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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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What is the remainder when -100 is divided by -30? [#permalink]

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12 Mar 2016, 05:30
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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.
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Aug 2009
Posts: 5649
Re: What is the remainder when -100 is divided by -30? [#permalink]

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12 Mar 2016, 05:37
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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,

If we know this RULE, we can answer the answer easily..

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

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

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14 Mar 2016, 16:59
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What is the remainder when -100 is divided by -30?

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

-> N,q,q,r are integers. p=divisor q=quotient, and r=remainder from N=pq+r, in which 0≤r<|p| is derived. That is, the remainder has no negative numbers. Thus, -100=(-30)(4)+20 -> 0≤20<|-30|=30. E is the answer.
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What is the remainder when -100 is divided by -30? [#permalink]

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16 Mar 2016, 23:32
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,

If we know this RULE, we can answer the answer easily..

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

hey chetan2u I too marked D but with a hesitation..
I remember in my class 6 my teacher telling me that Remainder is always less than or equal to zero and divisor must be greater than than the remainder
here remainder is positive => YES
but it isn't < the divisor..
AM i missing something?

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

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21 Mar 2017, 23:34
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What is the remainder [#permalink]

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28 Apr 2017, 15:40
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What is the remainder when -100 is divided by -30?
A. -10
B. 0
C. 10
D. 15
E. 20
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Re: What is the remainder [#permalink]

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28 Apr 2017, 18:21
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mkrishnabdrr wrote:
What is the remainder when -100 is divided by -30?
A. -10
B. 0
C. 10
D. 15
E. 20

The main point here is that the remainder is always POSITIVE
So don't get trapped in -100=-30*3-10 and take -10 as remainder.
The remainder will be -100=-120+20=-30*4+20...
20..
E
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Re: What is the remainder [#permalink]

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28 Apr 2017, 18:25
Why ×4? Why not ×5 or ×6?

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Re: What is the remainder [#permalink]

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28 Apr 2017, 18:48
When we are calculating remainders and we cancel out any signs/common terms it is imperative to add back the same to the final remainder to arrive at the final solution.
e.g remainder of 10/4 can be simplified to 5/2 (by cancelling out 2)---->5/2 gives us a remainder of 3
Hence the final remainder is 6 (3*2) <-----please note how 2 was multiplied back after arriving at the remainder by simplification

Applying the same concept in this problem, we can cancel the common term -1. In this case after removing the negative signs, Remainder of 100 divided by 30 is 10 and a negative remainder of -20 (Concept on Negative remainder discussed in the link/post below)

Now considering we had cancelled out the negative signs we need to multiply the same back. Thus the final remainders are -10 and 20.

Considering by definition remainders are positive (0<=r<d, where r=remainder and d=divisor), hence the solution is 20.

Please refer the below discussion for negative remainders
https://www.veritasprep.com/blog/2014/0 ... -the-gmat/

Kudos please if the post helped !
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Re: What is the remainder when -100 is divided by -30? [#permalink]

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29 Apr 2017, 02:23
mkrishnabdrr wrote:
What is the remainder when -100 is divided by -30?
A. -10
B. 0
C. 10
D. 15
E. 20

Merging topics. Please search before posting.

You sited the source of this question as Official Guide. It cannot be from OG because remainder questions are limited to positive integers on the GMAT. Because of this one can ignore this question altogether and move on.
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Re: What is the remainder when -100 is divided by -30? [#permalink]

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13 Aug 2017, 04:26
mkrishnabdrr wrote:
Why ×4? Why not ×5 or ×6?

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If we take x5, then remainder will be -50. But this is not valid because remainder cannot be greater than divisor
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Re: What is the remainder when -100 is divided by -30? [#permalink]

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19 Aug 2017, 22:56
Do we have some rule on taking modulus of divisor?

MathRevolution wrote:
What is the remainder when -100 is divided by -30?

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

-> N,q,q,r are integers. p=divisor q=quotient, and r=remainder from N=pq+r, in which 0≤r<|p| is derived. That is, the remainder has no negative numbers. Thus, -100=(-30)(4)+20 -> 0≤20<|-30|=30. E is the answer.
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Re: What is the remainder when -100 is divided by -30? [#permalink]

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04 Sep 2017, 15:47
remainder is always positive
in such I case I prefer to use modular arithmetic , if it's not too complicated clock-based method is sufficient
One important thing to remember ff the dividend is positive we step clockwise, if it's negative we step counter-clockwise
100 is 3 time 30 and leaves us with 10, so start counting counter-clockwise from 29 ( after 3 full clock circles)
29 28 27 26 25 24 23 22 21 20
Re: What is the remainder when -100 is divided by -30?   [#permalink] 04 Sep 2017, 15:47
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