Question

If a679b is a five digit no. that is divisible by 72 then a+b is

Answer 1

Heya User,

--> By divisibility, if 72 divides a679b, 9 also divides it..
=> 9 divides ( a + 6 + 7 + 9 + b )
=> 9 divides ( a + 7 + b )

However, a + 7 + b < 27 because they are integers.. So anyhow, 
--> a + 7 + b = 18 or = 9
--> a + b = 11 or  = 2  ----> (i)

But by divisibility of 8, 8 divides 79b
=> b = 2 ----> (ii)

From (i) and (ii) :->
--> a + b = 11 => a = 9 is the only soln.. 

Hence, a+b = 11 only..

Answer 2

$<b><i><u>Answer :</u>$

Given, A679B a number.

Need to find out it is divisible by 72.

⇒ Prime factors of 72 = 9 and 8

So, it is enough to check the given 5-digit number is divisible by 9 and 8.

⇒ To check the number is divisible by 8 last three digits must be divisible by 8.

⇒ 79B is divisible by 8 should be checked.

⇒ Now, from divisibility rule 100b + 10c + d

We get

⇒ 100(7) + 10(9) + B = 790 + B

Substitute a number in B which satisfy the equation using trail error method

⇒ B must be 2 to be divisible by 8

⇒ 792 is divisible by 8

∴ A679B = A6792 is divisible by 8

⇒ A6792 is divisible by 9 only if sum of the given digits is divisible by 9

⇒ A + 6 + 7 + 9 + 2 = A + 24

Put a value in A which satisfy the equation

A = 3

A + 24 = 27 is divisible by 9.

∴ A679B is divisible by 72 and the values of A = 3 and B = 2

Hence, 36792 is divisible by 72