Brain Teasers and Puzzles 

Workings

Hint
A very common sequence is hidden here.

Answer
Badger.

Reasoning
The length of the words is the same length as the months of the year.
   gorilla  = 7 = January
   hedgehog = 8 = February
   camel    = 5 = March
   mouse    = 5 = April
   fox      = 3 = May
   bear     = 4 = June
   mole     = 4 = July
   badger   = 6 = August

Workings

Hint
The answer to 'long root vegetable' is the longest word.

Answers
parsnip = long root vegetable
sprain  = twisted ankle
Paris   = capital of France
rasp    = coarse file
asp     = snake
as      = equally
a       = single article

Workings

Hint
Look at the first letters.

Answer
November.

This is the next month in alphabetical order:

April, August, December, February, January, July, June, March, May, November, October, September.

Workings

Hint
How many minutes are between the times?

Answer
50 minutes.

Reasoning
If we call the number of unknown minutes T.

Between four o'clock and eight o'clock, there are 240 minutes.

There is some point between these two times, before which we have 3 lots of T, and after which we have one lot of T plus 40 minutes.

Therefore, in the 240 minutes, there are 4 lots of T plus 40 minutes.

   240 = 4 x T + 40.

Therefore, T = 50 minutes.