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Is the integer k divisible by 4 ? (1) 8k is divisible by 16. (2) 9k is

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r019h
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Is the integer k divisible by 4 ? (1) 8k is divisible by 16. (2) 9k is [#permalink] New post  Updated on: 06 Jun 2019, 05:42
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Is the integer k divisible by 4 ?

(1) 8k is divisible by 16.
(2) 9k is divisible by 12.
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Originally posted by r019h on 30 Oct 2007, 20:27.
Last edited by Bunuel on 06 Jun 2019, 05:42, edited 3 times in total.
Edited the question and added the OA
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Bunuel
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Is the integer k divisible by 4 ? (1) 8k is divisible by 16. (2) 9k is [#permalink] New post  15 Mar 2015, 22:37
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Is the integer k divisible by 4?

(1) 8k is divisible by 16 --> \(\frac{8k}{16}=\frac{k}{2}=integer\) --> \(k\) is a multiple of 2, but it may or may not be a multiple of 4. Not sufficient.

(2) 9k is divisible by 12 --> \(\frac{9k}{12}=\frac{3k}{4}=integer\) --> in order \(\frac{3k}{4}\) to be an integer \(k\) must be a multiple of 4. Sufficient.

Answer: B
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Re: Is the integer k divisible by 4 ? (1) 8k is divisible by 16. (2) 9k is [#permalink] New post  26 Jun 2016, 22:23
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r019h wrote:
Is the integer k divisible by 4?

(1) 8k is divisible by 16
(2) 9k is divisible by 12


Statement 1: 8k is divisible by 16
In this case, k should have a power of 2, hence it has to be divisible by 2, but we are not sure if it will be divisible by 4
INSUFFICIENT

Statement 2: 9k is divisible by 12
For 9k to be divisible by 12, k should have a power of 3 and a power of 4. Hence it has to be a multiple of 4
SUFFICIENT

Correct Option: B
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Re: Is the integer k divisible by 4 ? (1) 8k is divisible by 16. (2) 9k is [#permalink] New post  14 Oct 2020, 18:23
Is the integer k divisible by 4 ?

(1) 8k is divisible by 16.

8k/16 = k/2. We are not certain whether k can be divisible by another 2. Not Sufficient.

(2) 9k is divisible by 12.

9k/12 = 3k/4. We know that k must be divisible by 4 because the constant 3 is reduced to its lowest factor, and we know the first expression is an integer.
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Re: Is the integer k divisible by 4 ? (1) 8k is divisible by 16. (2) 9k is [#permalink] New post  09 Aug 2022, 15:59
Is there any more posts/problems that talk more about remainders and divisors like this one? definitely struggling on the concept as a whole. thanks!
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Re: Is the integer k divisible by 4 ? (1) 8k is divisible by 16. (2) 9k is [#permalink] New post  10 Aug 2022, 02:22
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keykers1 wrote:
Is there any more posts/problems that talk more about remainders and divisors like this one? definitely struggling on the concept as a whole. thanks!


6. Remainders



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Re: Is the integer k divisible by 4 ? (1) 8k is divisible by 16. (2) 9k is [#permalink]
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