Brain Teasers and Puzzles 

Workings

Hint
The cube root of the given number is a good starting point.

Answer
71, 73, 79.

Reasoning
The cube root of 409,457 is around 74.

The closest consecutive prime numbers to 74 are: 61, 67, 71, 73, 79, 83, 89, 97.

Using a calculator, it is quickly seen that the answer can only be found using 71, 73 and 79.

Workings

Hint
The seventh word is WORTH.

Answer
A bird in the hand is worth two in the bush.

Workings

Hint
Start by filling the 7 gallon container.

Answer
Here are the contents of the containers after each stage:
A  B
0  7    fill B
3  4    fill A from B
0  4    empty A
3  1    fill A from B
0  1    empty A
1  0    fill A from B
1  7    fill B
3  5    fill A from B

This leaves 5 gallons in container B after 8 steps.

Workings

Hint
The answer involves months of the year.

Answer
6.

The number of letters each month has, starting with January, therefore, August has 6 letters.