Random Puzzles 

Workings

Hint
How many 1 x 1 squares are there?

Answer
91 squares.

Reasoning
Squares of size:
   1 x 1 = 36
   2 x 2 = 25
   3 x 3 = 16
   4 x 4 = 9
   5 x 5 = 4
   6 x 6 = 1

Total = 36 + 25 + 16 + 9 + 4 + 1 = 91.

Workings

Hint
Perhaps looking around the shapes will help.

Answer
C.

Reasoning
The shapes are the spaces between the digits in the numbers 27, 28, 29, and 30, therefore C is the correct answer, as it is the space between the digits in the number 31.

Workings

Hint
What numbers divide into 703?

Answer
The 37 pupils each received 19 sweets.

Reasoning
703 can only be broken down into 19 x 37, it has no other factors.

Workings

Hint
It will take a while to check 1 x 7, 2 x 7, 3 x 7. What do we know about the answer?

Answer
63,492 x 7 = 444,444

Reasoning
We can work backwards, as we know that the number multiplied by 7 has only 4's. We can try the following:
      4 ÷ 7 ≈ 0.57     x
     44 ÷ 7 ≈ 6.29     x
    444 ÷ 7 ≈ 63.43    x
  4,444 ÷ 7 ≈ 634.86   x
 44,444 ÷ 7 ≈ 6,349.14 x
444,444 ÷ 7 = 63,492