If the 8-digit number 123456xy is divisible by 8, then the total possible pairs of (x,y) are:

Correct option is B

Given:

The number is in the form of 123456xy.

The number is divisible by 8.

We need to find the total possible pairs (x, y) such that the number 123456xy is divisible by 8.

Concept Used:

A number is divisible by 8 if the last three digits of the number are divisible by 8.

Thus, we need to check the divisibility of the number formed by the last three digits 6xy by 8.

For divisibility, 6xy must be divisible by 8.

Solution:

We form numbers using 6xy, where x and y can be any digit from 0 to 9.

We check each combination of x and y such that 6xy is divisible by 8.

The possible values for (x, y) are:

600, 608, 616, 624, 632, 640, 648, 656, 664, 672, 680, 688, 696

This gives us 13 possible combinations.

Therefore, the total possible pairs (x, y) are 13.

Other Method: