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

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

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

Why ×4? Why not ×5 or ×6?

Please give kudos, help me unlock Gmatclub tests.

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.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/0 ... -the-gmat/


Kudos please if the post helped !

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.

If we take x5, then remainder will be -50. But this is not valid because remainder cannot be greater than divisor

Do we have some rule on taking modulus of divisor?

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

When \(-100\) is divided by \(-30\), what is the remainder?

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

Since the remainder is always positive, equation can not be -100 = (-30)*3 - 10
Therefore,
-100 = (-30)*4 + 20
Remainder = 20

Hence, E.

ammuseeru MathRevolution KarishmaB Bunuel pushpitkc pikolo2510 chetan2u niks18




Why we can not write:

\(-100\) is divided by \(-30\)

as

\(100\) is divided by \(30\) and get remainder as 1 after simplifying fractions?

Since you simplified the fractions, the remainder is also simplified.

To get the original remainder you need to multiply the current remainder (i.e. 1) with the number that you simplified with (i.e. -10)

Hence, now the remainder is -10

A remainder cannot be negative. subtract the negative remainder from the divisor to get the correct remainder
=30 - 10
=20

Hence answer is 20

P.S : - You can try the above with an example such as 60/25.

Hiii
Whenever we cancel out common terms before dividing to find reminder, always remember to multiply that common factor to get the actual remainder.
Please see this.

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 !?

Please see my detailed explanation, how to find remainder when we cancel out the common terms.



Posted from my mobile device

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