CAT 2006 — QA Question 20
2 Variable EquationsEasy
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?
Answer & solution
Correct answer: 6
- A
5
6
- C
7
- D
8
- E
10
Solution
Let 10x + y be a two digit number, where x and y are positive single digit integers and x > 0.
Its reverse = 10y + x
Now, |10y + x – 10x – y| = 18
∴ 9 |y – x| = 18
∴ |y – x| = 2
Thus y and x can be (1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8) and (7, 9)
∴ Other than 13, there are 6 such numbers.
Hence, option (b).