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If n is a positive integer, what is the smallest positive integer that

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Jazzmin
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If n is a positive integer, what is the smallest positive integer that [#permalink] New post  Updated on: 31 Oct 2018, 04:27
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If n is a positive integer, what is the smallest positive integer that is divisible by 6, 15 and n?

(1) 40 is the smallest integer that is divisible by 8 and n
(2) 60 is the smallest integer that is divisible by 12 and n.
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Originally posted by Jazzmin on 25 Oct 2018, 12:53.
Last edited by Jazzmin on 31 Oct 2018, 04:27, edited 1 time in total.
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Re: If n is a positive integer, what is the smallest positive integer that [#permalink] New post  25 Oct 2018, 13:08
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Jazzmin wrote:
If n is a positive integer, what is the smallest positive integer that is divisible by 6, 15 and n?
1. 40 is the smallest integer that is divisible by 8 and n
2. 60 is the smallest integer that is divisible by 12 and n.



1. 40 is the smallest integer that is divisible by 8 and n. ==> n=5,10,20,40
2. 60 is the smallest integer that is divisible by 12 and n.==> n=5,10,15,20,30,60
1+2).... n= 5,10,20
Ans E

Hello Jazzmin ....... would you like to revisit the Q.
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rajsngh87
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Re: If n is a positive integer, what is the smallest positive integer that [#permalink] New post  25 Oct 2018, 22:34
Dear expert.
Please explain me how D is the right answer. Thanks

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Re: If n is a positive integer, what is the smallest positive integer that [#permalink] New post  25 Oct 2018, 22:40
rajsngh87 wrote:
Dear expert.
Please explain me how D is the right answer. Thanks

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Its probably not ..... lets wait for the author Jazzmin to comeback on this one.
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Re: If n is a positive integer, what is the smallest positive integer that [#permalink] New post  25 Oct 2018, 23:25
Jazzmin wrote:
If n is a positive integer, what is the smallest positive integer that is divisible by 6, 15 and n?
1. 40 is the smallest integer that is divisible by 8 and n
2. 60 is the smallest integer that is divisible by 12 and n.



The smallest integer divisible by some numbers is the LCM of those numbers.
Therefore by statement 1 we get n as 40, which gives a unique answer to the question and similarly with statement 2, we get n as 60, hence sufficient.

Hence answer is D
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Re: If n is a positive integer, what is the smallest positive integer that [#permalink] New post  26 Oct 2018, 00:11
Ritu1009 there are multiple possible values of n from both the statements. We cannot say with surity that n will be 40 or 60. As has been rightly brought out by u1983.

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Re: If n is a positive integer, what is the smallest positive integer that [#permalink] New post  29 Oct 2018, 01:32
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Jazzmin wrote:
If n is a positive integer, what is the smallest positive integer that is divisible by 6, 15 and n?

(1) 40 is the smallest integer that is divisible by 8 and n
(2) 60 is the smallest integer that is divisible by 12 and n.


Question REPHRASED: LCM (6, 15, n) = ?

To answer the question we need
1) Exponent of 2, 3 and 5 in n and
2) Any other prime with it's exponent in n (if any)

Statement 1: 40 is the smallest integer that is divisible by 8 and n

i.e. LCM of 8 and n = 40
i.e. n may be 5, 10, 20 or 40

LCM (6, 15, n) = LCM (6, 15, 5) or LCM (6, 15, 10) or LCM (6, 15, 20) or LCM (6, 15, 40) =30 or 30 or60 or 120 respectively hence
NOT SUFFICIENT

Statement 2: 60 is the smallest integer that is divisible by 12 and n.

i.e. LCM (12, n) = 60
i.e n may be 5 or 10 or 15 or 20 or 30 or 60
LCM (6, 15, n) = LCM (6, 15, 5) or LCM (6, 15, 10) or LCM (6, 15, 20) etc =30 or 30 or 60 respectively etc hence
NOT SUFFICIENT

Combining the two statements

LCM (6, 15, n) = LCM (6, 15, 5) or LCM (6, 15, 10) or LCM (6, 15, 20) etc =30 or 30 or 60 respectively etc hence
NOT SUFFICIENT

Answer: Option E
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Re: If n is a positive integer, what is the smallest positive integer that [#permalink] New post  02 Nov 2018, 01:57
If n is a positive integer, what is the smallest positive integer that is divisible by 6, 15 and n?

(1) 40 is the smallest integer that is divisible by 8 and n
(2) 60 is the smallest integer that is divisible by 12 and n.

1. n can be 5, 10, 20, or 40. Hence, different answers are possible. Not sufficient.
2. n can be 5, 10, 20, or 60. Hence, different answers are possible. Not sufficient.
Together, n can be 5, 10, or 20. Still, different answers are possible. Not sufficient.
E.
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Re: If n is a positive integer, what is the smallest positive integer that [#permalink] New post  29 Sep 2020, 02:53
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