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Math Expert V
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If r is the remainder when integer n is divided by 7, what is the valu  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 76% (01:42) correct 24% (02:00) wrong based on 282 sessions

### HideShow timer Statistics 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

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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

##### General Discussion
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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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we are given n/7 = k + r (where "k" in an integer)

Stmt 1: n/21 = m + o (where "m" is an integer and "o" is odd remainder)
=> n = 21m +21o
=> n/7 = 3m + 3o (this does not gives a clear value for the remainder when n is divided by 7)

Stmt 2: n/28 = t + 3 (where "t" is an integer)
=> n = 28t + 28*3
=> n/7 = 4t + 4*3 = 4t + 12 = (4t + 7) + 5
=> the remainder when n id divided by 7 is 5 or r = 5

Since Stmt 2 is sufficient to get the answer, hence the answer would be 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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hunterdonald 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

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

Can't n b 12 in the second case?
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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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Amit0507 wrote:
hunterdonald 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

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

Can't n b 12 in the second case?

In the 2nd case, we have the equation of the form n=28k+3.

Put the value of k=0,1,2,3,etc.. you will get n =3,31,59,..etc.

Hence, n can never be 12
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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

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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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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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

1) When n is divided by 21, the remainder is an odd number.

when n = 1 , r = 1
when n = 3 , r = 3
NOT SUFF.

2). When n is divided by 28, the remainder is 3
it could be n=3, 31, 59, 87, . . .
the remainder is always 3 when n is divided by 7
2 is SUFF.
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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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