If the 6-digit numbers x35624 and 1257y4 are divisible by 11 and 72

If the 6-digit numbers x35624 and 1257y4 are divisible by 11 and 72, respectively, then what is the value of (5x-2y)?

 (a) 14

(b) 12

(c) 10

(d) 13

Sol:

In such questions directly check divisibility by 11, 9 and 8.

For a number to be divisible by 11, the difference of the sum of digits at odd or even

places must be divisible by 11.

For a number to be divisible by 9, the sum of numbers must be divisible by 9.

For divisibility by 8, the last 3 numbers must be divisible by 8.

5/6

Accordingly, For x35624 divisible by 11

(x+5+2)-(3+6+4) = 0 or 11

x=6

And For 1257y4 divisible by 72,

1+2+5+7+y+4 must be divisible by 9 and the only possible value of y is 9, here.

also, 784 is divisible by 8 so the desired value of y = 8

Then, 5x-2y = 30-16 = 14