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The remainder, when a number n is divided by 6, is p. The remainder, w

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The remainder, when a number n is divided by 6, is p. The remainder, w  [#permalink]

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New post 19 Feb 2017, 21:09
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The remainder, when a number n is divided by 6, is p. The remainder, when the same number n is divided by 12, is q. Is p < q?

(1) n is a positive number having 8 as a factor.
(2) n is a positive number having 6 as a factor.
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Re: The remainder, when a number n is divided by 6, is p. The remainder, w  [#permalink]

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New post 20 Feb 2017, 00:42
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ssr300 wrote:
The remainder, when a number n is divided by 6, is p. The remainder, when the same number n is divided by 12, is q. Is p < q?


1) n is a positive number having 8 as a factor.
2) n is a positive number having 6 as a factor.


Please kindly explain breakdown


My reasoning :

A...we have 8 as a factor --so numbers can be 8,16,24,32...
8 is divided by 6 we will get 2 as a remainder and when its is divided by 12 we will get 4 ..
24 will give 0 as as a remainder for both 6 and 12 ..so insuff...

B --6,12,18,24--here also it is insuff..

combining both we will the info that number have factor 8 and 6 ..
number can be 24 ,48 ..
so 6 and 12 will give 0 as a remainder ...
so p < q ..answer is no ..suff....
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Re: The remainder, when a number n is divided by 6, is p. The remainder, w  [#permalink]

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New post 04 Jul 2017, 07:25
C

(1) n could be 8, 16, 24, 32,40,48
the remainders for 6 is 2, 4, 0, 2, 4, 0 ......
for 12 8, 4, 0, 8, 4, 0
So p could be either smaller or equal to q, hence insufficient

(2) n could be 6 , 12, 18, 24......
Note that the remainder for 6 will always be 0
For 12 it will be 6 and 0 depending on whether n/6 is odd or even,
Again the P is smaller or equal to Q
hence insufficient

(1)& (2) Combining these 2 statement together we can clearly say that n/6 is always an even number and hence, the remainder of n/12 will always be 0. And P = Q
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Re: The remainder, when a number n is divided by 6, is p. The remainder, w  [#permalink]

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New post 04 Jul 2017, 09:33
To add on to the previous responses, once you realize that (1) & (2) are not sufficient, take the LCM of 6 and 8, or \(2^3\times 3\).

Since this contains the prime factors of 6 (\(2\times3\)) and 12 (\(2^2\times3\)), you will always have the answer of No to the question Is p < q?:

  • \((n\times 2^3\times 3) \bmod 6 = 0\)
  • \((n\times 2^3\times 3) \bmod 8 = 0\)
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Re: The remainder, when a number n is divided by 6, is p. The remainder, w  [#permalink]

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New post 10 Jul 2017, 16:39
Great explanations! I was able to answer this one correctly, however, it took me 5 minutes...Is there any way to look at this problem differently to cut down on time used?
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Re: The remainder, when a number n is divided by 6, is p. The remainder, w  [#permalink]

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Re: The remainder, when a number n is divided by 6, is p. The remainder, w   [#permalink] 03 Jul 2020, 02:57

The remainder, when a number n is divided by 6, is p. The remainder, w

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