Question

If the number 3422213pq is divisible by 99 ,find the missing digits p and q

Answer 1

On dividing 342221399 by 99 remainder is 49 .

Than subtract 49 from 342221399

we get 342221350.

so value of p is 5

and q is 0

Answer 2

The value of p=1 and q=9.

Step-by-step explanation:

Given : Number 3422213pq is divisible by 99.

To find : The missing digits p and q ?

Solution :

For a number to be divisible by 99, the given number has to be divisible by 9 and 11.

Divisible by 9 test - If sum of digits is divisible by 9 then the number is divisible by 9.

Divisible by 11 test - If sum of ODD positioned digits minus the sum of the EVEN positioned digits is divisible by 11 then the number is divisible by 11.

Sum of numbers 3422213pq,

3+4+2+2+2+1+3+p+q=17+p+q

For divisibility by 9 it is either 18 or 27

So, 17+p+q=18       or    17+p+q=27

     p+q=18 ....(1)     or      p+q=10 ....(2)

Odd- 3+2+2+3+q = 10+q

Even - 4+2+1+p=7+p

10+q-(7+p)=3+q-p is 0 or 11

3+q-p=0           or       3+q-p=11

q-p=-3  ....(3)     or       q-p=8  .....(4)

Taking conditions and solving them

q=9 and p=1

Therefore, the value of p=1 and q=9.

#Learn more

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