Reversing Digits Increase

CAT 2006 Slot 1 · QA · Easy · Quantitative Aptitude

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When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

  1. A.

    5

  2. B.

    6

  3. C.

    7

  4. D.

    8

  5. E.

    10

Answer

6

Explanation

Let the two-digit number be 10x+y10x + y. Reversed number =10y+x= 10y + x. Difference =(10y+x)−(10x+y)=9(y−x)=18  ⟹  y−x=2= (10y + x) - (10x + y) = 9(y - x) = 18 \implies y - x = 2. Possible pairs (x,y)(x, y) where x≥1x \ge 1 and y≤9y \le 9: (1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8), (7, 9). Total pairs =7= 7. Excluding 13 itself, there are 6 other such numbers (24, 35, 46, 57, 68, 79).

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