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# If n is a negative integer and q is a positive integer, then there is

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nick13 wrote:
If n is a negative integer and q is a positive integer, then there is only one negative integer m such that n= mq +r, where 0 ≤ r ≤ q. The Integer r is called the remainder when n is divided by q. What is the remainder when -100 is divided by 30?

A. -20
B. -10
C. 0
D. 10
E. 20

When x is divided by 5, the remainder is 3.
In other words, x is 3 more than a multiple of 5:
x = 5m + 3

When -100 is divided by 30, the remainder is r.
In other words, -100 is r more than a multiple of 30:
-100 = 30m + r

We can PLUG IN THE ANSWERS, which represent the value of r.
Since the prompt indicates that r ≥ 0, eliminate A and B.
When the correct answer is plugged in, the value of m must be a negative integer, as required by the prompt.

C: r=0
-100 = 30m + 0
-100 = 30m
m = -100/3
Since m is not an integer, eliminate C.

D: r=10
-100 = 30m + 10
-110 = 30m
m = -110/3
Since m is not an integer, eliminate D.

E: r=20
-100 = 30m + 20
-120 = 30m
m=-4
Success!
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Re: If n is a negative integer and q is a positive integer, then there is [#permalink]

nick13 wrote:
If n is a negative integer and q is a positive integer, then there is only one negative integer m such that n= mq +r, where 0 ≤ r ≤ q. The Integer r is called the remainder when n is divided by q. What is remainder when -100 is divided by 30?

A. -20
B. -10
C. 0
D. 10
E. 20

­I do not get it. If I divide -100 by 30, it divides 3 times and gives me the reminder -10, doesn't it?
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Re: If n is a negative integer and q is a positive integer, then there is [#permalink]
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mattsu wrote:
nick13 wrote:
If n is a negative integer and q is a positive integer, then there is only one negative integer m such that n= mq +r, where 0 ≤ r ≤ q. The Integer r is called the remainder when n is divided by q. What is remainder when -100 is divided by 30?

A. -20
B. -10
C. 0
D. 10
E. 20

­I do not get it. If I divide -100 by 30, it divides 3 times and gives me the reminder -10, doesn't it?

­You cannot have negative remainders. Remainders are always non-negative.

To convert negative remainder to positive add that to the divisor.
Hereit is 30+(-10) or 20
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Re: If n is a negative integer and q is a positive integer, then there is [#permalink]

mattsu wrote:
nick13 wrote:
If n is a negative integer and q is a positive integer, then there is only one negative integer m such that n= mq +r, where 0 ≤ r ≤ q. The Integer r is called the remainder when n is divided by q. What is remainder when -100 is divided by 30?

A. -20
B. -10
C. 0
D. 10
E. 20

­I do not get it. If I divide -100 by 30, it divides 3 times and gives me the reminder -10, doesn't it?

dividend = the integer being divided
divisor = the integer being divided into the dividend
quotient = the result after division
remainder = the portion of the dividend that REMAINS after division

Putting it all together:
dividend = (divisor)(quotient) + remainder

When the division of two integers yields a REMAINDER, the reason is that the product in blue is less than than the dividend, so part of the dividend REMAINS.

In the case at hand:
-100 = dividend
30 = divisor
Thus:
-100 = (30)(quotient) + R

Here, a quotient of -3 will make the product in blue GREATER than the dividend in red, so it would be illogical to claim that part of the dividend remains.
For this reason, the quotient here will generally be thought to be not -3 but -4, so that the product in blue is LESS than the dividend of -100:
-100 = (30)(-4) + R
R = 20
­
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If n is a negative integer and q is a positive integer, then there is [#permalink]
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n = mq + r

n = -ve, q = +ve, where 0 ≤ r ≤ q.

i.e. m MUST be -ve

What is remainder when -100 is divided by 30?

CONCEPT: Remainder is ALWAYS POSITIVE or zero
Negative remainder means: Dividend is short of the remainder amount to be divisible by the dividend
Positive remainder means: Dividend is in excess of the remainder amount without which it would be divisible by the dividend

When -100 is divided by 30 then Quotient is -3 and remainder is -10

but -10 remainder is same as remaindr 30-10 = +20

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nick13 wrote:
If n is a negative integer and q is a positive integer, then there is only one negative integer m such that n = mq + r, where 0 ≤ r ≤ q. The Integer r is called the remainder when n is divided by q. What is remainder when -100 is divided by 30?

A. -20
B. -10
C. 0
D. 10
E. 20­

­
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Re: If n is a negative integer and q is a positive integer, then there is [#permalink]
Are there any similar questions to practice?
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Re: If n is a negative integer and q is a positive integer, then there is [#permalink]
jayouh wrote:
Are there any similar questions to practice?

­Check PS Remainders Questions.
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Re: If n is a negative integer and q is a positive integer, then there is [#permalink]
Is this really a remainder question? You can really just fill in the missing values.

N=mq+r
N has to be -100
M is only one negative integer
q has to be 30
r has to be a integer that is positive -> that eliminates A) and B) already

New equation is: -100=(M)(30)+R
Literally just plug C,D,E into R and see if you can make equation work.

Only E) 20 works because M will equal -4

-100=(-4)(30) + 20
Re: If n is a negative integer and q is a positive integer, then there is [#permalink]
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