Question

if the number 2345p 60q is exactly divisible by 3 and 5 then the maximum value of (p+q) is. Show with the solution.

Answer 1

Here is your step by step solution.

If the given number is divisible by 3

=> sum of the digits of the given number should also be divisible by 3.

i.e., 20+p+q should be divisible by 3. ........(1)

Now, It's also divisible by 5 so by divisibility rule of 5 , q should be 0 or 5.

When q =0. putting the value of q in (1)

20+p should be divisible by 3.

For this possible values of p will be 1,4 or 7.

Therefore when q=0 and p=1,4 or 7 then possible values of

p+q are 1,4 or 7.

Again, when q=5 putting the value of q in (1) 25+p should be divisible by 3.

For this possible values of p will be 2,5 or 8.

Therefore when q= 5 and p= 2,5 or 8 then possible values of

p+q are 7,10 or 13.

Hence, among all the possible values of p+q 13 is the maximum so 13 will be the required answer.

I hope you will get it.