Question 13

The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B > A and B-A is perfectly divisible by 7, then which of the following is necessarily true?

Solution

Ā Let A = 100x + 10y + z Ā and B = 100z + 10y + x .According to given conditionĀ B - A = 99(z - x) As (B - A) is divisible by 7 . So clearly Ā (z - x) should beĀ Ā divisible by 7.Ā Ā z and x can have values 8,1 or 9,2 , such that 8-2=9-2=7 andĀ Ā y can have Ā value from 0 to 9.
So Lowest possible value of A lowest x,y and z which is Ā is 108 and the highest possible value of A is 299.Ā 

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