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Q.

Is the given statement true or false ?

The greatest 4-digit number is divisible by 3, 9 as well as 11.

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a

True

b

False

answer is A.

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Detailed Solution

The given statement is true.
Concept- The number whose sum of digits is a multiple of 3 is divisible by 3 and 9. The number is divisible by 11 if it leaves a remainder 0 when divided by 11.
Firstly, the greatest 4 digit number is 9999 as the next number is 10000 which is a 5 digit number.
9999 has its sum,

, thus a multiple of 3 and we have,

, thus proving the number is also divisible by 11.
Thus, 9999 is both divisible by 3, 9 and 11 and hence the statement is true.
Hence, the given statement is true.

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