In a certain code, the symbol for 0 (zero) is @ and for 1 is $. There are no other symbols for all other numbers greater than one. The numbers greater than 1 are to be written only by using the two symbols given above. The value of the symbol for 1 doubles itself every time it shifts one place to the left. Study the following examples :
'0' is written as @
'1' is written as $
'2' is written as $@
'3' is written as $$
'4' is written as $@@ and so on
Which of the following will represent the value of the product `3 xx 3 + 1` ?

Options

A. $ @ $ @
B. $ @ $ @ $
C. $ @ @ $ $
D. $ $

Answer

B

Explanation

`3 xx 3 + 1 = 10`. For 10, the binary form is :
`{:(10,0),(5,1),(2,0),(1,):}`
or, 1010 or, $@$@$. Correct choice (2).
Quicker method : Choices (1), (3) and (5) all have a $, i.e. a 1, in the rightmost place. By Tip 1 (A), it is not possible as 10 is an even number. This leaves only choices (2) and (5). Trying out (2), we see that it is indeed a right answer.