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

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Re: Number properties question from QR 2nd edition PS 164 [#permalink]

06 Mar 2011, 16:54

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Spidy001 wrote:

Bunuel,

I know in this case we don't have to make any assumption, because the question clearly states these are two positive integers.

i was referring more to scenarios like negative number division

-25 /7

-25 = 7(-3)+(-4)

Here remainder is -4 which is negative.

so lets say if question is like x,y are integers x/y . we cannot generalize and say remainder >=0 ,unless we assume that we are only talking about positive integers.

Two things:

1. Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers.
2. A remainder is a non-negative integer by definition (at least on the GMAT).

Anyway you are still wrong when calculating -25/7, it should be: -25=(-4)*7+3, so remainder=3>0.

TO SUMMARIZE, DON'T WORRY ABOUT NEGATIVE DIVIDENDS, DIVISORS OR REMAINDERS ON THE GMAT.
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Re: Number properties question from QR 2nd edition PS 164 [#permalink]

09 Jan 2013, 04:02

Bunuel wrote:

jpr200012 wrote:

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

My strategy was to create lists below:
n = 3, 4, 7, 8, 12
n-4 = -1(becomes 9), 0, 3, 4, 8
n/10 = R? = 3, 4, 7, 8, 4

There is no match between n-4 and n/10's R.

The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers?

Algebraic approach:

THEORY:
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.

Answer: C.

Hope it's clear.

So in this step are we substituting q=0,1 etc or is it something else?

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Re: Number properties question from QR 2nd edition PS 164 [#permalink]

09 Jan 2013, 04:24

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fozzzy wrote:

Bunuel wrote:

jpr200012 wrote:

So in this step are we substituting q=0,1 etc or is it something else?

Not entirely so.

From 10=nq+n-4:

Re-arrange: 14=nq+n;
Factor out n: 14=n(q+1).

So we have that the product of two positive integers (n and q+1) equals 14. 14 can be written as the product of two positive integers only in 2 way: 14=1*14 and 14=2*7. Now, since n\geq{4} then n can be 7 or 14.

Hope it's clear.
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Re: When 10 is divided by the positive integer n, the remainder [#permalink]

10 Jan 2013, 14:55

backsolving works best.

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

21 Feb 2013, 03:55

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

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

21 Feb 2013, 04:05

Hexe1567 wrote:

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

Merging similar topics. Please refer to the solutions provided.

Also, please provide answer choices for PS questions. Rule #8 here: rules-for-posting-please-read-this-before-posting-133935.html
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Re: When 10 is divided by the positive integer n, the remainder [#permalink]

21 Feb 2013, 04:41

Hexe1567 wrote:

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

I get the equation 14 = n (q +1) but I do not know what to do then.

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

21 Feb 2013, 04:47

Hexe1567 wrote:

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

I get the equation 14 = n (q +1) but I do not know what to do then.

Check here: number-properties-question-from-qr-2nd-edition-ps-96030.html#p739404

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

27 Feb 2013, 03:19

I want to follow this question.
hard one of course.

Re: When 10 is divided by the positive integer n, the remainder [#permalink] 27 Feb 2013, 03:19

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

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

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

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