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# When 10 is divided by the positive integer n, the remainder

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Math Expert
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When 10 is divided by the positive integer n, the remainder [#permalink]

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14 Mar 2014, 03:18
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

When 10 is divided by the positive integer n, the remainder is n - 4. Which of the following could be the value of n?

(A) 3
(B) 4
(C) 7
(D) 8
(E) 12

Problem Solving
Question: 164
Category: Algebra Properties of numbers
Page: 84
Difficulty: 600

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Kudos [?]: 128527 [0], given: 12180

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Kudos [?]: 128527 [0], given: 12180

Re: When 10 is divided by the positive integer n, the remainder [#permalink]

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16 Mar 2014, 05:55
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SOLUTION

When 10 is divided by the positive integer n, the remainder is n - 4. Which of the following could be the value of n?

(A) 3
(B) 4
(C) 7
(D) 8
(E) 12

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).

Original question says that when 10 is divided by the positive integer n, the remainder is n-4, so $$10=nq+(n-4)$$ and also $$n-4\geq{0}$$ or $$n\geq{4}$$ (remainder must be non-negative).

$$10=nq+n-4$$ --> $$14=n(q+1)$$ --> as $$14=1*14=2*7$$ and $$\geq{4}$$ then --> $$n$$ can be 7 or 14.

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Re: When 10 is divided by the positive integer n, the remainder [#permalink]

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27 Mar 2014, 21:08
Option A & B are ruled out as n>4

Plugged in 7 & got the answer

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When 10 is divided by the positive integer n, the remainder [#permalink]

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14 Mar 2015, 07:08
Bunuel wrote:
SOLUTION

When 10 is divided by the positive integer n, the remainder is n - 4. Which of the following could be the value of n?

(A) 3
(B) 4
(C) 7
(D) 8
(E) 12

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).

Original question says that when 10 is divided by the positive integer n, the remainder is n-4, so $$10=nq+(n-4)$$ and also $$n-4\geq{0}$$ or $$n\geq{4}$$ (remainder must be non-negative).

$$10=nq+n-4$$ --> $$14=n(q+1)$$ --> as $$14=1*14=2*7$$ and $$\geq{4}$$ then --> $$n$$ can be 7 or 14.

I simply did it this way:

$$y = 10n + (n - 4)$$

And then I just plugged in values for n. So:
$$10(0) + (0-4) = -4$$
$$10(1) + (1-4) = 7$$ <--my answer

Is this correct reasoning, or simply a lucky coincidence?

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Re: When 10 is divided by the positive integer n, the remainder [#permalink]

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14 Mar 2015, 07:39
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erikvm wrote:
Bunuel wrote:
SOLUTION

When 10 is divided by the positive integer n, the remainder is n - 4. Which of the following could be the value of n?

(A) 3
(B) 4
(C) 7
(D) 8
(E) 12

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).

Original question says that when 10 is divided by the positive integer n, the remainder is n-4, so $$10=nq+(n-4)$$ and also $$n-4\geq{0}$$ or $$n\geq{4}$$ (remainder must be non-negative).

$$10=nq+n-4$$ --> $$14=n(q+1)$$ --> as $$14=1*14=2*7$$ and $$\geq{4}$$ then --> $$n$$ can be 7 or 14.

I simply did it this way:

$$y = 10n + (n - 4)$$

And then I just plugged in values for n. So:
$$10(0) + (0-4) = -4$$
$$10(1) + (1-4) = 7$$ <--my answer

Is this correct reasoning, or simply a lucky coincidence?

hi erikvm,
here it is a lucky coincidence..
here you have found the value of y and not n...

$$10(1) + (1-4) = 7$$... here n=1 and y=7.... but the question asks us the value of n...
the equation that you have formed is wrong ..
it says when 10 is divided by the positive integer n, the remainder is n-4.. so the equation will be 10=xn+n-4..

what we have to find is that " when 10 is divided by n, the remainder is n-4"
now substitue the values
(A) 3.... 10/3 rem=1, which is not equal to n-4=3-4=-1.... not correct
(B) 4.... 10/4 rem=2, which is not equal to n-4=4-4=0.... not correct
(C) 7.... 10/7 rem=3, which is equal to n-4=7-4=3.... correct
(D) 8.... 10/8 rem=2, which is not equal to n-4=8-4=2.... not correct
(E) 12... 10/12 rem=10, which is not equal to n-4=10-4=6.... not correct

hope it is clear..
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: When 10 is divided by the positive integer n, the remainder [#permalink]

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02 Jun 2016, 11:38
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Re: When 10 is divided by the positive integer n, the remainder [#permalink]

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11 Jun 2017, 03:52
Hello from the GMAT Club BumpBot!

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Re: When 10 is divided by the positive integer n, the remainder   [#permalink] 11 Jun 2017, 03:52
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# When 10 is divided by the positive integer n, the remainder

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