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
