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remainder when a positive integer x is divided by 6

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remainder when a positive integer x is divided by 6  [#permalink]

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New post 16 Nov 2011, 19:11
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What is the remainder when a positive integer x is divided by 6?

1. When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0.
2. When x is divided by 12, the remainder is 3.


I chose B, but the OA says wrong. Can anyone please explain how do we derive a remainder from statement 1? Because from stmt 1, x can be 3 or anything in the form 3n, where n is odd.
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Re: remainder when a positive integer x is divided by 6  [#permalink]

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New post 16 Nov 2011, 20:50
statement one tells us that x is odd and is a multiple of 3. test few odd multiples of 3: 9,15,21,27 divided by 6 always give same remainder i.e. 3. So (1) is sufficient
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Re: remainder when a positive integer x is divided by 6  [#permalink]

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New post 16 Nov 2011, 20:59
Macsen wrote:
What is the remainder when a positive integer x is divided by 6?

1. When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0.
2. When x is divided by 12, the remainder is 3.


I chose B, but the OA says wrong. Can anyone please explain how do we derive a remainder from statement 1? Because from stmt 1, x can be 3 or anything in the form 3n, where n is odd.



Stmnt 1: When x is divided by 2, the remainder is 1; - It means x is odd.
and when x is divided by 3, the remainder is 0. - It means x is divisible by 3

So basically, stmnt 1 tells us that x is an odd multiple of 3 e.g. 3, 9, 15 etc. When you divide these numbers by 6, you will always get 3 as remainder.
Deduce it logically - x i.e. an odd multiple of 3 will always be 3 more than an even multiple of 3 since odd and even multiples of 3 will alternate (e.g. 3 (O), 6(E), 9(O), 12(E), 15(O), 18(E) etc)
Every even multiple of 3 is divisible by 6 so we can say that odd multiples of 3 are always 3 more than multiples of 6. Hence the remainder when you divide x by 6 will always be 3.

Stmnt 2: x is 3 more than a multiple of 12. Since 12 is divisible by 6, x is 3 more than a multiple of 6 too. Hence, remainder is always 3.

Answer (D)

For further theory on divisibility, check:
http://www.veritasprep.com/blog/2011/04 ... unraveled/
http://www.veritasprep.com/blog/2011/04 ... y-applied/
http://www.veritasprep.com/blog/2011/05 ... emainders/
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Re: remainder when a positive integer x is divided by 6  [#permalink]

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New post 16 Nov 2011, 21:04
We know X is odd because it's not evenly divisible by 2. We also know it is a multiple of 3 because 3 divides into it evenly. So, X is an odd multiple of 3: 3, 9, 15, 21, etc... Each of those numbers divided by 6 gives a remainder of 3.

Statement 2 tells us there's a remainder of 3 when X is divided by 12. Given that 12 = 2*6, we know the remainder there too.
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Re: remainder when a positive integer x is divided by 6  [#permalink]

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New post 17 Nov 2011, 19:10
Understand all the above points, but one part of my brain still finds it hard to reconcile to the fact that when 3 is divided by 6, it leaves a remainder > 0!!
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Re: remainder when a positive integer x is divided by 6  [#permalink]

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New post 17 Nov 2011, 19:11
3/6 = 0 with a remainder of 3. Does that make sense?
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Re: remainder when a positive integer x is divided by 6  [#permalink]

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New post 17 Nov 2011, 20:38
Macsen wrote:
Understand all the above points, but one part of my brain still finds it hard to reconcile to the fact that when 3 is divided by 6, it leaves a remainder > 0!!


When you divide 3 by 6, you are basically trying to group 3 balls into groups of 6 balls each. How many groups can you make? 0 - This is the quotient.
How many balls are remaining, lying around unused? 3 - This is the remainder.

Whenever you divide a smaller number by a greater number, the smaller number itself will be the remainder and quotient will be 0.
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Re: remainder when a positive integer x is divided by 6  [#permalink]

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New post 01 Mar 2017, 13:53
I solved it in a different way. Let me know if this approach is correct

S-1) From Statement 1 we have, x = 2k +1 and x = 3k. Solved simultaneously and got k =1. so x = 3.
Sufficient to get remainder.

S-2) x = 6*2k + 3. So remainder is 3. Sufficient
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Re: remainder when a positive integer x is divided by 6  [#permalink]

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