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# What is the remainder when the positive integer n is divided by 2?

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What is the remainder when the positive integer n is divided by 2?  [#permalink]

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08 Mar 2015, 03:59
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85% (hard)

Question Stats:

52% (02:35) correct 48% (02:27) wrong based on 162 sessions

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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?  [#permalink]

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08 Mar 2015, 06:43
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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.

Hope it's clear.
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Re: What is the remainder when the positive integer n is divided by 2?  [#permalink]

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09 Mar 2015, 13:05
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?  [#permalink]

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16 Nov 2016, 00:11
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?  [#permalink]

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16 Nov 2016, 00:41
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?  [#permalink]

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17 Nov 2016, 21:33
(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.

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Re: What is the remainder when the positive integer n is divided by 2?  [#permalink]

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29 Nov 2016, 15:45
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.

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Re: What is the remainder when the positive integer n is divided by 2?  [#permalink]

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14 Feb 2017, 06:01
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.

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?  [#permalink]

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14 Feb 2017, 06:06
1
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.

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 = 13q + 3 and n = 7p + 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?  [#permalink]

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15 Feb 2017, 15:19
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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.

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Re: What is the remainder when the positive integer n is divided by 2?  [#permalink]

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Re: What is the remainder when the positive integer n is divided by 2?   [#permalink] 07 Feb 2019, 20:30
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