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Find the greatest number of 4 digits and the least number of 5 digits which when divided by 789 leave a remainder 5 in each case.
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- 9473, 10262
- 9573, 10362
- 9673,10462
- 9676, 10465
Correct Option: A
The greatest number of 4 digits = 9999
Now, we divide 9999 by 789
Thus, when 9999 – 531= 9468 is divided by 789, no remainder is left.
The required greatest number of
4 digits = 9468 + 5 = 9473
The least number of 5 digits
= 10000
Remainder = 532
∴ The least number of 5 digits exactly divisible by 789
= 10000 + (789 – 532)
= 10000 + 257 = 10257
∴ The required number
= 10257 + 5 = 10262
Remark : If 532 is subtracted from 10000 the number obtained 9468 is exactly divisible by 789 but in that case, the number will not be of 5 digits but of 4 digits.