Question

If a nine-digit number 785x3678y is divisible by 72, then the value of (x - y) is :

• A. 0
• B. -2
• C. -1
• D. 2

Answer 1

Answer:

D. 2

Solution: Given: Given number is 785x3678y The number is divisible by 72 Concept used: If a number is divisible by 72 then the number will be divisible by 8 and 9 A number is divisible by 8 if the last three digits are divisible by 8. A number is divisible by 9 if the sum of its digits is divisible by 9. Calculation: As, the number 785x3678y is divisible by 8 ⇒ 78y is divisible by 8 For y = 4, the number is divisible by 8 As, the number 785x3678y is divisible by 9 ⇒ 7 + 8 + 5 + x + 3 + 6 + 7 + 8 + y is divisible by 9 ⇒ 44 + x + y is divisible by 9 ⇒ 44 + x + 4 is divisible by 9 ⇒ 48 + x is divisible by 9 Nearest integer to 48 is 54 which is divisible by 9 48 + x = 54 ⇒ x = 6 x – y = 6 – 4 ⇒ 2 ∴ The value of (x – y) is 2