A number n is such that 3n and n both have the same sum of digits. (Sum of digits means 17 has 1+7=8 as its sum of digits). n is a natural number. Then:

A. 3n is a multiple of 9

B. n is a multiple of 3

C. n is a multiple of 9

D. 3n is a multiple of 81.

E. 3n is a multiple of 3

Which of the above are DEFINITELY true?

Only E
A B C D E
A B C E
A B E

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3n is clearly a multiple of 3. Thus n having same digit sum, is a multiple of 3. If n = 3p, 3n = 9p. Thus 3n, is a multiple of 9.

n has same digit sum. Thus n is also a multiple of 9. Thus A,B,C,E are DEFINITELY true.