DIRECTIONS for the question:Solve the following question and mark the best possible option.
What is the probability that a two-digit positive integer N has the property that the difference of N and the number obtained by reversing the order of its digits is a perfect cube?
A)
4/45
B)
5/15
C)
6/45
D)
13/90
E)
8/45
D
Let the two digit number is xy. It is given that
(10x + y) – (10y + x) = perfect cube.
⇒ 9 (x – y) = perfect cube. So the perfect cube is a multiple of 9. Now the perfect cube divisible by 9 and less than 198 (as the sum of xy and yx can be maximum 198) is 27.
⇒ 9(x – y) = 27 ⇒ x – y = 3
So the numbers are 14, 25, 36, 47, 58, 69, 41, 52, 63, 74, 85, 96 and 30
So the required probability = 13/90.
