Correct Answer - Option 4 : 16
Given:
8 - digit number = 7y9745x2
Divisor = 72
Concept used:
First, we should have to know the factors of divisor if all the factors are divided the given number, then the number is divisibly by 72
Divisibility rule of 8: If the last three digits are divisible by then the number is divisible by 8
Divisibility of 9: If the sum of all digits is divisible by 9 then the number is divisible by 9
2 and 4 are the factors of 8 so, if the number is divisible by 8 is also divisible by 2 and 4
3 is the factor of 9 so, if the number is divisible by 9 then the number is divisible by 3
2 and 3 are the factors of 6
Calculations:
Factors of 72 = 1 , 2, 3, 4, 6, 8, 9
To verify the number is divisible by 8 last three digits = 5x2
If the 6x6 is divisible by 8 then the number must be 512 or 552 or 592
Hence, x = 1 or 5 or 9
To verify the number is divisible by 9 sum of digits =7 + y + 9 + 7 + 4 + 5 + x + 2
⇒ 34 + y + x
34 + y + x is divisible by 9 it must be 36 or 45
34 + y + x = 36
⇒ x + y = 36 - 34
⇒ x + y = 2
If we substitute x = 1
1 + y = 2
⇒ y = 2 - 1
⇒ y = 1
Here, the condition is x > y so x = 1 doesnot satisfy this condition
Let take the number must be 45
⇒ x + y = 45 - 34
⇒ x + y = 11
If we substitute x = 1
1 + y = 11
⇒ y = 11 - 1
⇒ y = 10
x > y but the codition doesnt satisfy 10 is a 2 - digit number
If we substitute x = 5
5 + y = 11
⇒ y = 11 - 5
⇒ y = 6
x < y for this condition so it doesnt satisfy
If we substitute x = 5
9 + y = 11
⇒ y = 11 - 9
⇒ y = 2
x > y so the condition satisfieed
2x - y = 2 × 9 - 2
⇒ 18 - 2 = 16
∴ The required value is 16
