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?

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

The correct option is B 6

Let the number be 10x + y.

Then, $(10y+x)-(10x+y)=18$

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

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 numbers 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.