Random Puzzles 

Workings

Hint
Look at the tops of the towers.

Answer
Add the two lines to the second tower from the left to complete the 'X' in the inverted letter sequence U, V, W, X, Y forming the towers' roofs.

Workings

Hint
What do the fractions add up to?

Answer
There are 980 coins in the collection.

Reasoning
Using fractions:

   ¹/₂ + ¹/₄ + ¹/₅ = ¹⁹/₂₀

The remaining ¹/₂₀ is 49 coins.

Therefore, the ²⁰/₂₀ must equal 20 lots of 49 = 980.

Alternative Reasoning
Using percentages:

   50% + 25% + 20% = 95%

The remaining 5% is 49 coins.

If 5% is 49 coins, 10% is 98 coins, 100% is 980 coins.

Double-Checking
¹/₂ of 980 is 490
¹/₄ of 980 is 245
¹/₅ of 980 is 196
and the remaining 49 coins.

And 490 + 245 + 196 + 49 = 980.

Workings

Hint
This is a very common sequence.

Answer
A.

August, from initial letters of the months of the year.

Workings

Hint
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, …

Answer
71.

The first twenty prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.