Question

Find the values of p & q ; if (p1998q) is divisible by 99

Answer 1

Step-by-step explanation:

To solve this you need to know the divisibility test by 11 and 9.

Since the number 3422213pq is divisible by 99, it needs to be divisible by 9 and 11.

Since p and q are single digits they are less than 9

Divisibility test by 9: The sum of the individual numbers of the number 3422213pq should be divisible by 9. So 3+4+2+2+2+1+3+p+q should be divisible by 9 or 17+p+q should be divisible by 9.

Divisibility test by 11: The subtraction of the alternate digits should add up to be divisible by 11. So 3–4+2–2+2–1+3-p+q or 3-p+q should be divisible by 11.

The possible cases for divisibility by 9 are p+q=1 or p+q=10.

The possible cases for divisibility by 11 are q-p=8 or q-p=-3.

The only combination which gives p and q as single digit whole numbers are p+q=10 and q-p=8 which gives p=1 and q=9.