Question

If a nine-digit number 785x3678y is divisible by 72, then the value of (x + y) is:
1. 5
2. 12
3. 10
4. 20

Answer 1

Correct Answer - Option 3 : 10

Given:

Nine digit number = 785x3678y

Concept used:

The Law of Divisibility by 8 is the last three digits must be divisible by 8.

The Sum of digits should be divisible by 9.

Calculation:

785x3678y

If the number is divisible by 72 (8 × 9) then it must be divisible by 8 and 9.

Divisible by 8

Law of Divisibility by 8 is last three digits must be divisible by 8

⇒ 78y = 780 + y

⇒ 97 × 8 + ( 4 + y ) is divisible by 8

So value of 4 + y = 8

⇒ y = 4

Divisible by 9

Sum of digits should be divisible by 9

⇒ 7 + 8 + 5 + x + 3 + 6 + 7 + 8 + 4

⇒ 48 + x

⇒ x = 6

x + y

⇒ 6 + 4

⇒ 10

∴ The value of (x + y) is 10.