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For every positive 2-digit number, a, with units digit x and tens digit y, let b be the 2-digit number formed by reversing the digits of a. Which of the following expressions is equivalent to a - b?
  • a)
    0
  • b)
    9x - y
  • c)
    9y - x
  • d)
    9(x - y)
  • e)
    9(y - x)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
For every positive 2-digit number, a, with units digit x and tens digi...
You are given that a is a number with units digit x and tens digit y. Therefore, x is equivalent to 10 times y, and a = xy = 10x + y. You are given that b is formed by reversing the digits of a. Therefore, b = yx = 10y + x. Set up an equation and solve for a - b as follows:
a − b = (10x + y) − (10y + x)
= 10x + y − 10y − x
= 9x − 9y
= 9(x − y)
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