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

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VP
Joined: 09 Mar 2016
Posts: 1234
Re: When 10 is divided by the positive integer n, the remainder  [#permalink]

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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.

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
Intern
Joined: 15 Oct 2016
Posts: 30
Re: When 10 is divided by the positive integer n, the remainder  [#permalink]

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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.
VP
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1355
Location: India
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Re: When 10 is divided by the positive integer n, the remainder  [#permalink]

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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.
_________________

"Do not watch clock; Do what it does. KEEP GOING."

Re: When 10 is divided by the positive integer n, the remainder &nbs [#permalink] 15 Mar 2018, 05:00

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