1. If a four digit number 132B is divisible by 3. How many possible values are the for the digit B?

Solution:

First, try dividing the first 3 digits by 3.

Take 132 divide by 3 and you’ll get 44

If 132 is divisible by 3, it would mean that digit B has to be a multiple of 3 as only when digit B is 3, 6 or 9 then 132B is divisible by 3.

Many students would think that 3 is the final answer for the number of possible values for B

But let’s no forget that 0 is also divisible by 3

Therefore final answer should be 4 possible values as 0, 3, 6 and 9 can all be possible values for digit B.

2. The desks in a classroom are arranged in straight rows. Each row has the same number of desks. William sits at the desk that is in the fourth row from the front and back. He sits at the centre of his row and there are 5 desks to his left. How many desk are in the classroom altogether?

Front

Back

From the question, we can derive that each row has the same number of desks.

William sits at the desk that if fourth row from the front and back. This means there are 3 rows in front of him and 3 rows behind. This would mean total of 7 rows.

He sits in the centre of his row and there are 5 desks to his left. As he is in the centre, it would mean that there are 5 desks to his right too. This gives us 11 desks (including William’s) in a row.

Therefore, 11 desks per row and total of 7 rows would give us a total of 7 x 11 = 77 desks

3. Study the pattern and find the sum of numbers in the 10th column.

2 | 4 | 4 | 8 | 6 | 12 | |

2 | 3 | 6 | 6 | 10 | 7 |

If we look at the top row and second row individually, we cannot distinguish any pattern formed. Simliarly, if we look at each column individually, we cannot distinguish any pattern formed

If we look at the numbers in a zig-zag pattern from left to right, starting with the top row, we can see that the digits increase by 1 for each passing column (highlighted in yellow)

Subsequently, look at the numbers in a zig-zag pattern from left to right, starting with the bottom row, we can see that the digits increase by 2 for each passing column

At the 10th column, we get 20 for the top row and 11 for the bottom row. Hence, the answer is 20 + 11 = 31 for the sum of numbers in the 10th column

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