Can remainder be negative?

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srisl11: Senior | Next Rank: 100 Posts; Posts: 72; Joined: Thu Nov 06, 2008 10:27 am; Location: Pittsburgh; Thanked: 4 times

by srisl11 » Wed Nov 19, 2008 11:39 am

There are different opinions regarding remainder in the following post
https://www.beatthegmat.com/remainder-y-3-t23172.html

Can someone please clarify whether remainder can be negative?

I read the definition in https://en.wikipedia.org/wiki/Remainder
but still unclear...
Please help

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Source: Beat The GMAT — Problem Solving | Wed Nov 19, 2008 11:39 am

uttara: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Sun Sep 07, 2008 7:22 am; Location: India; Thanked: 4 times; GMAT Score:700

by uttara » Wed Nov 19, 2008 12:07 pm

this is from GMATPrep:

Quotients and remainders
If x and y are positive integers, there exist unique integers q and r, called the quotient and remainder, respectively, such that y = xq + r and 0 ≤ r < x. For example, when 28 is divided by 8, the quotient is 3 and the remainder is 4 since 28 = ( 8 ) (3) + 4. Note that y is divisible by x if and only if the remainder r is 0; for example, 32 has a remainder of 0 when divided by 8 since 32 is divisible by 8. Also note that when a smaller integer is divided by a larger integer, the quotient is 0 and the remainder is the smaller integer. For example, 5 divided by 7 has the quotient 0 and the remainder 5 since 5 = (7)(0) + 5.

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srisl11: Senior | Next Rank: 100 Posts; Posts: 72; Joined: Thu Nov 06, 2008 10:27 am; Location: Pittsburgh; Thanked: 4 times

by srisl11 » Wed Nov 19, 2008 12:13 pm

[quote="uttara"]this is from GMATPrep:

Quotients and remainders
If x and y are positive integers, there exist unique integers q and r, called the quotient and remainder, respectively, such that y = xq + r and 0 ≤ r < x. For example, when 28 is divided by 8, the quotient is 3 and the remainder is 4 since 28 = ( 8 ) (3) + 4. Note that y is divisible by x if and only if the remainder r is 0; for example, 32 has a remainder of 0 when divided by 8 since 32 is divisible by 8. Also note that when a smaller integer is divided by a larger integer, the quotient is 0 and the remainder is the smaller integer. For example, 5 divided by 7 has the quotient 0 and the remainder 5 since 5 = (7)(0) + 5.[/quote]

According to the definition if both divisor and dividend are +ve , then remainder is +ve...
But what if either the divisor or dividend is negative?

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vishubn: Legendary Member; Posts: 574; Joined: Sun Jun 01, 2008 8:48 am; Location: Bangalore; Thanked: 28 times

by vishubn » Wed Nov 19, 2008 5:05 pm

THis post as well talks about remainders !!
and yes remainders can be negative

https://www.beatthegmat.com/remainders-t23169.html

vishu

KILL !! DIE !! or BEAT my FEAR !!! de@D END!!

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