Use this to find what design appears at positions 99, 122, and 148. Class 7
mediumUse this to find what design appears at positions 99, 122, and 148. Class 7
Question 1.
Use this to find what design appears at positions 99, 122, and 148. Class 7
| Position no. | Quotient on division by 3 | Remainder |
| 99 | 33 | 0 |
| 122 | 40 | 2 |
| 148 | 49 | 1 |
Solution:
Design C, Design B and Design A respectively. It is because 99 is a multiple of 3 (3 × 33), 122 = 120 + 2 is of the form 3n + 2 (3 × 40 + 2) and 148 = 147 + 1 is of the form 3n + 1 (3 × 49 + 1).
Question 2.
Will this always happen? How do you show this? Class 7
[Hint : Consider a general set of numbers that forms this shape. Take the number at the centre to be ‘a’. Express the other numbers in terms of‘a’.]
Solution:
Yes. General 3 × 3 grid.
| a | ||
| a + 6 | a + 7 | a + 8 |
| a + 14 |
Total sum = 3a + 21 + a + a + 14
= 5a + 35
= 5(a + 7),
i. e., five times the number at the centre.
Question 3.
Find other shapes for which the sum of the numbers within the figure is always a multiple of one of the numbers. Class 7
Solution:
Other shapes, the answer is yes.
| a | ||||
| a + 7 | ||||
| a + 12 | a + 13 | a + 14 | a + 15 | a + 16 |
| a + 21 | ||||
| a + 28 |
It is a 5 × 5 grid.
Here, total sum
= 5a + 70 + a + a + 7 + a + 21 + a + 28
= 9a + 70 + 56 = 9a + 126
= 9 (a + 14)
i. e., a multiple of the number at the centre.