Correct Option (2)
The given sequence of months is: January, January, December, October, X, March, October, Y, September.
A discernible pattern involves a progressive increase in the number of months moved backward in the calendar from one term to the next:
- From the 1st to the 2nd term (January to January): 0 steps backward.
- From the 2nd to the 3rd term (January to December): 1 step backward.
- From the 3rd to the 4th term (December to October): 2 steps backward (December → November → October).
- Applying this pattern, the 5th term (X) must be 3 steps backward from October. Counting backward: October → September → August → July. Therefore, X = July.
- From the 5th to the 6th term (July to March): This step confirms the pattern, as July → June → May → April → March represents 4 steps backward.
- From the 6th to the 7th term (March to October): This step further confirms the pattern, as March → February → January → December → November → October represents 5 steps backward.
- The 8th term (Y) must be 6 steps backward from October. Counting backward: October → September → August → July → June → May → April. Therefore, Y = April.
- From the 8th to the 9th term (April to September): This final step confirms the pattern, as April → March → February → January → December → November → October → September represents 7 steps backward.
Thus, the values for X and Y are July and April, respectively.
Incorrect Options:
Options 1, 3, and 4 propose combinations for X and Y that do not conform to the established logical sequence of progressively increasing backward steps in the calendar. The consistent pattern identified throughout the series necessitates X to be July and Y to be April.