Quote:
The absolute difference between a two digit number and the number formed by reversing the digits of that number is D. What is the number?
Step 1: Understanding the questionLet ten's digit of the number be x and unit's digit be y
Number = 10x + y
Reversed number = 10y + x
Absolute difference = D = |(10x + y) - (10y + x)|
= |10x + y - 10y -x| = |9x - 9y| = = 9| x - y| = 9(x - y) OR 9(y - x)
Step 2: Understanding statement 1 alone(1) D=36
36 = 9(x - y)
x - y = 4
When x = 4, y =0, number = 40
When x = 5, y = 1, number = 51
Insufficient
Step 3: Understanding statement 2 alone(2) The sum of the digits of the number is 12
x + y = 12
When x = 9, y = 3, number = 93
When x = 8, y = 4, number = 84
Insufficient
Step 4: Combining statement 1 and 2When x - y = 4 and x + y = 12
Solving
x = 8, y = 4, number = 84
OR
When y - x = 4 and x + y = 12
Solving x = 4, y = 8, number = 48
Insufficient
E is correct _________________
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