Brain Teasers and Puzzles 

Workings

Hint
The top number is 186.

Answer
186 x 39 = 7254.

Workings

Hint
Adding 900,000 to the number is the same as placing a 9 at the beginning.

Answer
23,076.

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

Placing the 9 at the end is equivalent to multiplying by 10 and adding 9 (for example, 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.

Workings

Hint
One answer changes Warm to Worm.

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

or

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

Workings

Hint
The words are all vegetables.

Answer
Caehikort, which is an anagram of artichoke.

The others all begin with the letter C: celery, carrot, cabbage, and cauliflower.