Mathematics
In each of the following replace '*' by (i) the smallest digit (ii) the greatest digit so that the number formed is divisible by 3:
(a) 4*672
(b) 4756*2
Answer
For a number to be divisible by 3, the sum of its digits must be divisible by 3.
(a) 4*672
Sum of given digits (except *) = 4 + 6 + 7 + 2 = 19.
We need 19 + * to be divisible by 3.
The values of * which make 19 + * divisible by 3 are 2 (gives 21), 5 (gives 24) and 8 (gives 27).
(i) The smallest digit is 2. The number formed is 42672.
(ii) The greatest digit is 8. The number formed is 48672.
(b) 4756*2
Sum of given digits (except *) = 4 + 7 + 5 + 6 + 2 = 24.
We need 24 + * to be divisible by 3.
The values of * which make 24 + * divisible by 3 are 0 (gives 24), 3 (gives 27), 6 (gives 30) and 9 (gives 33).
(i) The smallest digit is 0. The number formed is 475602.
(ii) The greatest digit is 9. The number formed is 475692.
Related Questions
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(i) 93573
(ii) 217944
(iii) 5034126
(iv) 901352
(v) 639210
(vi) 1790184
In each of the following replace '*' by a digit so that the number formed is divisible by 9:
(i) 4710*82
(ii) 70*356722
In each of the following replace * by a digit so that the number formed is divisible by 11:
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(ii) 9*53762
In each of the following replace * by (i) the smallest digit (ii) the greatest digit so that the number formed is divisible by 6:
(a) 2*4706
(b) 5825*34