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If r is the remainder when the positive integer n is divided by 7 what

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If r is the remainder when the positive integer n is divided by 7 what  [#permalink]

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New post 21 Sep 2010, 21:39
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If r is the remainder when the positive integer n is divided by 7, what is the value of r ?

(1) When n is divided by 21, the remainder is an odd number.
(2) When n is divided by 28, the remainder is 3.

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Re: If r is the remainder when integer n is divided by 7, what is the valu  [#permalink]

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New post 27 Oct 2014, 09:36
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Bunuel wrote:

Tough and Tricky questions: Remainders.



If r is the remainder when integer n is divided by 7, what is the value of r?

(1) When n is divided by 21, the remainder is an odd number
(2) When n is divided by 28, the remainder is 3


solution: From #1, if n = 5, remainder is 5 and is odd.
if n = 7, remainder is 7 and is odd.
However, remainder when n(5 or 7) is divided by 7 is different. Hence not sufficient
From #2, n=3, or 31, or 59 etc, remainder is 3,
Even when the above numbers are divided by 7, the remainder is still 3

Answer should be B
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Re: If r is the remainder when the positive integer n is divided by 7 what  [#permalink]

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New post 21 Sep 2010, 22:12
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If r is the remainder when the postive integer n is divided by 7, what is the value of r ?

Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

(1) when n is divided by 21 the remainder is an odd number --> \(n=21q+odd=7*3q+odd\), now as \(21q\) is itself divisible by 7 then if \(odd=1\) then \(n\) divided by 7 will yield the same reminder of 1 BUT if \(odd=3\) then \(n\) divided by 7 will yield the same reminder of 3. Two different answers, hence not sufficient.

Or try two different numbers for \(n\):
If \(n=22\) then \(n\) divided by 21 gives remainder of 1 and \(n\) divded by 7 also gives remainder of 1;
If \(n=24\) then \(n\) divided by 21 gives remainder of 3 and \(n\) divded by 7 also gives remainder of 3.
Two different answers, hence not sufficient.

(2) when n is divided by 28, the remainder is 3 --> \(n=28p+3=7*(4p)+3\), now as \(28p\) is itself divisible by 7, then \(n\) divided by 7 will give remainder of 3. Sufficient.

Answer: B.
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Re: If r is the remainder when the positive integer n is divided by 7 what  [#permalink]

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New post 03 Apr 2016, 14:13
Bunuel wrote:
If r is the remainder when the postive integer n is divided by 7, what is the value of r ?

Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

(1) when n is divided by 21 the remainder is an odd number --> \(n=21q+odd=7*3q+odd\), now as \(21q\) is itself divisible by 7 then if \(odd=1\) then \(n\) divided by 7 will yield the same reminder of 1 BUT if \(odd=3\) then \(n\) divided by 7 will yield the same reminder of 3. Two different answers, hence not sufficient.

Or try two different numbers for \(n\):
If \(n=22\) then \(n\) divided by 21 gives remainder of 1 and \(n\) divded by 7 also gives remainder of 1;
If \(n=24\) then \(n\) divided by 21 gives remainder of 3 and \(n\) divded by 7 also gives remainder of 3.
Two different answers, hence not sufficient.

(2) when n is divided by 28, the remainder is 3 --> \(n=28p+3=7*(4p)+3\), now as \(28p\) is itself divisible by 7, then \(n\) divided by 7 will give remainder of 3. Sufficient.

Answer: B.


Thanks Bunnel. Could you please explain the logic behind "when n is divided by 28, the remainder is 3 --> \(n=28p+3=7*(4p)+3\), now as \(28p\) is itself divisible by 7, then \(n\) divided by 7 will give remainder of 3. Sufficient." ?
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Re: If r is the remainder when the positive integer n is divided by 7 what  [#permalink]

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New post 03 Apr 2016, 21:23
Keysersoze10 wrote:
Bunuel wrote:
If r is the remainder when the postive integer n is divided by 7, what is the value of r ?

Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

(1) when n is divided by 21 the remainder is an odd number --> \(n=21q+odd=7*3q+odd\), now as \(21q\) is itself divisible by 7 then if \(odd=1\) then \(n\) divided by 7 will yield the same reminder of 1 BUT if \(odd=3\) then \(n\) divided by 7 will yield the same reminder of 3. Two different answers, hence not sufficient.

Or try two different numbers for \(n\):
If \(n=22\) then \(n\) divided by 21 gives remainder of 1 and \(n\) divded by 7 also gives remainder of 1;
If \(n=24\) then \(n\) divided by 21 gives remainder of 3 and \(n\) divded by 7 also gives remainder of 3.
Two different answers, hence not sufficient.

(2) when n is divided by 28, the remainder is 3 --> \(n=28p+3=7*(4p)+3\), now as \(28p\) is itself divisible by 7, then \(n\) divided by 7 will give remainder of 3. Sufficient.

Answer: B.


Thanks Bunnel. Could you please explain the logic behind "when n is divided by 28, the remainder is 3 --> \(n=28p+3=7*(4p)+3\), now as \(28p\) is itself divisible by 7, then \(n\) divided by 7 will give remainder of 3. Sufficient." ?


28p gives the remainder of 0, when divided by 7 and 3 gives the remainder of 3 when divided by 7.
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Re: If r is the remainder when integer n is divided by 7, what is the valu  [#permalink]

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New post 04 Oct 2016, 22:00
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Quote:
If r is the remainder when integer n is divided by 7, what is the value of r?

(1) When n is divided by 21, the remainder is an odd number
(2) When n is divided by 28, the remainder is 3


\(\frac{n}{7} = q + r\)

(1) \(\frac{n}{21}\) = quotient + Some odd value

Minimum value of n could be 22 , 24 , 26 -- Not sufficient

(2) \(\frac{n}{28}\) = quotient + 3

Minimum value of n will be 31 that will satisfy above. So r = 3. --Sufficient

Ans. B
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Re: If r is the remainder when integer n is divided by 7, what is the valu  [#permalink]

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New post 20 Apr 2018, 07:36
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Bunuel wrote:

Tough and Tricky questions: Remainders.



If r is the remainder when integer n is divided by 7, what is the value of r?

(1) When n is divided by 21, the remainder is an odd number
(2) When n is divided by 28, the remainder is 3


We can use a variety of divisibility rules to solve this, or we can list possible values of n based on the statements. The rule for listing possible values of n is as follows:
If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .

Target question: What is the value of r?

Statement 1: When n is divided by 21, the remainder is an odd number.
There are several possible values of n that satisfy this condition. Here are two:
Case a: n = 1 (since 1 divided by 21 leaves remainder 1, which is odd). Here, r = 1
Case b: n = 3 (since 3 divided by 21 leaves remainder 3, which is odd). Here, r = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When n is divided by 28, the remainder is 3
Possible values of n: 3, 31, 59, 87, . . .
We can see that for all possible values of n, the remainder is always 3 when n is divided by 7
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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Re: If r is the remainder when integer n is divided by 7, what is the valu  [#permalink]

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New post 16 Jun 2019, 01:33
GMATPrepNow wrote:
Bunuel wrote:

Tough and Tricky questions: Remainders.



If r is the remainder when integer n is divided by 7, what is the value of r?

(1) When n is divided by 21, the remainder is an odd number
(2) When n is divided by 28, the remainder is 3


We can use a variety of divisibility rules to solve this, or we can list possible values of n based on the statements. The rule for listing possible values of n is as follows:
If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .

Target question: What is the value of r?

Statement 1: When n is divided by 21, the remainder is an odd number.
There are several possible values of n that satisfy this condition. Here are two:
Case a: n = 1 (since 1 divided by 21 leaves remainder 1, which is odd). Here, r = 1
Case b: n = 3 (since 3 divided by 21 leaves remainder 3, which is odd). Here, r = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When n is divided by 28, the remainder is 3
Possible values of n: 3, 31, 59, 87, . . .
We can see that for all possible values of n, the remainder is always 3 when n is divided by 7
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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how statement 2 is sufficient?

when 69/28 remainder is =3; when 69/7 remainder =6
when 87/28 r=3 ; when 87/7 r=3
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Re: If r is the remainder when integer n is divided by 7, what is the valu  [#permalink]

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New post 16 Jun 2019, 10:50
SUNILAA wrote:
how statement 2 is sufficient?

when 69/28 remainder is =3; when 69/7 remainder =6
when 87/28 r=3 ; when 87/7 r=3


You do not get a remainder of 3 when you divide 69 by 28.

If Statement 2 is true, then n is 3 larger than a multiple of 28. But every multiple of 28 is a multiple of 7 too, so that means n is 3 larger than a multiple of 7. That's another way of saying "the remainder is 3 when you divide n by 7", so Statement 2 is sufficient.
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Re: If r is the remainder when the positive intreger n is  [#permalink]

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Re: If r is the remainder when the positive intreger n is   [#permalink] 21 Oct 2019, 10:12
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