Let `E = [(1)/(3) + (1)/(50)]+[(1)/(3)+(2)/(50)]+[(1)/(3)+(3)/(50)]+……..` upto `50` terms where `[.]` denotes the greatest integer terms then

Options

A. `E` is divisible by exactly `2` primes
B. `E` is prime
C. `E ge 30`
D. `E le 35`

Answer

B, D

Explanation

For `1 le x le 33`
`(1)/(3) lt (1)/(3) + (x)/(50) lt 1 rArr [(1)/(3) + (x)/(50)] = 0`
for `34 le x le 50`
`1 lt 1/3 + x/50 lt 4/3`
`1 lt [(1)/(3) + (x)/(50)] = 1`
`:. E = 17`