Study the following pattern. In each case write the next three steps :
111 ÷ 3 = 37
222 ÷ 6 = 37
333 ÷ 9 = 37
444 ÷ 12 = 37
Answer
111 ÷ 3 = 37
222 ÷ 6 = 37
333 ÷ 9 = 37
444 ÷ 12 = 37
The numerator increases by 111 and the divisor increases by 3.
Thus, next three steps are :
555 ÷ 15 = 37
666 ÷ 18 = 37
777 ÷ 21 = 37
Study the following pattern. In each case write the next three steps :
999999 x 1 = 0999999
999999 x 2 = 1999998
999999 x 3 = 2999997
999999 x 4 = 3999996
Answer
999999 x 1 = 0999999
999999 x 2 = 1999998
999999 x 3 = 2999997
999999 x 4 = 3999996
The multiplier increases by 1 and the pattern continues accordingly.
Thus, next three steps are :
999999 x 5 = 4999995
999999 x 6 = 5999994
999999 x 7 = 6999993
Study the following pattern. In each case write the next three steps :
12345679 x 9 = 111111111
12345679 x 18 = 222222222
12345679 x 27 = 333333333
12345679 x 36 = 444444444
Answer
12345679 x 9 = 111111111
12345679 x 18 = 222222222
12345679 x 27 = 333333333
12345679 x 36 = 444444444
The multiplier increases by 9 each time and the product forms repeated digits.
Thus, next three steps are :
12345679 x 45 = 555555555
12345679 x 54 = 666666666
12345679 x 63 = 777777777
Observe the following pattern and answer the questions that follow :
1 + 2 + 3 + 4 + 5 = 15
2 + 3 + 4 + 5 + 6 = 20
3 + 4 + 5 + 6 + 7 = 25
(i) By which number should we multiply the middle number to get the sum?
(ii) Write the row of the pattern which gives the sum as 75.
(iii) Can there be any row of the pattern which gives the sum as 92?
Answer
(i) Observing the pattern:
1 + 2 + 3 + 4 + 5 = 15. The middle number is 3 and 3 x 5 = 15.
2 + 3 + 4 + 5 + 6 = 20. The middle number is 4 and 4 x 5 = 20.
3 + 4 + 5 + 6 + 7 = 25. The middle number is 5 and 5 x 5 = 25.
The pattern shows that we should multiply the middle number by 5 to get the sum.
(ii) Using the rule from part (i), we can find the middle number for a sum of 75:
Middle number = 75 ÷ 5 = 15.
The row consists of five consecutive numbers with 15 as the middle number.
The two numbers before 15 are 13 and 14.
The two numbers after 15 are 16 and 17.
Hence, the row is 13 + 14 + 15 + 16 + 17 = 75.
(iii) For a sum of 92, the middle number would have to be:
Middle number = 92 ÷ 5 = 18.4
Since the numbers in the pattern are always integers, the middle number must also be an integer. As 92 is not exactly divisible by 5 (it has a remainder of 2), there cannot be a row of this pattern that gives a sum of 92.
Hence, there will not be any row of the above pattern which gives the sum as 92.
Complete the following magic square by supplying the missing numbers :
Answer
Complete the following magic square by supplying the missing numbers :
Answer
Complete the following magic square by supplying the missing numbers :
Answer
Complete the following magic square by supplying the missing numbers :
Answer
