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

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ashiima
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If n is an integer, is n/15 an integer? [#permalink] New post  29 Nov 2011, 19:02
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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


DS37602.01
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Re: If n is an integer, is n/15 an integer? [#permalink] New post  17 Jun 2017, 19:36
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Shan30 wrote:
If n is an integers, is n/15 an integer?
(1) 3n/15 is an integer. (2) 8n/15 is an integer

Can anyone please explain me why B is the answer. TIA


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)

Answer (B)...

Hope its clear now.

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Re: If n is an integer, is n/15 an integer? [#permalink] New post  30 Nov 2011, 00:37
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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] New post  30 Nov 2011, 12:10
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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] New post  30 Nov 2011, 12:12
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] New post  12 Dec 2011, 12:47
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] New post  13 Dec 2011, 16:36
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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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Re: If n is an integer, is n/15 an integer? [#permalink] New post  30 Jul 2020, 07:55
ashiima wrote:
If n is an integer, is n/15 an integer?

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


DS37602.01


(1) 3n/15 can be divisible by 3 and the answer will be n/5.
If n/5, it cannot be clearly stated that n/15 is an integer using the reference that n/5.

(2) 8n/15.
If 8n is divisible by 15 then n must be divisible by 15.

Hence, B
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Re: If n is an integer, is n/15 an integer? [#permalink] New post  12 Nov 2020, 10:18
If n is an integer, is \(\frac{n}{15}\) an integer?

(1) 3n/15 is an integer.

If 3n/15 is an integer, then n/5 is an integer. This piece of information tells us that is a multiple of 5. Therefore we can't say for sure whether n/15 is an integer. INSUFFICIENT.

(2) 8n/15 is an integer

If 8n/15 is an integer, then we can say with certainty that 8n is a multiple of 15. If 8n is a multiple of 15, we can say n is a multiple of 15. Why? 8 does not share any common factors with 15. Within n, we can guarantee that it has the factors needed. SUFFICIENT.

Answer is B.
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Re: If n is an integer, is n/15 an integer? [#permalink] New post  19 Mar 2021, 20:58
1) 3n/15 is basically the same as n/5, telling us that n is divisible by 5. but not about 15, INSUFFICIENT.
2) 8n/15 is an integer -> since 8 and 15 have no factor in common, thus n must be divisible by 15, So SUFFICIENT
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Re: If n is an integer, is n/15 an integer? [#permalink] New post  06 Jun 2022, 07:14
Condition B.

(8*n/15) is an integer, if this has to be an integer then (n/15) has to be an integer.

Hence B is correct.

Hope it helps !
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Re: If n is an integer, is n/15 an integer? [#permalink]
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