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# Is a positive integer k is divisible by 3?

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Math Expert
Joined: 02 Sep 2009
Posts: 52143
Is a positive integer k is divisible by 3?  [#permalink]

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04 Dec 2018, 02:35
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Difficulty:

35% (medium)

Question Stats:

68% (00:53) correct 32% (00:46) wrong based on 121 sessions

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Is a positive integer k is divisible by 3?

(1) $$\sqrt{k}$$ is divisible by 9

(2) k^2 is divisible by 3

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Re: Is a positive integer k is divisible by 3?  [#permalink]

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04 Dec 2018, 02:47
1
1

1) This means that k is divisible by 81 ==> it is definitely divisible by 3!
2) this is only true for square numbers (9, 36, 81) whose roots (3, 6, 9) are divisible by 3 themselves. Yes!
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Re: Is a positive integer k is divisible by 3?  [#permalink]

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24 Dec 2018, 00:31
Bunuel wrote:
Is a positive integer k is divisible by 3?

(1) $$\sqrt{k}$$ is divisible by 9

(2) k^2 is divisible by 3

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Re: Is a positive integer k is divisible by 3?  [#permalink]

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29 Dec 2018, 05:33
The only catch in this question is to remember that k is a positive integer such as 1 or 2 or 3 or so on...

Let's look at the statements:

Statement 1: If $$\sqrt{k}$$ is divisible by 9, naturally k will be divisible by 3 also since $$3^2$$=9

Statement 2: Now, here's where the catch comes into play. If $$k^2$$ is divisible by 3 and k is a positive integer, k will definitely be divisible by 3 too. Note here, that we cannot take k to be a value such as $$\sqrt{3}$$, this is because k is a positive integer.

So, clearly, both statements are sufficient and answer is D
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Re: Is a positive integer k is divisible by 3? &nbs [#permalink] 29 Dec 2018, 05:33
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