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# Is the integer n a multiple of 15?

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Is the integer n a multiple of 15? [#permalink]

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28 Apr 2010, 07:59
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Is the integer n a multiple of 15?

(1) n is a multiple of 20
(2) n+6 is a multiple of 3.
[Reveal] Spoiler: OA
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Re: Is the integer n a multiple of 15? [#permalink]

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28 Apr 2010, 08:10
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zz0vlb wrote:
Is the integer n a multiple of 15?

(1) n is a multiple of 20
(2) n+6 is a multiple of 3.

[Reveal] Spoiler:
C

can someone give an example of this problem?

Statement 1: if n = 40 then answer is no, if n = 60 , answer is yes.
Thus not sufficient.

Statement 2: n+6 is a multiple of 3 => n + 6 = 3m => n = 3m -6

=> n = 3( m - 2) , now if 7 = 3, its true , if m = 4 not true.

thus not sufficient.

If you combine both , n is multiple of both 3 and 5(as multiple of 20)
=> n is multiple of 15.

Thus C
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Last edited by gurpreetsingh on 28 Apr 2010, 11:03, edited 1 time in total.
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Re: Is the integer n a multiple of 15? (1) n is a multiple of 20 [#permalink]

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12 Aug 2012, 06:55
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vishu1414 wrote:

1.n is a multiple of 20 ...I understand its not Sufficient

2.n+6 is a multiple of 3

considering n a multiple of 15 ,all possible multiples of 15 and +6 is always divisible by 3 ..So it should be sufficient ?
Not sure why OA- C ?

It should be the other way around: any multiple of 15 plus 6 is a multiple of 3, but it's possible $$n+6$$ to be a multiple of 3 so that $$n$$ not to be a multiple of 15. Consider $$n=3$$.

Is the integer n a multiple of 15?

(1) n is a multiple of 20. If $$n=20$$, then the answer is NO but if $$n=60$$, then the answer is YES. Not sufficient.
From this statement though notice that $$n$$ must be a multiple of 5.

(2) n+6 is a multiple of 3. If $$n=3$$, then the answer is NO but if $$n=15$$, then the answer is YES. Not sufficient.
From this statement though notice that $$n$$ must be a multiple of 3, since $$n+6=3q$$ --> $$n=3(q-2)$$.

(1)+(2) From above we have that $$n$$ is a multiple of both 5 and 3, thus it must be a multiple of 5*3=15. Sufficient.

Hope it's clear.
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Re: Is the integer n a multiple of 15? [#permalink]

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28 Apr 2010, 11:00
Gurpreetsingh Thank you so much.

Last edited by zz0vlb on 28 Apr 2010, 11:07, edited 1 time in total.
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Re: Is the integer n a multiple of 15? [#permalink]

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28 Apr 2010, 11:04
zz0vlb wrote:
Gurpreetsingh Thanks. but n + 6 = 3m => n = 3m +6 should be n= 3m-6 => 3(m-2)

yes right, that's typo error. I have updated my post.
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Re: Is the integer n a multiple of 15? (1) n is a multiple of 20 [#permalink]

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12 Aug 2012, 04:45

1.n is a multiple of 20 ...I understand its not Sufficient

2.n+6 is a multiple of 3

considering n a multiple of 15 ,all possible multiples of 15 and +6 is always divisible by 3 ..So it should be sufficient ?
Not sure why OA- C ?
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Re: Is the integer n a multiple of 15? [#permalink]

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16 Aug 2012, 22:32
1 statement tels us that there are at least 2*2*5 as prime factors in n, but we are not sure that 3*5 are among the prime factors - so insufficient.
2 statement indicates that n is a multiple of 3 so it could be 0, 3, 15 ... - not sufficient
1+2 statements, here we see that n is a number which has 2*2*5 and 3 in its primes, so it must be a multiple of 15!
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Re: Is the integer n a multiple of 15? [#permalink]

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09 Sep 2014, 05:40
For a n to be multiple of 15, it has to be divisible its prime factors 3 and 5.

Statement 1 - n is multiple of 20 - divisible by prime factors 2 and 5. Not know about 3. Hence not sufficient.
Statement 2 - n+6 multiple of 3 - meaning n is divisible by 3. Not know about 5. Hence not sufficient.

Combing both. n is divisible by 2, 3, 5. Hence n will be multiple of 15.
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Is the integer n a multiple of 15? [#permalink]

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09 Sep 2014, 06:44
The question asks whether n is a multiple of 15.

1) n is a multiple of 20. Clearly insufficient. However, notice that this means that 5,2,2 are prime factors of n. Thus, for n to be a multiple of 15, it also has to be a multiple of 3, to multiply with the 5 to get 15. We're looking to see if n is a multiple of 3.

2) n+6 is a multiple of 3. Notice this only says that n is a multiple of 3; if n+6 is a multiple of 3, then n+3 and n are also multiples of 3. On its own, it's insufficient, but it's precisely the information we were looking for from number 1.

Together, we have the information we need. Answer: C
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Re: Is the integer n a multiple of 15? [#permalink]

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Re: Is the integer n a multiple of 15? [#permalink]

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09 Feb 2017, 11:05
"Is the integer n a multiple of 15?" is really asking "Does n have both 3 and 5 as factors?" or alternately "Is n a multiple of both 3 and 5?"

Statement (1) tells you that n is a multiple of 20. You want to know if n has 3 and 5 as factors. Well, the 5 is taken care of, because 5 is a factor of 20. But what about the 3? It's not clear.

You can also illustrate this by picking numbers that fit the condition of St (1). Examples would be n = 20, 40, 60, 80, etc
All of those have 5 as a factor, but not all of them have 3 as a factor. INSUFFICIENT.

Statement (2) says n+6 is a multiple of 3. The tricky thing here is to realize that 6 is a multiple of 3, and thus if n+6 is a multiple of 3, n itself must also be a multiple of 3.

Again, you can test numbers to verify this. n could equal 0, 3, 6, 9, etc. All those values of n are already multiples of 3.

So St (2) really just says "n is a multiple of 3."

Unfortunately, we don't know about the 5, so we can't say if n is a multiple of 15. INSUFFICIENT.

Together, (1) tells us n has 5 as a factor and (2) tells us n has 3 as a factor. Therefore, since n has both 5 and 3 as factors, it must also have 3*5 = 15 as a factor. SUFFICIENT

Ans: C
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Re: Is the integer n a multiple of 15? [#permalink]

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09 Feb 2017, 11:06
"Is the integer n a multiple of 15?" is really asking "Does n have both 3 and 5 as factors?" or alternately "Is n a multiple of both 3 and 5?"

Statement (1) tells you that n is a multiple of 20. You want to know if n has 3 and 5 as factors. Well, the 5 is taken care of, because 5 is a factor of 20. But what about the 3? It's not clear.

You can also illustrate this by picking numbers that fit the condition of St (1). Examples would be n = 20, 40, 60, 80, etc
All of those have 5 as a factor, but not all of them have 3 as a factor. INSUFFICIENT.

Statement (2) says n+6 is a multiple of 3. The tricky thing here is to realize that 6 is a multiple of 3, and thus if n+6 is a multiple of 3, n itself must also be a multiple of 3.

Again, you can test numbers to verify this. n could equal 0, 3, 6, 9, etc. All those values of n are already multiples of 3.

So St (2) really just says "n is a multiple of 3."

Unfortunately, we don't know about the 5, so we can't say if n is a multiple of 15. INSUFFICIENT.

Together, (1) tells us n has 5 as a factor and (2) tells us n has 3 as a factor. Therefore, since n has both 5 and 3 as factors, it must also have 3*5 = 15 as a factor. SUFFICIENT

Ans: C
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Re: Is the integer n a multiple of 15?   [#permalink] 09 Feb 2017, 11:06
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