Find the largest possible value of n, for which a 6-digit number 34159n is divisible by 6.

Correct option is B

Given:

6-digit number = 34159n

Divisible by 6 means divisible by both 2 and 3.

Formula used:

Divisibility rules:

A number is divisible by 2 if its last digit is even.

A number is divisible by 3 if the sum of its digits is divisible by 3.

Solution:

Digits of 34159n = 3, 4, 1, 5, 9, n

Divisibility by 2: n must be even. Possible values: 2, 4, 6, 8

Divisibility by 3: Sum of digits = 3 + 4 + 1 + 5 + 9 + n = 22 + n

For divisibility by 3: 22 + n should be divisible by 3.

Check for each even n:

If n = 2: 22 + 2 = 24 (divisible by 3)

If n = 4: 22 + 4 = 26 (not divisible by 3)

If n = 6: 22 + 6 = 28 (not divisible by 3)

If n = 8: 22 + 8 = 30 (divisible by 3)

Largest possible n = 8