When is the difference between quotRem and divMod useful?

(x `quot` y)*y + (x `rem` y) == x
(x `div`  y)*y + (x `mod` y) == x

Prelude> (-12) `quot` 5
-2
Prelude> (-12) `div` 5
-3

(-11)/5 = -2
(-11)%5 = -1
5*((-11)/5) + (-11)%5 = 5*(-2) + (-1) = -11.

(-11)/5 = -3
(-11)%5 = 4
5*((-11)/5) + (-11)%5 = 5*(-3) + 4 = -11.

let buggyOdd x = x `rem` 2 == 1
buggyOdd 1 // True
buggyOdd (-1) // False (wrong!)

let odd x = x `mod` 2 == 1
odd 1 // True
odd (-1) // True

let odd x = x `rem` 2 /= 0
odd 1 // True
odd (-1) // True