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# If n is an integer, is n/15 an integer?

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If n is an integer, is n/15 an integer?  [#permalink]

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29 Nov 2011, 20:02
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Difficulty:

25% (medium)

Question Stats:

73% (00:51) correct 27% (01:13) wrong based on 178 sessions

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If n is an integer, is n/15 an integer?

(1) 3n/15 is an integer.
(2) 8n/15 is an integer
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Re: If n is an integer, is n/15 an integer?  [#permalink]

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30 Nov 2011, 01:37
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1
1. 3n/15 = n/5
We know that n is divisible by 5 . Therefore, one of n's prime factors is 5.
We do not know whether or not n is also divisible by 3.
Insufficient

2. 8n/15 = is also an integer
For 8n/15 to be an integer, n must be divisible by 15.
Sufficient

B.
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Re: If n is an integer, is n/15 an integer?  [#permalink]

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30 Nov 2011, 13:10
I know i got it wrong but can someone please tell me what is wrong with this approach?

Stat 1) 3n/15 is an integer.
=> 3*(n/15) is an integer.
Wont this be only possible if n/15 is an integer?
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Re: If n is an integer, is n/15 an integer?  [#permalink]

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30 Nov 2011, 13:12
iamgame wrote:
I know i got it wrong but can someone please tell me what is wrong with this approach?

Stat 1) 3n/15 is an integer.
=> 3*(n/15) is an integer.
Wont this be only possible if n/15 is an integer?

Ah. I correct myself...this is also possible for n=5. in that case n/15 is not an integer, given 3n/15 is an integer.
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Re: If n is an integer, is n/15 an integer?  [#permalink]

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12 Dec 2011, 13:47
B

stmt1 : 3n/15 is an integer. the multiples of 15 are 3 and 5 and we are given a 3 in 3n. so we know that n at least has a multiple of 5 but we do not know if it contains a multiple of 3. insuff

stmt 2: 8n/15 is an integer. Using the same logic above we need a 3 and a 5. 8 is 2^3 do we know that n has the multiples of 3 and 5 so suff
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Re: If n is an integer, is n/15 an integer?  [#permalink]

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13 Dec 2011, 17:36
I agree with B.
Question rephrased as is n divisible by 3 and 5?

(1) 3n/15 is integer. Tells us n is divisible by 5 but is insufficient to tell us if n is divisible by 3. INSUFF.
(2) 8n/15 is integer. This is only possible if n is multiple of 15 as 8 does not have any prime factors same as 15. SUFF.
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If n is an integers, is n/15 an integer?  [#permalink]

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Updated on: 18 Jun 2017, 02:30
If n is an integers, is n/15 an integer?

(1) 3n/15 is an integer.
(2) 8n/15 is an integer

Originally posted by Prashanth3007 on 17 Jun 2017, 20:25.
Last edited by Bunuel on 18 Jun 2017, 02:30, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If n is an integers, is n/15 an integer?  [#permalink]

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17 Jun 2017, 20:36
Shan30 wrote:
If n is an integers, is n/15 an integer?
(1) 3n/15 is an integer. (2) 8n/15 is an integer

To find out is $$\frac{n}{15}$$ an integer.

(1) $$\frac{3n}{15}$$ is an integer

Lets take n = 5

$$\frac{3*5}{15}$$ = 1 ----- Integer.

$$\frac{n}{15} = \frac{5}{15} = \frac{1}{3}$$ ---------- (Not an integer)

Lets take n = 15

$$\frac{3*15}{15} = 3$$

$$\frac{n}{15} = \frac{15}{15} = 1$$ --------- (Integer)

I has multiple values therefore I is Not Sufficient.

(2) $$\frac{8n}{15}$$ is an integer

Given $$\frac{8n}{15}$$ is an integer.

Factors of 8 are 1,2,4,8.

15 is not a factor of 8. Hence 15 has to be a factor of n.

Therefore $$\frac{n}{15}$$ is an integer. ------------ (II is Sufficient)

Hope its clear now.

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Re: If n is an integer, is n/15 an integer?  [#permalink]

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18 Jun 2017, 02:33
Shan30 wrote:
If n is an integers, is n/15 an integer?

(1) 3n/15 is an integer.
(2) 8n/15 is an integer

Merging topics.

Please follow the rules when posting a question. Pay attention to rules 1 and 3. Thank you.
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Re: If n is an integer, is n/15 an integer?  [#permalink]

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24 Aug 2018, 01:26
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