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

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

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New post 04 Mar 2018, 05:47
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}
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.


Bunuel - from this \(14=n(q+1)\) how did you get this as \(14=1*14=2*7\) I mean how did you figure out that 7 is n and q is 1 and not some other number combination yielding 14
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Re: When 10 is divided by the positive integer n, the remainder  [#permalink]

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New post 04 Mar 2018, 09:55
nonameee wrote:
Quote:
remainder is always non-negative


Bunuel, I have to disagree with you on that:

http://en.wikipedia.org/wiki/Remainder


As per the formal definition, the remainder is always positive.

However, the concept of negative remainders can be used to ease out calculations.

So, as far as formal treatment (as in case of GMAT) is concerned, please stick to positive remainders.
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Re: When 10 is divided by the positive integer n, the remainder  [#permalink]

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New post 15 Mar 2018, 05:00
vksunder 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


10 = nq + n - 4

take q = 1, we get

10 = n*1 + n - 4

14 = 2n

(C)

Back solving is also a good approach.
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Re: When 10 is divided by the positive integer n, the remainder &nbs [#permalink] 15 Mar 2018, 05:00

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