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Is it true that there is a natural number n for which $4 n$ ends with the digit 0?

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True

False

answer is B.

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Detailed Solution

We have been given a natural number n.
The number which ends with the digit 0, should be divisible by 2 and 5 as their prime factors.
The given condition is that, the expression

4 n

end with digit zero then its factorization should contain the number 5.
Since the factorization of the given expression contains only the form of

(2) 2 n,

and 5 is not present in the prime factorization.
So, there is no natural number n for which

4 n

ends with the digit 0.
Hence, the statement that there is a natural number n for which

4 n

ends with the digit 0 is false.
Correct statement is that there does not exist a natural number n for which

4^{n}

ends with 0.
Therefore, the correct answer is option (2).

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