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

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Current Student
Joined: 11 Jul 2016
Posts: 25
Location: Thailand
GMAT 1: 700 Q48 V38
The remainder, when a number n is divided by 6, is p. The remainder, w  [#permalink]

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19 Feb 2017, 22:09
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Difficulty:

75% (hard)

Question Stats:

57% (02:49) correct 43% (02:31) wrong based on 149 sessions

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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.

Director
Joined: 14 Nov 2014
Posts: 624
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: The remainder, when a number n is divided by 6, is p. The remainder, w  [#permalink]

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20 Feb 2017, 01:42
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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.

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....
Manager
Joined: 24 Dec 2016
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Location: United States
Concentration: Statistics
Schools: Duke Fuqua
GMAT 1: 720 Q49 V40
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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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04 Jul 2017, 08:25
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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Current Student
Joined: 04 Jan 2016
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Concentration: General Management
Schools: Tuck '20 (M)
GMAT 1: 750 Q48 V44
WE: Management Consulting (Consulting)
Re: The remainder, when a number n is divided by 6, is p. The remainder, w  [#permalink]

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04 Jul 2017, 10:33
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?:

• $$(n\times 2^3\times 3) \bmod 6 = 0$$
• $$(n\times 2^3\times 3) \bmod 8 = 0$$
Intern
Joined: 30 Jun 2017
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Concentration: Finance, Entrepreneurship
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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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10 Jul 2017, 17:39
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?
Re: The remainder, when a number n is divided by 6, is p. The remainder, w   [#permalink] 10 Jul 2017, 17:39
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