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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.

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

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24 Oct 2013, 15:08

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.

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.

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.

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

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24 Nov 2014, 10:21

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

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: \(1=9*0+1\).

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

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03 Aug 2015, 08:59

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.

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).
_________________

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.

We need to determine the remainder when n is divided by 12.

Statement One Alone:

When n is divided by 6, the remainder is 1.

The information in statement one is not sufficient to answer the question. We see that when n = 7, 7/12 has a remainder of 7; however when n = 13, 13/12 has a remainder of 1.

Statement Two Alone:

When n is divided by 12, the remainder is greater than 5.

The information in statement two is not sufficient to answer the question, since when n is divided by 12, it can be any one of these possible remainders: 6, 7, 8, 9, 10, and 11.

Statements One and Two Together:

Using the information from statements one, we see that n can be values such as:

7, 13, 19, 25, …..

We also see that when we divide these values by 12, we get a pattern of remainders:

7/12 has a remainder of 7

13/12 has a remainder of 1

19/12 has a reminder of 7

25/12 has a remainder of 1

Since we have found a pattern, we do not have to test any further numbers. Furthermore, since statement two tells us that the remainder when N is divided by 12 is greater than 5, the only possible remainder is 7.

Answer: C
_________________

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