a^2 * b = 36 q ... equation 1
we know a = 60 n ...equation 2

Divide 1 by 2 a* b = 36/60 qn
a* b = 6/10 qn
if qn= 80 or any other multiple of 80, yes ...but otherwise no
so insufficient

so A by itself is sufficient

thanks
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Quote:
a*b is divisible by 540

a*b = 540 s

540 not a mutliple of 48 and so a*b not divisible by 48...
sufficient

I don't agree with this. Say a*b = 8640(=540*16). Here a=60 & b = 144. Meets all the conditions. and is divisible by 48. but if a*b = 540, its not divisible by 48. So Not sufficient.

Quote:
a^2 * b is divisible by 36

a^2 * b = 36 q ... equation 1
we know a = 60 n ...equation 2

Divide 1 by 2 a* b = 36/60 qn
a* b = 6/10 qn
if qn= 80 or any other multiple of 80, yes ...but otherwise no
so insufficient

Agree with this. So 2 alone is insufficient.

Now, combine 1 & 2 -

Say a* b is 8640(a=60 and b=144) here all conditions are satisfied and is divisible by 48.
Now, say a* b is 540(a=60, b= 9) , here also all the conditions are satisfied but not divisible by 48.
So Insufficient.
Hence E.
Pls. let me know if I'm missing anything.
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