The correct option is E 1
Using statement A alone,
Sum of dates of last Monday of previous month and 1st Thursday of next month is 38 is possible only if last Monday is 31st and 1st Thursday is 7th.
(Since if we take 30 + 8 = 38, then 30 can be last Monday of any month but 8th can not be the 1st Thursday of any month)
So, 31st of last month is a Monday. Hence 7th of current month,14th of current month, 21st of current month, 28th of current month will be a Monday.
Now, if current month is a month with 30 days, then 5th of next month will be a Monday, so 7th of next month cannot be a Thursday.
If current month is a month with 31 days, then 4th of next month will be a Monday, so 7th of next month will be a Thursday. Finally, we can conclude that previous month and current month, both are having 31 days. Since both the dates are of the same year, so current month is August. We cannot find the answer using statement B alone.