Question

(i) The difference between the two numbers appearing on two opposite faces of a die is 1. Find the product of these two numbers.
(3 Marks)

(ii) How many minimum squares should be painted blue to make the given figure symmetrical?


(2 Marks)

Answer 1

Solution:
(i) 12
(ii) 3


Explanation:
(i) The sum of the digits on opposite faces of a die = 7
It is given that the difference between the two numbers appearing on two opposite faces of a die is 1.
(1 Mark)
The pair of the numbers on the opposite faces are
1, 6 (6 - 1 = 5)
2, 5 (5 - 2 = 3)
3, 4 (4 - 3 = 1)
So, the pair of the numbers when the difference between the two numbers appearing on two opposite faces of a die is are 4, 3.
(1 Mark)
Product of 4 and 3 = 4 × 3 = 12
(1 Mark)

(ii) The total number of squares in the given figure = 9
Paint 3 squares in the given shape as shown below, the given shape will become symmetrical.
Also, painting all squares in the given shape, then also it will become symmetrical.
But the question is asking for the minimum number of squares that are needed to be painted blue.
So, 3 squares will be minimum.
(1 Mark)

(1 Mark)