3s nd 9s
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?
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1 solution
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.