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# If r is the remainder when the positive integer n is divided

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Manager
Joined: 23 Sep 2009
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If r is the remainder when the positive integer n is divided  [#permalink]

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21 Sep 2010, 20:39
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Difficulty:

15% (low)

Question Stats:

77% (01:34) correct 23% (01:59) wrong based on 247 sessions

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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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Remainder.JPG [ 73.19 KiB | Viewed 3749 times ]

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Re: What is the remainder?  [#permalink]

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21 Sep 2010, 21:12
4
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.

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Re: What is the remainder?  [#permalink]

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22 Sep 2010, 15:32
Yep...Followed the same approach while reviewing and got it rite...
I think I am pushing the panic button even during my practice tests..
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Re: What is the remainder?  [#permalink]

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22 Sep 2010, 16:50
You may consider taking some pain in typing the questions. It will make searches to work in forum. I normally search with start of the question text and hit the discussion for that question
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Re: What is the remainder?  [#permalink]

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23 Sep 2010, 10:58
saxenashobhit wrote:
You may consider taking some pain in typing the questions. It will make searches to work in forum. I normally search with start of the question text and hit the discussion for that question

Sure buddy...going forward I will do it. !!
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Re: If r is the remainder when the positive integer n is divided  [#permalink]

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15 Aug 2013, 21:33
n=7A+r

What is r?

(1).

n=21B +R (Odd)

R can be anything 7,9,11,13,...,19

INsufficient

(2).

n=28C + 3
n= 7(4C) +3 . Since 3<7

REM (n/7)=3
Sufficient

(B) it is !
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Re: If r is the remainder when the positive integer n is divided  [#permalink]

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03 Apr 2016, 13:13
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.

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  [#permalink]

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03 Apr 2016, 20:23
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.

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 the positive integer n is divided  [#permalink]

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02 Jul 2018, 22:11
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Re: If r is the remainder when the positive integer n is divided &nbs [#permalink] 02 Jul 2018, 22:11
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