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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:

I have one doubt for this question -Please help me to understand

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.

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! _________________

If you found my post useful and/or interesting - you are welcome to give kudos!

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.

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

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

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22 Mar 2016, 04:12

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