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If A and B are positive integers and A^3 is divisible by 24

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If A and B are positive integers and A^3 is divisible by 24  [#permalink]

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24 Dec 2018, 12:58
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If A and B are positive integers and $$A^3$$ is divisible by 24, then is $$AB^2$$ a multiple of 216?

(1) B is a multiple of 6

(2) B is divisible by 30

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Re: If A and B are positive integers and A^3 is divisible by 24  [#permalink]

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24 Dec 2018, 19:13
If A and B are positive integers and $$A^3$$ is divisible by 24, then is $$AB^2$$ a multiple of 216?

If A^3 is divisible by 24, that is $$2^3*3$$, so A will be divisible by 2*3=6..
Now we are looking for AB^2 is divisible by 216, that is $$2^3*3^3$$..
Since A is divisible by atleast a 6, we are looking if B^2 is divisible by 216/6=36=6^2, or is B divisible by 6...

(1) B is a multiple of 6
Yes sufficient..

(2) B is divisible by 30
Again B is divisible by 6..
Yes sufficient

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If A and B are positive integers and A^3 is divisible by 24 &nbs [#permalink] 24 Dec 2018, 19:13
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