Brain Teasers and Puzzles 

Workings

Hint
Look at the vowels (AEIOU).

Answer
7.00pm.

Each vowel (AEIOU) of the country is worth 2 hours, and each consonant is worth 3 hours.

The time shown is the number of hours past midnight of the return trip.

Workings

Hint
How many rooms could Alex clear in 36 hours?

Answer
12 hours.

In 36 hours Alex can clear 2 rooms, Billie can also clear 2 rooms, and Drew would fill 1 room. So 2 + 2 - 1 = 3 rooms in 36 hours. Which is 12 hours for a single room.

Alternatively:

Alex and Billie each clear 1/18 of the room in 1 hour, but Drew is filling 1/36 of the room in one hour. So in one hour we have 1/18 + 1/18 - 1/36 = 1/12. So it takes 12 hours to complete the task.

Workings

Hint
The top number is 186.

Answer
186 x 39 = 7254.

Workings

Hint
What's a mathematical way to describe placing a 9 at the beginning?

Answer
23,076.

Reasoning
Placing the 9 at the beginning is equivalent to adding 900,000 (e.g. 12,345 + 900,000 becomes 912,345).

Placing the 9 at the end is equivalent to multiplying by 10 and adding 9 (e.g. 12,345 x 10 + 9 becomes 123,459).

Let's call the unknown number k, and we know that one of these numbers is 4 times the other, so:

 k + 900,000 = 4 x (10k + 9)

 k + 900,000 = 40k + 36

900,000 - 36 = 40k - k

     899,964 = 39k

899,964 ÷ 39 = k

Therefore k = 23,076.

Double-Checking
923,076 = 4 x 230,769. This confirms the answer.