State True or False.

The number 2070 is divisible by 6.

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True

False

answer is A.

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Detailed Solution

The given statement is the number 2070 is divisible by 6.
We use the rule for checking the divisibility of any number by 6.
It says that if the number is divisible both by 2 and 3, we deduce that the same number is divisible by 6.
We know that the number is divisible by 2 when it ends with a digit 0 or any even number.
We also know that the number is divisible by 3 only when the sum of all the constituent digits of the number is divisible by 3.
We find that the given number has 0 at its end, and hence it is divisible by 2.
Now, we get this result as the sum of all the constituent digits of the number.
⇒2+0+7+0 = 9
We know this resultant number is divisible by 3 as

9 ÷ 3 = 3

.
That is, abiding by the rule of divisibility of any number by 6, we get that the number 2070 is divisible by 6.
Therefore, the given statement is true.
Hence the correct answer is option (1).

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