Symbiosis National Aptitude Test SNAP 2017 Paper

8!+9!+ 10! + .............+ 100!=7.6!+ 8.7.6!+ 9.8.7.61 + .......+ 100! is completely divisible by 7 as each of the terms contain at least one 7 in it.
Now, 1!+ 2!+ 3 !+ 4 !+ 5!+ 6!
= 1 + 2 + 6 + 24 + 120 + 720 = 873
which leaves a remainder of 5 when divided by 7.