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Divisiblty

by goyalsau » Tue Oct 05, 2010 6:35 pm
If a*b*c divisible by 24 ?

(1) a,b,and c are consecutive integers
(2) a*b is divisible by 12
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by Rahul@gurome » Tue Oct 05, 2010 7:07 pm
Solution:
If a = 1, b = 2 and c= 3, abc = 6 is not divisible by 24.
But if a = 2, b= 3 and c= 4, then abc = 24 is divisible by 24.
Since nothing definite can be said, (1) alone is not sufficient.
Next consider (2) alone.
If let a = 3, b= 4 and c = 7, so abc = 84 which is not divisible by 24 and ab=12 is divisible by 12.
Next let a = 6, b= 4 and c = 1, so abc = 24 is divisible by 24 and ab = 24 is divisible by 12.
Again nothing definite can be said and so (2) alone is not sufficient.

Now combine both the statements together and check.
Let a = 3, b = 4 and c = 5. Here a, b and c are consecutive and ab is div. by 12 but abc = 60 is not divisible by 24.
Next let a = 8, b = 9 and c = 10. Here again a, b and c are consecutive, ab = 72 and abc = 720 is div. by 24.
Again nothing definite can be said from (1) and (2) combined.

The correct answer is (E).
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