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

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Math Expert
Joined: 02 Sep 2009
Posts: 59588
If a and b are positive integers, is 3a^2*b divisible by 60?  [#permalink]

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20 Dec 2015, 06:00
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35% (medium)

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70% (01:29) correct 30% (01:31) wrong based on 259 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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Re: If a and b are positive integers, is 3a^2*b divisible by 60?  [#permalink]

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20 Dec 2015, 06:25
1
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]

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30 Jan 2016, 14:53
1
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]

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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]

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

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