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divisible by 7?

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by grandh01 » Wed Sep 19, 2012 12:28 pm
How many of the three different positive integers
a,b, and c are divisible by 7?

1) The product of abc is divisible by 3, but only
c is divisible by 21.
2) Each of the three positive integers is divisible
by 3, but only c is divisible by 21.

OA IS B
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by Anurag@Gurome » Wed Sep 19, 2012 11:18 pm
consider 1st option:
The product of abc is divisible by 3, but only c is divisible by 21.
The product of abc is divisible by 3 => atleast one of the a,b,c is a multiple of 3.
but only C is divisible by 21 => c is a multiple of 3 and 7.
for a and b not to be divisible by 21 (7*3) they should not be a multiple of 7 or 3 or both.
there is no information whether a and b is a multiple of 7 or not.
a = 7, b = 3
a = 7, b = 7
a = 10, b = 8
all these satisfy the above conditions.
so we can`t answer with A alone.

consider 2nd option:
Each of the three positive integers is divisible by 3, but only c is divisible by 21.
a = 3k
b = 3m
c = 21n
for a and b not to be divisible by 21 (7*3) they should not be a multiple of 7.
so only C is a multiple of 7.
hence, it can be answered by B alone
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