If a nine-digit number 985x3678y is divisible by 72, then the value of (4x – 3y) is :

 Q) If a nine-digit number 985x3678y is divisible by 72, then the value of (4x – 3y) is : 

(a) 5 

(b) 4 

(c) 3 

(d) 6 

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 solution:

(b) (985x3678y /72) ,

(8×9= 72) so we apply divisibility rule of 8 & 9 

Divisibility rule for 8 => last 3 digits must be divisible by 8.

Then (78y ÷ 8 ) 

If y = 4 then number became 784 it is divisible by 8

here y must be 4

 Divisibility rule for 9 => sum of digits must be divisible by 9. 

Then (9+8+5+x+3+6+7+8+4 50 + x)

here x must be 4 ,

 x = 4, y = 4 

4x –3y = 16 – 12 = 4

Correct answer is : B = 4

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