Question
If a six digit number 3x 7z 8y is divisible by 7, 11,
13, then the average value of x, y, z is:Solution
LCM of 7, 11 and 13 is 1001 Any number of the form abcabc is always divisible by 1001 So, abcabc will be divisible by 7, 11 and 13. Comparing with given number, we find x = 8, z = 3 and y = 7 Hence,sum of x + y + z = 8 + 3 + 7 = 18 ∴ Average of x, y and z = 18/3 = 6
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