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# Is Integer k divisible by 18?

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Intern
Joined: 26 Jun 2015
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Is Integer k divisible by 18?  [#permalink]

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04 Jul 2017, 19:06
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55% (hard)

Question Stats:

59% (01:14) correct 41% (01:15) wrong based on 112 sessions

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Is Integer k divisible by 18?

(1) 2k is divisible by 9
(2) 9k is divisible by 2
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Joined: 02 Aug 2009
Posts: 7757
Re: Is Integer k divisible by 18?  [#permalink]

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04 Jul 2017, 19:39
hotcool030 wrote:
Is Integer K divisible by 18?
1) 2k is divisible by 9
2) 9k is divisible by 2

Please give Kudos if you like.

Let's see the statements...

1) 2k is div by 9..
It tells us that k is div by 9
K is 9... Divisible by 9 but not by 18.
K is 18... Div by both 9 and 18..
Insufficient

2)9k is div by 2..
It tells us that k is div by 2..
Insufficient..

Combined..
K is div by 2 and 9..
Hence k is divisible by 18..
Sufficient
C
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Re: Is Integer k divisible by 18?  [#permalink]

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04 Jul 2017, 19:49
We can also do in this way.

1) 2k is divisible by 9. Lets take 2k = 9 then k = 4.5. but k must be an integer. so take 2k=18, then k = 9  which is not divisible by 18.

when 2k=36, k = 18 which is divisible by 18.

So statement 1 is not sufficient.

2) 9k is divisible by 2 which means 9k is even

so, k must be even which means k can be.

But 2 is not divisible by 18.

Same time 18 is also even, 18 is divisible by 18. So statement 2 is also not sufficient.

Combining we can say, k must be even and divisible by 9. so obviously as it includes 2, 2 x (multipliers of 9) always will be divided by 18.

Please give Kudos if you like.

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Re: Is Integer k divisible by 18?  [#permalink]

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17 Jul 2017, 22:32
hotcool030 wrote:
Is Integer k divisible by 18?

(1) 2k is divisible by 9
(2) 9k is divisible by 2

We could just use prime factorization to make things easier

St 1

2 x k / 3 x 3 - we can conclude K is a multiple of 9 - so

k/9 though we could just have 9 which would be too small or we could have 3^4 which using prime factorization we can see

3 x 3 x 3 x 3 / 3 x 3 x 2 would not be an integer insuff

St 2
3 x 3 x K/ 2 - therefore K must be a multiple of 2 or K/2 but we could have many values such as 4, which is too small, or 36 which would actually fit- but we can't be certain it's 36 with the info

St 1 & St 2

LCM(9,4) = 3 x 3 x 2 x 2

3 x 3 x 2 x 2/ 3 x 3 x 3 = some integer

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Re: Is Integer k divisible by 18?  [#permalink]

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30 Jul 2017, 17:29
hotcool030 wrote:
Is Integer k divisible by 18?

(1) 2k is divisible by 9
(2) 9k is divisible by 2

We need to determine whether k/18 = integer.

Statement One Alone:

2k is divisible by 9.

Since 2k/9 = integer and 2 is relatively prime with 9, meaning that they share no prime factors, k must be a multiple of 9. However, since all multiples of 9 are not necessarily multiples of 18, statement one alone is not sufficient to answer the question.

Statement Two Alone:

9k is divisible by 2.

Since 9k/2 = integer and 9 is relatively prime with 2, k must be a multiple of 2. However, since all multiples of 2 are not necessarily multiples of 18, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

From both statements, we see that k is a multiple of 2 and 9, and thus it's a multiple of 18.

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Re: Is Integer k divisible by 18?  [#permalink]

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24 Oct 2018, 14:53
hotcool030 wrote:
Is Integer k divisible by 18?

(1) 2k is divisible by 9
(2) 9k is divisible by 2

2k/9 = integer

Means k could be 9,18,27,36 etc.. 9/18 not divisible

18/18 divisible. So insufficient.

9k/2 = integer

Means k could be 2,4,6,8,10.... 18 etc.. we get two different answers. Insufficient.

Combined we get that k must be a multiple of 2 and 9 so it must be a multiple of 18.

Sufficient.

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Re: Is Integer k divisible by 18?   [#permalink] 24 Oct 2018, 14:53
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