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24 Dec 2018, 13:58
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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
(1) B is a multiple of 6
(2) B is divisible by 30
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24 Dec 2018, 20:13
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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?
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
D
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
D
30 Aug 2020, 08:02
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