Question

When the digits of two-digit, positive integer M are reversed, the result is the two-digit, positive integer N. If M > N, what is the value of M?

(1) The integer (M - N) has 12 unique factors.
(2) The integer (M - N) is a multiple of 9.

Answer 1

Option (2) is the correct answer for the above question.

Step-by-step explanation:

When the user takes two digits of positive integer represented by M but the reverse of M is represented by N. but when M>N then M-N is a multiple of 9.

Just for example if a user takes--

• M=21 then N=12 then M-N= 9.
• M=31 then N=13 then M-N=18.
• M=41 then N=14 then M-N=27.

Here when a user takes a two-digit number for M and N will be reverse of M then M-N is always the multiple of 9 in which M-N lies in (9 to 72). where only 72 have 12 factors. so option 1 is only correct for M-N=72. Hence Option 1 is not correct. but option 2 is correct.