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What is the remainder when the positive integer n is divided by 12?
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Updated on: 29 Oct 2017, 00:32
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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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Originally posted by windofchange on 07 Oct 2013, 03:05.
Last edited by Bunuel on 29 Oct 2017, 00:32, edited 2 times in total.
Renamed the topic and edited the question.




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Re: What is the remainder when the positive integer n is divided by 12?
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07 Oct 2013, 04:34
What is the remainder when the positive integer n is divided by 12?The remainder is always nonnegative 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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Re: What is the remainder when the positive integer n is divided by 12?
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24 Oct 2013, 16:08
Bunuel wrote: What is the remainder when the positive integer n is divided by 12?
The remainder is always nonnegative 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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Re: What is the remainder when the positive integer n is divided by 12?
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25 Oct 2013, 02:00
saintforlife wrote: Bunuel wrote: What is the remainder when the positive integer n is divided by 12?
The remainder is always nonnegative 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: remainders144665.htmlAll DS remainders problems to practice: search.php?search_id=tag&tag_id=198All PS remainders problems to practice: search.php?search_id=tag&tag_id=199Hope this helps.
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Re: What is the remainder when the positive integer n is divided by 12?
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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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Re: What is the remainder when the positive integer n is divided by 12?
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23 Sep 2014, 00:36
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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Re: What is the remainder when the positive integer n is divided by 12?
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24 Nov 2014, 11:21
Bunuel wrote: What is the remainder when the positive integer n is divided by 12?
The remainder is always nonnegative 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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Re: What is the remainder when the positive integer n is divided by 12?
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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 nonnegative 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: \(1=9*0+1\).
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Re: What is the remainder when the positive integer n is divided by 12?
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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 611. 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 by 12?
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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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Re: What is the remainder when the positive integer n is divided by 12?
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30 Nov 2017, 06:04
Instead of testing values, You can just divide the number by 12(or anything for any question) and check for the remainders



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Re: What is the remainder when the positive integer n is divided by 12?
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04 Dec 2017, 11:45
windofchange 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. 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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Re: What is the remainder when the positive integer n is divided by 12?
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30 Dec 2017, 10:56
Hi, Please, I have problem understanding why c. In my opinio, the answer is E because not only 7 meets the criteria but also 31 ! can you tell me where am i wrong ?
Thank you !



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Re: What is the remainder when the positive integer n is divided by 12?
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30 Dec 2017, 11:03
hichem wrote: Hi, Please, I have problem understanding why c. In my opinio, the answer is E because not only 7 meets the criteria but also 31 ! can you tell me where am i wrong ?
Thank you ! The question asks to find the value of r not n. What is the remainder when the positive integer n is divided by 12? That being said, n can take infinitely many values: 7, 19, 31, 43, ... not just the two you mention.
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Re: What is the remainder when the positive integer n is divided by 12?
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31 Dec 2017, 23:48
windofchange 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 first number to satisfy both conditions is 17 all the number satisfying both condition will be 17+ k. minimum multiple of 6 and 12 =17+ k. 12 so, we find that the remainder is alway 2. C is correct we need to find the minimum multitude of 6 and 12. which is 12. the question will become more dificult if it is harder to find minimum multiple of 6 and 12



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Re: What is the remainder when the positive integer n is divided by 12?
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14 May 2018, 03:14
We can also use the Dividend and Divisor property.
Statement 1: When n is divided by 6, the remainder is 1.
This means that n = 6 * q + 1 (1 Equation and 2 Variables) [Clearly not sufficient]
Statement 2: When n is divided by 12, the remainder is greater than 5
This means that n = 12 * q + 6 (or the range can be anything) (1 Equation and 2 Variables) [Clearly not sufficient]
Combining Statement 1 + Statement 2 = We can easily solve for both the equations in 2 varibles.
Answer choice C



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Re: What is the remainder when the positive integer n is divided by 12?
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27 Jan 2019, 22:06
dheerajt94 wrote: We can also use the Dividend and Divisor property.
Statement 1: When n is divided by 6, the remainder is 1.
This means that n = 6 * q + 1 (1 Equation and 2 Variables) [Clearly not sufficient]
Statement 2: When n is divided by 12, the remainder is greater than 5
This means that n = 12 * q + 6 (or the range can be anything) (1 Equation and 2 Variables) [Clearly not sufficient]
Combining Statement 1 + Statement 2 = We can easily solve for both the equations in 2 varibles.
Answer choice C Hey i may be late but i wanted to point out that your approach is flawed! Both the "q" values u have taken are same in both equations of "n". But actually there will be two different values!



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Re: What is the remainder when the positive integer n is divided by 12?
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14 Mar 2019, 12:52
Here are my two cents for this question Using Even ODD concept. division by 12 can yield any reminder from 0 to 11 Now \(\frac{n}{6}\)reminder is 1 we can write this algebraically as n=6K+1 now when \(\frac{n}{12}\) =\(\frac{6K+1}{12} w\)e can have two possible out comes reminder If K is even we have 1 as remainder and if K is odd , reminder as 7 Now as per second statement when \(\frac{n}{12}\) we get a reminder which is greater than 5, so reminder can be any number from 6 to 11 or we can write it allergically as n= 12Q+R Now combining both we have ( if some one did miss the first inference that reminder can be 1 or 7) we could see that 12Q+R=6K+1 where 5<R<11 so we have 12Q6K=1R Recognize that 6(2QK)= 1R LHS is Even So RHS must be even so R must be odd. Possible values of R are 7,9,11 But recognize that LHS is multiple of 6 so should also be RHS . the only value which gives us multiple of 6 on RHS is if the value of R is 7 hence we can say the remainder is 7 Hence we can answer out question using both statements Probus
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Re: What is the remainder when the positive integer n is divided by 12?
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