Random Puzzles 

Workings

Hint
As we don't know how of the people were library members, you can try a random number and see what happens.

Answer
4,200 books.

Reasoning
It doesn't matter how many library members there were, as ¹/₂ of them accepted the books, and each accepted 6 books, which is 3 books per member on average.

Similarly, it doesn't matter how many non-members there were as ³/₄ of them accepted the books, and each accepted 4 books, which is again 3 books per non-member on average.

Double-Checking
Both the members and non-members accepted, on average, 3 books each.

And 1400 x 3 = 4200.

Workings

Hint
Try starting with the cube root of the number.

Answer
42, 44, and 46.

Reasoning
As we require 3 numbers that are multiplied together, we can start with the cube root of 85,008 ≈ 43.97.

We can now check that 44 divides 85,008 exactly: 85,008 ÷ 44 = 1,932, which means that 44 is likely to be one of the numbers.

And as we know that we need consecutive even numbers, we soon find 42 and 46 as the remaining numbers.

Double-Checking
42 x 44 x 46 = 85,008.

Workings

Hint
Think of the whole alphabet, and not just the vowels (AEIOU).

Answer
8,300.

Each letter of the country is worth 100 miles based on its position in the alphabet.

Therefore, Germany = 7 + 5 + 18 + 13 + 1 + 14 + 25 = 83 x 100 miles.

Workings

Hint
The word APRIL appears 34 times.

Answer
The word APRIL appears 34 times.