Question

A palindrome number is a number that remains the same when its digits are reversed, for example 83438. The number x and x + 32 are three digit and four digit palindromes respectively. What is the sum of the digits of the number x? Select one:

Answer 1

$$\begin{gathered} \mathrm{Since},\mathrm{x}\mathrm{is}\mathrm{a}3-\mathrm{digit}\mathrm{number}\mathrm{and}\mathrm{x}+32\mathrm{is}\mathrm{a}4-\mathrm{digit}\mathrm{number}. \\ \mathrm{As}999\mathrm{is}\mathrm{the}\mathrm{largest}3-\mathrm{digit}\mathrm{number},\mathrm{then}\mathrm{x}+32\mathrm{is}\mathrm{less}\mathrm{than}\mathrm{or}\mathrm{equal}\mathrm{to}1031. \\ \mathrm{Therefore},\mathrm{x}+32\mathrm{lies}\mathrm{between}1000\mathrm{and}1031.\mathrm{Clealy},1001\mathrm{is}\mathrm{the}\mathrm{only}\mathrm{palindrome} \\ \mathrm{number}\mathrm{between}1000\mathrm{and}1031. \\ \mathrm{Hence},\mathrm{x}+32=1001 \\ \mathrm{and}\mathrm{x}=1001-32=969,\mathrm{which}\mathrm{also}\mathrm{is}\mathrm{a}\mathrm{palindrome}\mathrm{number}. \\ \mathrm{The}\mathrm{sum}\mathrm{of}\mathrm{digits}\mathrm{of}\mathrm{number}\mathrm{x}=969\mathrm{is} \\ 9+6+9=24. \end{gathered}$$