Explanation:

Correct option 4 -   4

Given:
The six digit number = 5z3x4y
Concept used:
Divisibility rule of 7 - The difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to 0.
Divisibility rule of 11 - If the difference between the sum of the digits at the odd and even places equals 0 or divisible by 11, then the number is divisible by 11.
Divisibility rule of 13 - A number is divisible by 13 when the ones place digit of a number is multiplied by 4 and the product is added to the rest of the number either gives 0 or a multiple of 13.
7 x 11 x 13 = 1001, when any three digit number multiplied by 1001 then it repeats itself and always completely divisible by 7, 11 and 13.

Solution