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What is the remainder when the positive integer n is divided by 2?
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08 Mar 2015, 04:59
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What is the remainder when the positive integer n is divided by 2? (1) When n is divided by 13, the remainder is 3 (2) n + 2 is a multiple of 7
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Re: What is the remainder when the positive integer n is divided by 2?
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08 Mar 2015, 07:43
What is the remainder when the positive integer n is divided by 2?The remainder upon division n by 2 can be 0 (when n is even) or 1 (when n is odd). So, the question basically asks whether n is even or odd. (1) When n is divided by 13, the remainder is 3 > n = 13q + 3 > n can be: 3, 16, 29, 42, 55, 68, ... So, n can be even as well as odd. Not sufficient. (2) n + 2 is a multiple of 7 > n is 2 less than a multiple of 7, or, which is the same, n is 5 more than a multiple of 7 > n = 7p + 5: 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, ... So, n can be even as well as odd. Not sufficient. (1)+(2) From n = 13q + 3 and n = 7p + 5, we can get that n = 91k + 68 (check HERE to know to to derive general formula from these two), so n can be 68, 159, ... So, again, n can be even as well as odd. Not sufficient. Answer: E. Hope it's clear.
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Re: What is the remainder when the positive integer n is divided by 2?
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09 Mar 2015, 14:05
Thanks Bunuel. Basically, i was confused about finding n = 91k + 68. Now, its clear.



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Re: What is the remainder when the positive integer n is divided by 2?
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16 Nov 2016, 01:11
Could someone explain how n = 7p + 5 was derived?
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Re: What is the remainder when the positive integer n is divided by 2?
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16 Nov 2016, 01:41
Mimster wrote: Could someone explain how n = 7p + 5 was derived? There is a link provided in the solution: ...check HERE to know to to derive general formula from these two...
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Re: What is the remainder when the positive integer n is divided by 2?
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17 Nov 2016, 22:33
(1) n = 13q+3 (3,16,29,...)
if we try to divide each possible value of n by 2, we find R is not consistent (i.e. R = 1, R=0, R=1...)
NOT SUFFICIENT
(2) n+2 =7#
say n+2=7 > n=5 > 5/2 > R = 1 say n+2=14 > n=12 > 12/2 > R = 0
inconsistent remainders, thus NOT SUFFICIENT
(1) + (2) 13q+5=7#
13 is a prime number. There is no way we would be able to obtain 13 by subtracting 5 from a multiple of 7.
Thus, insufficient.
E



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Re: What is the remainder when the positive integer n is divided by 2?
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29 Nov 2016, 16:45
TARGET730 wrote: What is the remainder when the positive integer n is divided by 2?
(1) When n is divided by 13, the remainder is 3 (2) n + 2 is a multiple of 7 We need to determine the remainder when the positive integer n is divided by 2. Keep in mind that when a positive integer is divided by 2, the remainder is either 0 (if the number is even) or 1 (if the number is odd). Statement One Alone:When n is divided by 13, the remainder is 3. There are many possible values for n. For example, n could be 16 or n could be 29. If n = 16, the remainder is 0 when n is divided by 2. However, if n = 29, the remainder is 1 when n is divided by 2. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D. Statement Two Alone:n + 2 is a multiple of 7. There are many possible values for n. For example, n could be 5 or n could be 12. If n = 5, the remainder is 1 when n is divided by 2. However, if n = 12, the remainder is 0 when n is divided by 2. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B. Statements One and Two Together:Even with the two statements, there are still many possible values for n. For example, n could be 68 or n could be 159. If n = 68, the remainder is 0 when n is divided by 2. However, if n = 159, the remainder is 1 when n is divided by 2. The two statements together are still not sufficient to answer the question. Answer: E
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Re: What is the remainder when the positive integer n is divided by 2?
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14 Feb 2017, 07:01
Bunuel wrote: What is the remainder when the positive integer n is divided by 2?The remainder upon division n by 2 can be 0 (when n is even) or 1 (when n is odd). So, the question basically asks whether n is even or odd. (1) When n is divided by 13, the remainder is 3 > n = 13q + 3 > n can be: 3, 16, 29, 42, 55, 68, ... So, n can be even as well as odd. Not sufficient. (2) n + 2 is a multiple of 7 > n is 2 less than a multiple of 7, or, which is the same, n is 5 more than a multiple of 7 > n = 7p + 5: 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, ... So, n can be even as well as odd. Not sufficient. (1)+(2) From n = 13q + 3 and n = 7p + 5, we can get that n = 91k + 68 (check HERE to know to to derive general formula from these two), so n can be 68, 159, ... So, again, n can be even as well as odd. Not sufficient. Answer: E. Hope it's clear. Hi Bunuel, Could you please advise if we can just add one equation to another? In that case we would have n=20k+1. By picking the numbers we see that it can either be even OR odd, so we get E as the answer. This approach is presented by MGM for tackling extra remainders problems. Thanks.



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Re: What is the remainder when the positive integer n is divided by 2?
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14 Feb 2017, 07:06
Alexey1989x wrote: Bunuel wrote: What is the remainder when the positive integer n is divided by 2?The remainder upon division n by 2 can be 0 (when n is even) or 1 (when n is odd). So, the question basically asks whether n is even or odd. (1) When n is divided by 13, the remainder is 3 > n = 13q + 3 > n can be: 3, 16, 29, 42, 55, 68, ... So, n can be even as well as odd. Not sufficient. (2) n + 2 is a multiple of 7 > n is 2 less than a multiple of 7, or, which is the same, n is 5 more than a multiple of 7 > n = 7p + 5: 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, ... So, n can be even as well as odd. Not sufficient. (1)+(2) From n = 13q + 3 and n = 7p + 5, we can get that n = 91k + 68 (check HERE to know to to derive general formula from these two), so n can be 68, 159, ... So, again, n can be even as well as odd. Not sufficient. Answer: E. Hope it's clear. Hi Bunuel, Could you please advise if we can just add one equation to another? In that case we would have n=20k+1. By picking the numbers we see that it can either be even OR odd, so we get E as the answer. This approach is presented by MGM for tackling extra remainders problems. Thanks. No, this would be incorrect. You cannot add n = 13 q + 3 and n = 7 p + 5 to get n = 20k + 1. Notice that the quotients there are different: q and p. The way you can get the general formula is given in the solution.
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Re: What is the remainder when the positive integer n is divided by 2?
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15 Feb 2017, 16:19
TARGET730 wrote: What is the remainder when the positive integer n is divided by 2?
(1) When n is divided by 13, the remainder is 3 (2) n + 2 is a multiple of 7 We need to determine the remainder when n is divided by 2. Statement One Alone:When n is divided by 13, the remainder is 3. Statement one alone is not sufficient to answer the question. For example, when n = 3, the remainder when n is divided by 2 is 1. However, when n = 16, the remainder when n is divided by 2 is 0. Statement Two Alone:n + 2 is a multiple of 7. Statement two alone is not sufficient to answer the question. For instance, when n = 5, the remainder when n is divided by 2 is 1. However, when n = 12, the remainder when n is divided by 2 is 0. Statements One and Two Together:Let’s list out possible values of n from statement one: From statement one: n = 3, 16, 29, 42, 55, 68 We see that from the above list, 68 (since 68 + 2 = 70 is a multiple of 7) fulfills both statements one and two and provides a remainder of 0 when divided by 2. To determine the next value in the list, we can use the least common multiple of 13 and 7, which is 13 x 7 = 91. Thus, the next number that could be n is 68 + (7 x 13) = 159. Since 159 has a remainder of 1 when divided by 2, the two statements together are still not sufficient to answer the question. Answer: E
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