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If n = 3k, is k an integer?

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If n = 3k, is k an integer? [#permalink]

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New post 27 Jul 2015, 23:44
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Re: If n = 3k, is k an integer? [#permalink]

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New post 28 Jul 2015, 02:30
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Bunuel wrote:
If n = 3k, is k an integer?

(1) n is an integer.

(2) n/6 is an integer.

Kudos for a corrector solution.



IMO : B

n= 3k

St 1: n is an integer
k = n/3
for n = 1,2 -> k is fraction
for n=3,6 --> k is integer
not suff

St 2: n/6 is an integer.
n=3k
3k/6 = integer
k/2 = integer
k = 2* integer
Thus k = integer * integer will definitely be an integer
Suff
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Re: If n = 3k, is k an integer? [#permalink]

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New post 28 Jul 2015, 03:30
Bunuel wrote:
If n = 3k, is k an integer?

(1) n is an integer.

(2) n/6 is an integer.

Kudos for a corrector solution.


Question redefined : Is n a Multiple of 3?

Statement 1: n is an integer.

now n may or may NOT be a multiple of 3 despite being an Integer, Hence,
NOT SUFFICIENT

Statement 2: n/6 is an integer.

n must be a multiple of 6 and consequently a multiple of 3 as well because 6=2*3, Hence,
SUFFICIENT

Answer: option B
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Re: If n = 3k, is k an integer? [#permalink]

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New post 29 Jul 2015, 21:18
Hi All,

This question can be solved by TESTing VALUES.

We're told that N = 3K. We're asked if K is an integer. This is a YES/NO question.

Fact 1: N is an INTEGER.

IF...
N = 1
1 = 3K... So 1/3 = K and the answer to the question is NO.

IF...
N = 3
3 = 3K.. So 1 = K and the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: N/6 is an INTEGER

This tells us that N is a multiple of 6

IF...
N = 6
6 = 3K... So 2 = K and the answer to the question is YES.

IF...
N = 12
12 = 3K... So 4 = K and the answer to the question is YES.

IF...
N = 0
0 = 3K... So 0 = K and the answer to the question is YES.

Since every multiple of 6 is ALSO a multiple of 3, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer:
[Reveal] Spoiler:
B


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Re: If n = 3k, is k an integer? [#permalink]

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New post 06 Feb 2018, 20:01
1)
N=3k
K can be 1/3 or any integer
A insufficient
2)
N =3k
N/6=3k/6
N/6 =I
I=k/2
K =integer

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Re: If n = 3k, is k an integer? [#permalink]

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New post 06 Feb 2018, 21:59
Bunuel wrote:
If n = 3k, is k an integer?

(1) n is an integer.

(2) n/6 is an integer.

Kudos for a corrector solution.


n = 3k also means that k = n/3. So k will be an integer if n is divisible by 3.

(1) n is an integer, but no information about its divisibility by 3. Not sufficient.

(2) n is divisible by 6, then it must be divisible by 3 also (because 3 is a factor of 6). So Sufficient to answer as YES to the question asked.

Hence B answer
Re: If n = 3k, is k an integer?   [#permalink] 06 Feb 2018, 21:59
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