Brain Teasers and Puzzles 

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.

Workings

Hint
One answer changes Warm to Worm.

Answer
WARM, WORM, WORK, CORK, COOK, COOL

or

WARM, WORM, WORD, WOOD, WOOL, COOL.