If a nine-digit number 785x3678y is divisible by 72, then the value of (x + y) is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e 10.
Divisibility law of 8: A number divisible by 8 if its last three digits are divisible by 8
Divisibility law of 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
The nine-digit number is 785x3678y is divisible by 72, so we can say the number also divisible by 8 and 9.
785x3678y is divisible by 8 if the last digit three-digit 78y is divisible by 8.
78y is divisible by 8 if y = 4
785x36784 is divisible by 9 if the sum of its digits is divisible by 9.
⇒ 7 + 8 + 5 + x + 3 + 6 + 7 + 8 + 4
⇒ 48 + x
Put x = 6
⇒ 48 + 6 = 54
As we know, 54 is divisible by 9.
Now,
Value of (x + y) = 6 + 4 = 10