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

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Bunuel
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If a and b are positive integers, is 3a^2*b divisible by 60? [#permalink] New post   20 Dec 2015, 06:00
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A
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68% (01:30) correct 32% (01:34) wrong based on 334 sessions
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If a and b are positive integers, is 3a^2*b divisible by 60?

(1) a is divisible by 10.

(2) b is divisible by 18.
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A
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Re: If a and b are positive integers, is 3a^2*b divisible by 60? [#permalink] New post   20 Dec 2015, 06:25
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Bunuel wrote:
If a and b are positive integers, is 3a^2*b divisible by 60?

(1) a is divisible by 10.

(2) b is divisible by 18.


Question: \(\frac{3b*a^2}{60}\)
(1) \(\frac{3b*(10k)^2}{60}\) = \(\frac{b*(10k)^2}{20}\) a is a multiple of 10 and >0 means even if it's only equal to 10 it's divisible by 20 in the last expression. Sufficient
(2) Clearly not sufficient
Answer A
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Re: If a and b are positive integers, is 3a^2*b divisible by 60? [#permalink] New post   30 Jan 2016, 14:53
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Some people may choose c because they forget to take into account that the question stem has a^2 in it.
So, if a is divisible by 10 = 5*2.
a^2 will have at least two 5s and two 2s.

Thats what the question stem is indirectly asking. Does a^2b have two 2s and one 5.

Thus, 1 is sufficient.

Hence, the answer is A.
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Re: If a and b are positive integers, is 3a^2*b divisible by 60? [#permalink] New post   16 Mar 2016, 05:32
For a moment i was about to mark C
then realised that 10 *10 which is the least value of A^2 will be divisible by 20
hence choose A
nice question
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Re: If a and b are positive integers, is 3*a^2*b [#permalink] New post   05 Sep 2017, 07:59
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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Re: If a and b are positive integers, is 3*a^2*b [#permalink]
05 Sep 2017, 07:59
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Bunuel
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