Question 56

If a 10-digit number 6220x558y2 is divisible by 88, then the value of (5x + 5y) can be:

Solution

we have : 6220x558y2 and the number is divisible by 88 
Now 88 = 8* 11 
So we can say the number is divisible by both 8 and 11
Now we know that for a number to be divisible by 8 , the last three digits should be divisible by 8
So we can say y can be either 3 or 7
Now taking y =7
we get the number as 6220x55872
Now taking divisibility of 11 which says |sum of digits at even places - sum of digits at odd places | mod 11 =0
so taking that we get :|17-20-x| mod 11 =0
we get x=8
Now 5x+5y = 105
Now similarly taking case y=3
we get number as 6220x55832
Now taking divisibility of 11 :
we get 17-16-x mod 11=0
we get x=1
Now 5x+5y =20
So from options we can say
5x+5y can be 20


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