Aptitude - Numbers

99 = 11 x 9, where 11 and 9 are co-prime.

By hit and trial, we find that 114345 is divisibleby 11 as well as 9. So, it is divisible by 99.

This is an A.P. in which a = 6, d = 6 and S_n = 1800

	n	[2 x 6 + (n - 1) x 6] = 1800
	2

3n (n + 1) = 1800

n(n + 1) = 600

n² + n - 600 = 0

n² + 25n - 24n - 600 = 0

n(n + 25) - 24(n + 25) = 0

(n + 25)(n - 24) = 0

n = 24

Number of terms = 24.

This is an A.P. in which a = 51, l = 100 and n = 50.

Sum =	n	(a + l)	=	50	x (51 + 100)   = (25 x 151)   = 3775.
	2			2

Unit digit in 7⁹⁵ = Unit digit in [(7⁴)²³ x 7³]
= Unit digit in [(Unit digit in(2401))²³ x (343)]
= Unit digit in (1²³ x 343)
= Unit digit in (343)
= 3

Unit digit in 3⁵⁸ = Unit digit in [(3⁴)¹⁴ x 3²]
= Unit digit in [Unit digit in (81)¹⁴ x 3²]
= Unit digit in [(1)¹⁴ x 3²]
= Unit digit in (1 x 9)
= Unit digit in (9)
= 9

Unit digit in (7⁹⁵ - 3⁵⁸) = Unit digit in (343 - 9) = Unit digit in (334) = 4.

So, Option B is the answer.