Question

Consider the following statements:

(i) If $(2{)}_N\times (4{)}_N=(8{)}_N,where(X{)}_N$ is a number written in a system of writing having N digits, then N can have infinite values.
(ii) If $(4{)}_N\times (5{)}_N=(24{)}_N,$ where $(X{)}_N$ is a number written in a system of writing having N digits, then N will have more than 1, but finite values.
(iii) If $(5{)}_N\times (6{)}_N=(3A{)}_N,$ where $(X{)}_N$ is a number written in a system of writing having N digits and A is the units digit of this number (3A) written in a system of writting the numbers having N digits, then A can have four values.
How many of the above mentioned statements are true?

• A. 1
• B. 2
• C. 3
• D. None of these

Answer 1

The correct option is A 1

Statement I: It is right and N has infinite value greater than 8.
Statement II: It is wrong because it is possible only on base 8
Statement III: It is wrong A has only three vlues 6, 3, and 0 on base 8, 9 and 10, respectively.