Question

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? (CAT 2006)

• A. 5
• B. 6
• C. 7
• D. 8
• E. 10

Answer 1

The correct option is B 6

Option (b):

Let the number be (10y + x)- (10x + y) = 18

$\Rightarrow 9(y-x)=18\Rightarrow y-x=2$

So, the possible pairs of (x, y) are

(1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8) and (7, 9).

But we want the number other than 13. Thus, there are 6 possible numbers, i.e., 24, 35, 46, 57, 68,79.

So, total number of possible numbers are 6.