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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 by 7 what  [#permalink]

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Question Stats: 77% (01:37) correct 23% (01:54) wrong based on 249 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.

Attachment: Remainder.JPG [ 73.19 KiB | Viewed 4651 times ]

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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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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

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

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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 by 7 what  [#permalink]

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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 integer n is divided by 7, what is the valu  [#permalink]

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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

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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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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

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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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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

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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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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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