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 numbers will be represented by $@@@$ ?

Options

A. 22
B. 31
C. 14
D. 17

Answer

D

Explanation

`"@@@$" = 10001`
`= 1 xx 2^(4) + 0 xx 2^(3) + 0 xx 2^(2) + 0 xx 2^(1) + 1 xx 2^(0)`
= 16 + 1 = 17
Correct choice (4).
Quicker method : We write 1, 2, 4, 8 and 16 below the digits and add only those that fall below the 1s.
`{:(1,0,0,0,1),(16,8,4,2,1):}`
`therefore" "16 + 1 = 17`