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# What is the remainder when -100 is divided by -30?

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Re: What is the remainder when -100 is divided by -30?  [#permalink]

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06 Aug 2018, 04:48
1
gmatbusters

I could get your solution, but to ensure what I understood,
I would like to take a similar example of -12 / -5

Remainder = 2 quotient = 2
Since common factor = -1 , actual remainder is 2 * -1 ie -2 (invalid since negative remainder)

Now comes the turning point, we did not need to use dividend = (divisor) * integer quotient + remainder

What chetan2u and you did was to simply arrange terms to get a positive remainder.

In this example:
How can I write -12 :

-12 = (-5) * 3 + 3

The 3 (next to 5) is next successive number than what I got earlier as a quotient. The 3 after addition sign is my remainder

So actual remainder is 3.

dave13

Quote:
WHY $$\frac{-100}{-30}$$= $$3.10$$ isnt it correct answer arithmetically-mathematically

Did you by chance took inverse ratio of fraction ?
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Re: What is the remainder when -100 is divided by -30?  [#permalink]

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06 Aug 2018, 05:58
You are right...
Perfect.

Posted from my mobile device
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Re: What is the remainder when -100 is divided by -30?  [#permalink]

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06 Aug 2018, 06:27
1
@dave13, when we use actual division to calculate remainder. Follow the steps
1. Divide and find the decimal part.
2. Multiply decimal part by quotient.

In your approach, -100/ -30 = 3.3333
Decimal part = 0.333333..
Remainder = 0.3333...*(-30) = -10.

So remainder ( which is taken positive) = -10 +30 = 20.

(Always add absolute value of quotient to negative remainder to get the final remainder)

Hope it is clear now, don't hesitate to tag me in case of any doubt.

dave13 wrote:
gmatbusters $$\frac{-100}{-30}$$ isnt this fraction valid ? division of two negative numbers yields positive number, right ? IF SO, then

WHY $$\frac{-100}{-30}$$= $$3.10$$ isnt it correct answer arithmetically-mathematically !?

Posted from my mobile device[/quote]

gmatbusters your explanation is DETAILED. thank you for taking time to explain. But I cant see those DETAILS its impossible for me to decode your handwritten DETAILS [/quote]
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Re: What is the remainder when -100 is divided by -30?  [#permalink]

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06 Aug 2018, 06:38
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dave13,
Bro it seems in place of quoting, I edited your post by mistake.
Forgive me
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Re: What is the remainder when -100 is divided by -30?  [#permalink]

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06 Aug 2018, 06:42
Perfect.
gmatbusters

I could get your solution, but to ensure what I understood,
I would like to take a similar example of -12 / -5

Remainder = 2 quotient = 2
Since common factor = -1 , actual remainder is 2 * -1 ie -2 (invalid since negative remainder)

Now comes the turning point, we did not need to use dividend = (divisor) * integer quotient + remainder

What chetan2u and you did was to simply arrange terms to get a positive remainder.

In this example:
How can I write -12 :

-12 = (-5) * 3 + 3

The 3 (next to 5) is next successive number than what I got earlier as a quotient. The 3 after addition sign is my remainder

So actual remainder is 3.

dave13

Quote:
WHY $$\frac{-100}{-30}$$= $$3.10$$ isnt it correct answer arithmetically-mathematically

Did you by chance took inverse ratio of fraction ?

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Re: What is the remainder when -100 is divided by -30?  [#permalink]

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13 May 2019, 09:35
chetan2u wrote:
MathRevolution wrote:
What is the remainder when -100 is divided by -30?

A. -10
B. 0
C. 10
D. 15
E. 20

* A solution will be posted in two days.

Hi,

RULE- REMAINDER is always positive....

here $$-100 = -30*3-10$$so remainder is -10, which is not VALID answer
$$-100= -30*4+20..$$
Now th eremainder is 20, a positive quantity
ans 20
E

Hi Chetan,

But there also a point that for example: if we take 7 divided by 8 the remainder is either 7 or -1. So is it always true to say that remainder is +ve. Please correct me if I am wrong.

Regards,

Aviral
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Re: What is the remainder when -100 is divided by -30?  [#permalink]

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08 Sep 2019, 02:49
when we divide -100/-30, we got -10 and the reminder can not be negative so we add 30 to correct it the solution will be 20
Re: What is the remainder when -100 is divided by -30?   [#permalink] 08 Sep 2019, 02:49

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