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What is the remainder when the positive integer n is divided

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What is the remainder when the positive integer n is divided by 12?

(1) When n is divided by 6, the remainder is 1.
(2) When n is divided by 12, the remainder is greater than 5.

My approach:
[Reveal] Spoiler:
From (1): \(n = 6p +1\)
\(p = 1\) ==> \(n = 7\) ==> remainder of \(\frac{n}{12} = 7\)
\(p = 2\) ==> \(n = 13\) ==> remainder of \(\frac{n}{12} = 1\)
\(p = 3\) ==> \(n = 19\) ==> remainder of \(\frac{n}{12} = 7\)
\(p = 4\) ==> \(n = 25\) ==> remainder of \(\frac{n}{12} = 1\)
\(p = 5\) ==> \(n = 31\) ==> remainder of \(\frac{n}{12} = 7\)
\(p = 6\) ==> \(n = 37\) ==> remainder of \(\frac{n}{12} = 1\)
So remainder can be 7 or 1 ==> insufficient

From (2): we can say that \(5 < R < 12\), so \(R = 6; 7; 8; 9; 10; 11\) ==> insufficient

From (1) and (2): remainder = 7


However my approach is time-consuming. Please share yours. Thanks :)
[Reveal] Spoiler: OA

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Last edited by Bunuel on 07 Oct 2013, 04:28, edited 1 time in total.
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What is the remainder when the positive integer n is divided by 12?

The remainder is always non-negative integer less than divisor \(0\leq{r}<d\), so in our case \(0\leq{r}<12\).

(1) When n is divided by 6, the remainder is 1 --> \(n=6q+1\), thus n can be 1, 7, 13, 19, 25, ... This means that the remainder upon division n by 12 can be 1 or 7. Not sufficient.

(2) When n is divided by 12, the remainder is greater than 5. This implies that \(5<{r}<12\). Not sufficient.

(1)+(2) Since from (2) \(5<{r}<12\), the from (1) r=7. Sufficient.

Answer: C.

Hope it's clear.
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New post 24 Oct 2013, 16:08
Bunuel wrote:
What is the remainder when the positive integer n is divided by 12?

The remainder is always non-negative integer less than divisor \(0\leq{r}<d\), so in our case \(0\leq{r}<12\).

(1) When n is divided by 6, the remainder is 1 --> \(n=6q+1\), thus n can be 1, 7, 13, 19, 25, ... This means that the remainder upon division n by 12 can be 1 or 7. Not sufficient.

(2) When n is divided by 12, the remainder is greater than 5. This implies that \(5\leq{r}<12\). Not sufficient.

(1)+(2) Since from (2) \(5\leq{r}<12\), the from (1) r=7. Sufficient.

Answer: C.

Hope it's clear.

Hi Bunuel, can you post some practice problems for the 'Remainders' topic? I got this in my GMAT Prep exam and I got it wrong. I'd like to review this topic a bit more. Thanks.

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saintforlife wrote:
Bunuel wrote:
What is the remainder when the positive integer n is divided by 12?

The remainder is always non-negative integer less than divisor \(0\leq{r}<d\), so in our case \(0\leq{r}<12\).

(1) When n is divided by 6, the remainder is 1 --> \(n=6q+1\), thus n can be 1, 7, 13, 19, 25, ... This means that the remainder upon division n by 12 can be 1 or 7. Not sufficient.

(2) When n is divided by 12, the remainder is greater than 5. This implies that \(5\leq{r}<12\). Not sufficient.

(1)+(2) Since from (2) \(5\leq{r}<12\), the from (1) r=7. Sufficient.

Answer: C.

Hope it's clear.

Hi Bunuel, can you post some practice problems for the 'Remainders' topic? I got this in my GMAT Prep exam and I got it wrong. I'd like to review this topic a bit more. Thanks.


Theory on remainders problems: remainders-144665.html

All DS remainders problems to practice: search.php?search_id=tag&tag_id=198
All PS remainders problems to practice: search.php?search_id=tag&tag_id=199

Hope this helps.
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New post 22 Sep 2014, 12:20
Hi Bunuel,

Maybe I'm just rusty on remainder theory, but you would please explain how you were able to see this:

Quote:
This means that the remainder upon division n by 12 can be 1 or 7. Not sufficient.


Thanks,
MDL

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mdlyman wrote:
Hi Bunuel,

Maybe I'm just rusty on remainder theory, but you would please explain how you were able to see this:

Quote:
This means that the remainder upon division n by 12 can be 1 or 7. Not sufficient.


Thanks,
MDL


1, 7, 13, 19, 25,

1 divided by 12 gives the remainder of 1;
7 divided by 12 gives the remainder of 7;
13 divided by 12 gives the remainder of 1;
19 divided by 12 gives the remainder of 7;
25 divided by 12 gives the remainder of 1;
...

Check links for theory on remainders in my post above.

Hope it helps.
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New post 24 Nov 2014, 11:21
Bunuel wrote:
What is the remainder when the positive integer n is divided by 12?

The remainder is always non-negative integer less than divisor \(0\leq{r}<d\), so in our case \(0\leq{r}<12\).

(1) When n is divided by 6, the remainder is 1 --> \(n=6q+1\), thus n can be 1, 7, 13, 19, 25, ... This means that the remainder upon division n by 12 can be 1 or 7. Not sufficient.

(2) When n is divided by 12, the remainder is greater than 5. This implies that \(5\leq{r}<12\). Not sufficient.

(1)+(2) Since from (2) \(5\leq{r}<12\), the from (1) r=7. Sufficient.

Answer: C.

Hope it's clear.



I have a doubt here , like u said \(n=6q+1\), thus n can be 1, 7, 13, 19, 25 so we are substituting q with 0,1 ,2,3 ... so on ... But I wanted to know if we can substitude 0 . .... That means if i divide 1/6 ---is the remainder 1 . But here I cannot divide in the first place only. Please clear my concept , i guess i m missing something . I thought we can only get remainder when the no is atleast divisible once , means p/q where p > q .... thanks in advance

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New post 25 Nov 2014, 07:28
hanschris5 wrote:
Bunuel wrote:
What is the remainder when the positive integer n is divided by 12?

The remainder is always non-negative integer less than divisor \(0\leq{r}<d\), so in our case \(0\leq{r}<12\).

(1) When n is divided by 6, the remainder is 1 --> \(n=6q+1\), thus n can be 1, 7, 13, 19, 25, ... This means that the remainder upon division n by 12 can be 1 or 7. Not sufficient.

(2) When n is divided by 12, the remainder is greater than 5. This implies that \(5\leq{r}<12\). Not sufficient.

(1)+(2) Since from (2) \(5\leq{r}<12\), the from (1) r=7. Sufficient.

Answer: C.

Hope it's clear.



I have a doubt here , like u said \(n=6q+1\), thus n can be 1, 7, 13, 19, 25 so we are substituting q with 0,1 ,2,3 ... so on ... But I wanted to know if we can substitude 0 . .... That means if i divide 1/6 ---is the remainder 1 . But here I cannot divide in the first place only. Please clear my concept , i guess i m missing something . I thought we can only get remainder when the no is atleast divisible once , means p/q where p > q .... thanks in advance


Let me ask you a question: how many leftover apples would you have if you had 1 apple and wanted to distribute in 6 baskets evenly? Each basket would get 0 apples and 1 apple would be leftover (remainder).

When a divisor is more than dividend, then the remainder equals to the dividend, for example:
3 divided by 4 yields the reminder of 3: \(3=4*0+3\);
9 divided by 14 yields the reminder of 9: \(9=14*0+9\);
1 divided by 9 yields the reminder of 1: \(1=9*0+1\).

Theory on remainders problems: remainders-144665.html

All DS remainders problems to practice: search.php?search_id=tag&tag_id=198
All PS remainders problems to practice: search.php?search_id=tag&tag_id=199

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Hi Bunuel,

The statement 2 tells us that the remainder is greater than 5. But, you have written it as 5≤r<12. Can the remainder equal to 5?
My understanding is that the remainder needs to be greater than 5 and therefore 5<r<12.

Thank you.

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New post 20 Apr 2015, 09:53
nick2014 wrote:
Hi Bunuel,

The statement 2 tells us that the remainder is greater than 5. But, you have written it as 5≤r<12. Can the remainder equal to 5?
My understanding is that the remainder needs to be greater than 5 and therefore 5<r<12.

Thank you.

___________
Typo edited. Thank you.
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What is the remainder when the positive integer n is divided by 12? [#permalink]

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What is the remainder when the positive integer n is divided by 12?
1. When n is divided by 6, the remainder is 1
2. When n is divided by 12, the remainder is greater than 5

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Re: What is the remainder when the positive integer n is divided by 12? [#permalink]

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New post 03 Aug 2015, 09:59
naeln wrote:
What is the remainder when the positive integer n is divided by 12?
1. When n is divided by 6, the remainder is 1
2. When n is divided by 12, the remainder is greater than 5


The question is asking what would the remainder be when n is divided by 12. We know that remainder obtained when n is divided by p is < p. Thus remainders when any integer is divided is divded by 12 will be one of 0,1,2,3,4,5,6,7,8,9,10,11.

Per statement 1, n =6p+1 --> n = 7 (remainder when divided by 12 = 7), or n =13 (remainder when divided by 12 = 1). Thus we get 2 different values for the remainder. Not suficient.

Per statement 2, n =12q+ r where r >5 ---> r could be one of 6-11. Thus not sufficient.

Combining, we get that the remainder will be either 1 or 7 and that the remainder will be >5 . Thus remainder will be 7. C is the correct answer.
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Re: What is the remainder when the positive integer n is divided [#permalink]

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New post 03 Aug 2015, 13:00
mdlyman wrote:
Hi Bunuel,

Maybe I'm just rusty on remainder theory, but you would please explain how you were able to see this:

Quote:
This means that the remainder upon division n by 12 can be 1 or 7. Not sufficient.


Thanks,
MDL



The best way to think of remainders is using the Number line. We all know that every 3rd number starting at 3 is multiple of 3. Looking at this another way, every 3rd number on the number line starting with 3, yields a remainder of 0 when divided by 3. Similarly, every 3rd number on the number line starting with the number 4, will yield a remainder of 1 when divided by 3.

In the problem above, a number that yields a remainder of 1 when divided by six would be every sixth number on the number line starting a 1 (i.e., 1, 7, 13, 19, .....). Dividing these same numbers by 12, yields remainders of 1 (13) or 7 (19).
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Question. Whne 7 is divided by 12, isn't the answer 0 remainder 12?

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