sequences topic

Question

(1) the digits of a positive integer ,having 3 digits when taken in order are in arithmetic progression and their sum is 18 .the number obtained by reversing the digits is 396 less than the original number.what is the number.

 

(a)468

(b)864

(c)594

(d)792

Answer 1

You have a choice (and you should realize that):  either [1] work to answer the problem , then find the correct answer among (a)-(d), or [2] try the problem procedure using each of the possible answers to find the correct one.  Let’s do the latter.

(a) is 4,6,8 an arithmetic progression? Is 4+6+8=18?  Is 468-864=396?
(b) Is 8,6,4 an arithmetic progression? Is 8+6+4=18?  Is 864-468=396?
(c) Is 5,9,4 an arithmetic progression? Is 5+9+4=18?  Is 594-495=396?
(d) Is 7,9,2 an arithmetic progression? Is 7+9+2=18? Is 792-297=396?

Try this yourself, but I get:
     (a)  yes, yes, no
     (b)  yes, yes, yes
     (c)   no, yes, no
     (d)  no, yes, no
 
p.s., using a computer, the method called "exhaustive enumeration" is practical.  The program would try all the three digit numbers (from 000 to 999), add the digits to see if they sum to 18, then reverse them and subtract to see if the difference is 396.  If everything is true, print out the number.  Just for fun, it took me 3 minutes to write the program, and it ran faster than I could time, and the computer says this is true for 783, 864, and 945.  How about that? (and this also explains why they put in 594 to confuse you)