Question

N is an even number when written in the decimal system. If S is the sum of the digits of N, when it is written in base 7, we can surely say that S would always be:

• A. Even
• B. Odd
• C. Composite
• D. Both (a) and (c)

Answer 1

The correct option is D Both (a) and (c)

Assume some values of N.
Eg. Case 1: N = 520
Converting 521 on base 7, we get 1342. S = 1 + 3 + 4 + 2 = 10
Case 2: N = 116
Converting 110 on base 7, we get 224. S = 2 + 2 + 4 = 8.
Hence, S can be both even and composite.