100,1001,110001, 1100001,1111001, ?, 100100001

Options

A. 10010011
B. 10101001
C. 11011011
D. None of these

Answer

B

Explanation

The given sequence of number is in Binary system and follows the pattern Squares of the consecutive prime numbers
i.e. `2^(2), 3^(2), 5^(2), 7^(2), 11^(2), 13^(2)," and " 17^(2)`.
Converting this Binarysystem into Decimalsystem, we get
`100implies1xx2^2+0xx2^1+0xx2^0`
`implies4+0+0=4=2^(2)`
`1001implies1xx2^3+0xx2^2+0xx2^1+1xx2^0`
`8+0+0+1=9=3^(2)`.
`11001implies1xx2^4+1xx2^3+0xx2^2+0xx2^1+1xx2^0`.
`16+8+0+0+1=25=5^(2)`
`110001implies1xx2^5+1xx2^4+0xx2^3+0xx2^2+0^1xx2^(2)`.
`implies32+16+0+0+0+1=49=7^(2)`
`1111001implies1xx2^6+1xx2^5+1xx2^4+1xx2^3+0xx2^2+0xx2^1+1+2^0`
`64+32+16+8+0+0+1=21=11^(2)`
`10101001implies1xx2^7+0xx2^6+1xx2^5+0xx2^4+1xx2^3+0xx2^2+0+2^1+1xx2^0`
`implies128+0+32+0+8+0+0+1=169=13^(2)`
`100100001implies1xx2^8+0xx2^7+0xx2^6+1xx2^5+0xx2^4+0xx2^3+0+2^2+0xx2^1+1xx2^0`
`implies256+0+0+32+0+0+0+1=289=17^(2)`.