Random Puzzles 

Workings

Hint
How old was the person in second place?

Answer
# Name    Age
1 Drew    30
2 Emery   24
3 Glen    27
4 Alex    32

Reasoning
By (2), because Glen was three years older, the person in 2^nd place was either 24 or 27.

But 2^nd place can't have been 27, because, by (4), Emery was ahead, but didn't win.

So 2^nd place was 24, and Glen was 27.

By (3), Drew could only be 27 or 30, but we now know what Glen was 27, so Drew was 30.

By (1), the person who came last was 32:
1
2         24
3
4         32

By (4), the 27-year-old can't have won,
1 Drew    30
2         24
3 Glen    27
4         32

By (4), Emery beat the 27-year-old:
1 Drew    30
2 Emery   24
3 Glen    27
4         32

Leaving Alex in last place.
1 Drew    30
2 Emery   24
3 Glen    27
4 Alex    32

Workings

Hint
The first word begins with L.

Answer
Look before you leap.

Using the initial letters of each word.

Workings

Hint
How many rats can one cat catch in 5 minutes?

Answer
5.

  5 cats can catch 5 rats in 5 minutes.

So

  1 cat can catch 1 rat in 5 minutes.

  1 cat can catch 2 rats in 10 minutes.

  1 cat can catch 20 rats in 100 minutes.

Therefore

  5 cats can catch 100 rats in 100 minutes.

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.