pushkarajnjadhav wrote:

If a and b are positive integers, is 3*a^2*b divisible by 60?

1) a is divisible by 10.

2) b is divisible by 18.

Kudos if it helps.

Is \(3a^2b\) divisible by 60?

- We can change 60 into \(2^2*3*5\).

- Because we already have 3 in the numerator, so our job is to make sure whether a or b has \(2^2\) and 5 as its factor.

#1

- a divisible by 10 or \(2^5\). Since our numerator change a into \(a^2\), so we MUST HAVE \(2^2*5^2\) in our numerator.

- Whatever value of b, \(3a^2b\) divisible by 60.

SUFFICIENT.

#2

- b divisible by 18 or \(2*3^2\), Since we still need to have 5 as factor, we do not know whether a have this factor.

- Divisibility of \(3a^2b\) by 60 depends solely on the a value - which we don't know here.

INSUFFICIENT.

A.

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