Question

If the number 579683pq is divisible by both 5 and 8, then the smallest possible values of p and q will be:
1. P = 2,q = 2
2. P = 2,q = 0
3. P = 4,q = 3
4. P = 3,q = 0

Answer 1

Correct Answer - Option 2 : P = 2,q = 0

Given:

Number = 579683pq

Concept:

Divisibility test of 5 = Numbers, which last with digits, 0 or 5 are always divisible by 5.

Divisibility test of 8 = If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.

Calculation:

To divisible by 8, q must be zero as when q = 5 then number is not divisible by 8.

For p = 1, last three digit number formed is 310 which is not divisible by 8.

For p = 2, last three digit number formed is 320 which is divisible by 8.

∴ Smallest values of p = 2 and q = 0.